Merge loops/minikanren into architecture: full miniKanren-on-SX library
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Squash merge of 76 commits from loops/minikanren. Adds lib/minikanren/
— a complete miniKanren-on-SX implementation built on top of
lib/guest/match.sx, validating the lib-guest unify-and-match kit as
intended.

Modules (20 .sx files, ~1700 LOC):
  unify, stream, goals, fresh, conde, condu, conda, run, relations,
  peano, intarith, project, nafc, matche, fd, queens, defrel, clpfd,
  tabling

Phases 1–5 fully done (core miniKanren API, all classic relations,
matche, conda, project, nafc).

Phase 6 — native CLP(FD): domain primitives, fd-in / fd-eq / fd-neq /
fd-lt / fd-lte / fd-plus / fd-times / fd-distinct / fd-label, with
constraint reactivation iterating to fixed point. N-queens via FD:
4-queens 2 solutions, 5-queens 10 solutions (vs naive timeout past N=4).

Phase 7 — naive ground-arg tabling: table-1 / table-2 / table-3.
Fibonacci canary: tab-fib(25) = 75025 in seconds, naive fib(25) times
out at 60s. Ackermann via table-3: A(3,3) = 61.

71 test files, 644+ tests passing across the suite. Producer/consumer
SLG (cyclic patho, mutual recursion) deferred — research-grade work.

The lib-guest validation experiment is conclusive: lib/minikanren/
unify.sx adds ~50 lines of local logic (custom cfg, deep walk*, fresh
counter) over lib/guest/match.sx's ~100-line kit. The kit earns its
keep ~3× by line count.
This commit is contained in:
2026-05-08 23:01:54 +00:00
parent 416546cc07
commit 57a84b372d
91 changed files with 7571 additions and 53 deletions

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;; lib/minikanren/clpfd.sx — Phase 6: native CLP(FD) on miniKanren.
;;
;; The substitution dict carries an extra reserved key "_fd" that holds a
;; constraint-store record:
;;
;; {:domains {var-name -> sorted-int-list}
;; :constraints (... pending constraint closures ...)}
;;
;; Domains are sorted SX lists of ints (no duplicates).
;; Constraints are functions s -> s-or-nil that propagate / re-check.
;; They are re-fired after every label binding via fd-fire-store.
(define fd-key "_fd")
;; --- domain primitives ---
(define
fd-dom-rev
(fn
(xs acc)
(cond
((empty? xs) acc)
(:else (fd-dom-rev (rest xs) (cons (first xs) acc))))))
(define
fd-dom-insert
(fn
(x desc)
(cond
((empty? desc) (list x))
((= x (first desc)) desc)
((> x (first desc)) (cons x desc))
(:else (cons (first desc) (fd-dom-insert x (rest desc)))))))
(define
fd-dom-sort-dedupe
(fn
(xs acc)
(cond
((empty? xs) (fd-dom-rev acc (list)))
(:else (fd-dom-sort-dedupe (rest xs) (fd-dom-insert (first xs) acc))))))
(define fd-dom-from-list (fn (xs) (fd-dom-sort-dedupe xs (list))))
(define fd-dom-empty? (fn (d) (empty? d)))
(define
fd-dom-singleton?
(fn (d) (and (not (empty? d)) (empty? (rest d)))))
(define fd-dom-min (fn (d) (first d)))
(define
fd-dom-last
(fn
(d)
(cond ((empty? (rest d)) (first d)) (:else (fd-dom-last (rest d))))))
(define fd-dom-max (fn (d) (fd-dom-last d)))
(define fd-dom-member? (fn (x d) (some (fn (y) (= x y)) d)))
(define
fd-dom-intersect
(fn
(a b)
(cond
((empty? a) (list))
((empty? b) (list))
((= (first a) (first b))
(cons (first a) (fd-dom-intersect (rest a) (rest b))))
((< (first a) (first b)) (fd-dom-intersect (rest a) b))
(:else (fd-dom-intersect a (rest b))))))
(define
fd-dom-without
(fn
(x d)
(cond
((empty? d) (list))
((= (first d) x) (rest d))
((> (first d) x) d)
(:else (cons (first d) (fd-dom-without x (rest d)))))))
(define
fd-dom-range
(fn
(lo hi)
(cond
((> lo hi) (list))
(:else (cons lo (fd-dom-range (+ lo 1) hi))))))
;; --- constraint store accessors ---
(define fd-store-empty (fn () {:domains {} :constraints (list)}))
(define
fd-store-of
(fn
(s)
(cond ((has-key? s fd-key) (get s fd-key)) (:else (fd-store-empty)))))
(define fd-domains-of (fn (s) (get (fd-store-of s) :domains)))
(define fd-with-store (fn (s store) (assoc s fd-key store)))
(define
fd-domain-of
(fn
(s var-name)
(let
((doms (fd-domains-of s)))
(cond ((has-key? doms var-name) (get doms var-name)) (:else nil)))))
(define
fd-set-domain
(fn
(s var-name d)
(cond
((fd-dom-empty? d) nil)
(:else
(let
((store (fd-store-of s)))
(let
((doms-prime (assoc (get store :domains) var-name d)))
(let
((store-prime (assoc store :domains doms-prime)))
(fd-with-store s store-prime))))))))
(define
fd-add-constraint
(fn
(s c)
(let
((store (fd-store-of s)))
(let
((cs-prime (cons c (get store :constraints))))
(let
((store-prime (assoc store :constraints cs-prime)))
(fd-with-store s store-prime))))))
(define
fd-fire-list
(fn
(cs s)
(cond
((empty? cs) s)
(:else
(let
((s2 ((first cs) s)))
(cond ((= s2 nil) nil) (:else (fd-fire-list (rest cs) s2))))))))
(define
fd-store-signature
(fn
(s)
(let
((doms (fd-domains-of s)))
(let
((dom-sizes (reduce (fn (acc k) (+ acc (len (get doms k)))) 0 (keys doms))))
(+ dom-sizes (len (keys s)))))))
(define
fd-fire-store
(fn
(s)
(let
((s2 (fd-fire-list (get (fd-store-of s) :constraints) s)))
(cond
((= s2 nil) nil)
((= (fd-store-signature s) (fd-store-signature s2)) s2)
(:else (fd-fire-store s2))))))
;; --- user-facing goals ---
(define
fd-in
(fn
(x dom-list)
(fn
(s)
(let
((new-dom (fd-dom-from-list dom-list)))
(let
((wx (mk-walk x s)))
(cond
((number? wx)
(cond ((fd-dom-member? wx new-dom) (unit s)) (:else mzero)))
((is-var? wx)
(let
((existing (fd-domain-of s (var-name wx))))
(let
((narrowed (cond ((= existing nil) new-dom) (:else (fd-dom-intersect existing new-dom)))))
(let
((s2 (fd-set-domain s (var-name wx) narrowed)))
(cond ((= s2 nil) mzero) (:else (unit s2)))))))
(:else mzero)))))))
;; --- fd-neq ---
(define
fd-neq-prop
(fn
(x y s)
(let
((wx (mk-walk x s)) (wy (mk-walk y s)))
(cond
((and (number? wx) (number? wy))
(cond ((= wx wy) nil) (:else s)))
((and (number? wx) (is-var? wy))
(let
((y-dom (fd-domain-of s (var-name wy))))
(cond
((= y-dom nil) s)
(:else
(fd-set-domain s (var-name wy) (fd-dom-without wx y-dom))))))
((and (number? wy) (is-var? wx))
(let
((x-dom (fd-domain-of s (var-name wx))))
(cond
((= x-dom nil) s)
(:else
(fd-set-domain s (var-name wx) (fd-dom-without wy x-dom))))))
(:else s)))))
(define
fd-neq
(fn
(x y)
(fn
(s)
(let
((c (fn (s-prime) (fd-neq-prop x y s-prime))))
(let
((s2 (fd-add-constraint s c)))
(let
((s3 (c s2)))
(cond ((= s3 nil) mzero) (:else (unit s3)))))))))
;; --- fd-lt ---
(define
fd-lt-prop
(fn
(x y s)
(let
((wx (mk-walk x s)) (wy (mk-walk y s)))
(cond
((and (number? wx) (number? wy))
(cond ((< wx wy) s) (:else nil)))
((and (number? wx) (is-var? wy))
(let
((yd (fd-domain-of s (var-name wy))))
(cond
((= yd nil) s)
(:else
(fd-set-domain
s
(var-name wy)
(filter (fn (v) (> v wx)) yd))))))
((and (is-var? wx) (number? wy))
(let
((xd (fd-domain-of s (var-name wx))))
(cond
((= xd nil) s)
(:else
(fd-set-domain
s
(var-name wx)
(filter (fn (v) (< v wy)) xd))))))
((and (is-var? wx) (is-var? wy))
(let
((xd (fd-domain-of s (var-name wx)))
(yd (fd-domain-of s (var-name wy))))
(cond
((or (= xd nil) (= yd nil)) s)
(:else
(let
((xd-prime (filter (fn (v) (< v (fd-dom-max yd))) xd)))
(let
((s2 (fd-set-domain s (var-name wx) xd-prime)))
(cond
((= s2 nil) nil)
(:else
(let
((yd-prime (filter (fn (v) (> v (fd-dom-min xd-prime))) yd)))
(fd-set-domain s2 (var-name wy) yd-prime))))))))))
(:else s)))))
(define
fd-lt
(fn
(x y)
(fn
(s)
(let
((c (fn (sp) (fd-lt-prop x y sp))))
(let
((s2 (fd-add-constraint s c)))
(let
((s3 (c s2)))
(cond ((= s3 nil) mzero) (:else (unit s3)))))))))
;; --- fd-lte ---
(define
fd-lte-prop
(fn
(x y s)
(let
((wx (mk-walk x s)) (wy (mk-walk y s)))
(cond
((and (number? wx) (number? wy))
(cond ((<= wx wy) s) (:else nil)))
((and (number? wx) (is-var? wy))
(let
((yd (fd-domain-of s (var-name wy))))
(cond
((= yd nil) s)
(:else
(fd-set-domain
s
(var-name wy)
(filter (fn (v) (>= v wx)) yd))))))
((and (is-var? wx) (number? wy))
(let
((xd (fd-domain-of s (var-name wx))))
(cond
((= xd nil) s)
(:else
(fd-set-domain
s
(var-name wx)
(filter (fn (v) (<= v wy)) xd))))))
((and (is-var? wx) (is-var? wy))
(let
((xd (fd-domain-of s (var-name wx)))
(yd (fd-domain-of s (var-name wy))))
(cond
((or (= xd nil) (= yd nil)) s)
(:else
(let
((xd-prime (filter (fn (v) (<= v (fd-dom-max yd))) xd)))
(let
((s2 (fd-set-domain s (var-name wx) xd-prime)))
(cond
((= s2 nil) nil)
(:else
(let
((yd-prime (filter (fn (v) (>= v (fd-dom-min xd-prime))) yd)))
(fd-set-domain s2 (var-name wy) yd-prime))))))))))
(:else s)))))
(define
fd-lte
(fn
(x y)
(fn
(s)
(let
((c (fn (sp) (fd-lte-prop x y sp))))
(let
((s2 (fd-add-constraint s c)))
(let
((s3 (c s2)))
(cond ((= s3 nil) mzero) (:else (unit s3)))))))))
;; --- fd-eq ---
(define
fd-eq-prop
(fn
(x y s)
(let
((wx (mk-walk x s)) (wy (mk-walk y s)))
(cond
((and (number? wx) (number? wy))
(cond ((= wx wy) s) (:else nil)))
((and (number? wx) (is-var? wy))
(let
((yd (fd-domain-of s (var-name wy))))
(cond
((and (not (= yd nil)) (not (fd-dom-member? wx yd))) nil)
(:else
(let
((s2 (mk-unify wy wx s)))
(cond ((= s2 nil) nil) (:else s2)))))))
((and (is-var? wx) (number? wy))
(let
((xd (fd-domain-of s (var-name wx))))
(cond
((and (not (= xd nil)) (not (fd-dom-member? wy xd))) nil)
(:else
(let
((s2 (mk-unify wx wy s)))
(cond ((= s2 nil) nil) (:else s2)))))))
((and (is-var? wx) (is-var? wy))
(let
((xd (fd-domain-of s (var-name wx)))
(yd (fd-domain-of s (var-name wy))))
(cond
((and (= xd nil) (= yd nil))
(let
((s2 (mk-unify wx wy s)))
(cond ((= s2 nil) nil) (:else s2))))
(:else
(let
((shared (cond ((= xd nil) yd) ((= yd nil) xd) (:else (fd-dom-intersect xd yd)))))
(cond
((fd-dom-empty? shared) nil)
(:else
(let
((s2 (fd-set-domain s (var-name wx) shared)))
(cond
((= s2 nil) nil)
(:else
(let
((s3 (fd-set-domain s2 (var-name wy) shared)))
(cond
((= s3 nil) nil)
(:else (mk-unify wx wy s3))))))))))))))
(:else s)))))
(define
fd-eq
(fn
(x y)
(fn
(s)
(let
((c (fn (sp) (fd-eq-prop x y sp))))
(let
((s2 (fd-add-constraint s c)))
(let
((s3 (c s2)))
(cond ((= s3 nil) mzero) (:else (unit s3)))))))))
;; --- labelling ---
(define
fd-try-each-value
(fn
(x dom s)
(cond
((empty? dom) mzero)
(:else
(let
((s2 (mk-unify x (first dom) s)))
(let
((s3 (cond ((= s2 nil) nil) (:else (fd-fire-store s2)))))
(let
((this-stream (cond ((= s3 nil) mzero) (:else (unit s3))))
(rest-stream (fd-try-each-value x (rest dom) s)))
(mk-mplus this-stream rest-stream))))))))
(define
fd-label-one
(fn
(x)
(fn
(s)
(let
((wx (mk-walk x s)))
(cond
((number? wx) (unit s))
((is-var? wx)
(let
((dom (fd-domain-of s (var-name wx))))
(cond
((= dom nil) mzero)
(:else (fd-try-each-value wx dom s)))))
(:else mzero))))))
(define
fd-label
(fn
(vars)
(cond
((empty? vars) succeed)
(:else (mk-conj (fd-label-one (first vars)) (fd-label (rest vars)))))))
;; --- fd-distinct (pairwise distinct via fd-neq) ---
(define
fd-distinct-from-head
(fn
(x others)
(cond
((empty? others) succeed)
(:else
(mk-conj
(fd-neq x (first others))
(fd-distinct-from-head x (rest others)))))))
(define
fd-distinct
(fn
(vars)
(cond
((empty? vars) succeed)
((empty? (rest vars)) succeed)
(:else
(mk-conj
(fd-distinct-from-head (first vars) (rest vars))
(fd-distinct (rest vars)))))))
;; --- fd-plus (x + y = z, ground-cases propagator) ---
(define
fd-bind-or-narrow
(fn
(w target s)
(cond
((number? w) (cond ((= w target) s) (:else nil)))
((is-var? w)
(let
((wd (fd-domain-of s (var-name w))))
(cond
((and (not (= wd nil)) (not (fd-dom-member? target wd))) nil)
(:else
(let
((s2 (mk-unify w target s)))
(cond ((= s2 nil) nil) (:else s2)))))))
(:else nil))))
(define
fd-plus-prop
(fn
(x y z s)
(let
((wx (mk-walk x s)) (wy (mk-walk y s)) (wz (mk-walk z s)))
(cond
((and (number? wx) (number? wy) (number? wz))
(cond ((= (+ wx wy) wz) s) (:else nil)))
((and (number? wx) (number? wy))
(fd-bind-or-narrow wz (+ wx wy) s))
((and (number? wx) (number? wz))
(fd-bind-or-narrow wy (- wz wx) s))
((and (number? wy) (number? wz))
(fd-bind-or-narrow wx (- wz wy) s))
(:else s)))))
(define
fd-plus
(fn
(x y z)
(fn
(s)
(let
((c (fn (sp) (fd-plus-prop x y z sp))))
(let
((s2 (fd-add-constraint s c)))
(let
((s3 (c s2)))
(cond ((= s3 nil) mzero) (:else (unit s3)))))))))
;; --- fd-times (x * y = z, ground-cases propagator) ---
(define
fd-times-prop
(fn
(x y z s)
(let
((wx (mk-walk x s)) (wy (mk-walk y s)) (wz (mk-walk z s)))
(cond
((and (number? wx) (number? wy) (number? wz))
(cond ((= (* wx wy) wz) s) (:else nil)))
((and (number? wx) (number? wy))
(fd-bind-or-narrow wz (* wx wy) s))
((and (number? wx) (number? wz))
(cond
((= wx 0) (cond ((= wz 0) s) (:else nil)))
((not (= (mod wz wx) 0)) nil)
(:else (fd-bind-or-narrow wy (/ wz wx) s))))
((and (number? wy) (number? wz))
(cond
((= wy 0) (cond ((= wz 0) s) (:else nil)))
((not (= (mod wz wy) 0)) nil)
(:else (fd-bind-or-narrow wx (/ wz wy) s))))
(:else s)))))
(define
fd-times
(fn
(x y z)
(fn
(s)
(let
((c (fn (sp) (fd-times-prop x y z sp))))
(let
((s2 (fd-add-constraint s c)))
(let
((s3 (c s2)))
(cond ((= s3 nil) mzero) (:else (unit s3)))))))))

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;; lib/minikanren/conda.sx — Phase 5 piece A: `conda`, the soft-cut.
;;
;; (conda (g0 g ...) (h0 h ...) ...)
;; — first clause whose head g0 produces ANY answer wins; ALL of g0's
;; answers are then conj'd with the rest of that clause; later
;; clauses are NOT tried.
;; — differs from condu only in not wrapping g0 in onceo: condu
;; commits to the SINGLE first answer, conda lets the head's full
;; answer-set flow into the rest of the clause.
;; (Reasoned Schemer chapter 10; Byrd 5.3.)
(define
conda-try
(fn
(clauses s)
(cond
((empty? clauses) mzero)
(:else
(let
((cl (first clauses)))
(let
((head-goal (first cl)) (rest-goals (rest cl)))
(let
((peek (stream-take 1 (head-goal s))))
(if
(empty? peek)
(conda-try (rest clauses) s)
(mk-bind (head-goal s) (mk-conj-list rest-goals))))))))))
(defmacro
conda
(&rest clauses)
(quasiquote
(fn
(s)
(conda-try
(list
(splice-unquote
(map
(fn (cl) (quasiquote (list (splice-unquote cl))))
clauses)))
s))))

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;; lib/minikanren/conde.sx — Phase 2 piece C: `conde`, the canonical
;; miniKanren and-or form, with implicit Zzz inverse-eta delay so recursive
;; relations like appendo terminate.
;;
;; (conde (g1a g1b ...) (g2a g2b ...) ...)
;; ≡ (mk-disj (Zzz (mk-conj g1a g1b ...))
;; (Zzz (mk-conj g2a g2b ...)) ...)
;;
;; `Zzz g` wraps a goal expression in (fn (S) (fn () (g S))) so that
;; `g`'s body isn't constructed until the surrounding fn is applied to a
;; substitution AND the returned thunk is forced. This is what gives
;; miniKanren its laziness — recursive goal definitions can be `(conde
;; ... (... (recur ...)))` without infinite descent at construction time.
;;
;; Hygiene: the substitution parameter is gensym'd so that user goal
;; expressions which themselves bind `s` (e.g. `(appendo l s ls)`) keep
;; their lexical `s` and don't accidentally reference the wrapper's
;; substitution. Without gensym, miniKanren relations that follow the
;; common (l s ls) parameter convention are silently miscompiled.
(defmacro
Zzz
(g)
(let
((s-sym (gensym "zzz-s-")))
(quasiquote
(fn ((unquote s-sym)) (fn () ((unquote g) (unquote s-sym)))))))
(defmacro
conde
(&rest clauses)
(quasiquote
(mk-disj
(splice-unquote
(map
(fn
(clause)
(quasiquote (Zzz (mk-conj (splice-unquote clause)))))
clauses)))))

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;; lib/minikanren/condu.sx — Phase 2 piece D: `condu` and `onceo`.
;;
;; Both are commitment forms (no backtracking into discarded options):
;;
;; (onceo g) — succeeds at most once: takes the first answer
;; stream-take produces from (g s).
;;
;; (condu (g0 g ...) (h0 h ...) ...)
;; — first clause whose head goal succeeds wins; only
;; the first answer of the head is propagated to the
;; rest of that clause; later clauses are not tried.
;; (Reasoned Schemer chapter 10; Byrd 5.4.)
(define
onceo
(fn
(g)
(fn
(s)
(let
((peek (stream-take 1 (g s))))
(if (empty? peek) mzero (unit (first peek)))))))
;; condu-try — runtime walker over a list of clauses (each clause a list of
;; goals). Forces the head with stream-take 1; if head fails, recurse to
;; the next clause; if head succeeds, commits its single answer through
;; the rest of the clause.
(define
condu-try
(fn
(clauses s)
(cond
((empty? clauses) mzero)
(:else
(let
((cl (first clauses)))
(let
((head-goal (first cl)) (rest-goals (rest cl)))
(let
((peek (stream-take 1 (head-goal s))))
(if
(empty? peek)
(condu-try (rest clauses) s)
((mk-conj-list rest-goals) (first peek))))))))))
(defmacro
condu
(&rest clauses)
(quasiquote
(fn
(s)
(condu-try
(list
(splice-unquote
(map
(fn (cl) (quasiquote (list (splice-unquote cl))))
clauses)))
s))))

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;; lib/minikanren/defrel.sx — Prolog-style defrel macro.
;;
;; (defrel (NAME ARG1 ARG2 ...)
;; (CLAUSE1 ...)
;; (CLAUSE2 ...)
;; ...)
;;
;; expands to
;;
;; (define NAME (fn (ARG1 ARG2 ...) (conde (CLAUSE1 ...) (CLAUSE2 ...))))
;;
;; This puts each clause's goals immediately after the head, mirroring
;; Prolog's `name(Args) :- goals.` shape. Clauses are conde-conjoined
;; goals — `Zzz`-wrapping is automatic via `conde`, so recursive
;; relations terminate on partial answers.
(defmacro
defrel
(head &rest clauses)
(let
((name (first head)) (args (rest head)))
(list
(quote define)
name
(list (quote fn) args (cons (quote conde) clauses)))))

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;; lib/minikanren/fd.sx — Phase 6 piece A: minimal finite-domain helpers.
;;
;; A full CLP(FD) engine (arc consistency, native integer domains, fd-plus
;; etc.) is Phase 6 proper. For now we expose two small relations layered
;; on the existing list machinery — they're sufficient for permutation
;; puzzles, the N-queens-style core of constraint solving:
;;
;; (ino x dom) — x is a member of dom (alias for membero with the
;; constraint-store-friendly argument order).
;; (all-distincto l) — all elements of l are pairwise distinct.
;;
;; all-distincto uses nafc + membero on the tail — it requires the head
;; element of each recursive step to be ground enough for membero to be
;; finitary, so order matters: prefer (in x dom) goals BEFORE
;; (all-distincto (list x ...)) so values get committed first.
(define ino (fn (x dom) (membero x dom)))
(define
all-distincto
(fn
(l)
(conde
((nullo l))
((fresh (a d) (conso a d l) (nafc (membero a d)) (all-distincto d))))))

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;; lib/minikanren/fresh.sx — Phase 2 piece B: `fresh` for introducing
;; logic variables inside a goal body.
;;
;; (fresh (x y z) goal1 goal2 ...)
;; ≡ (let ((x (make-var)) (y (make-var)) (z (make-var)))
;; (mk-conj goal1 goal2 ...))
;;
;; A macro rather than a function so user-named vars are real lexical
;; bindings — which is also what miniKanren convention expects.
;; The empty-vars form (fresh () goal ...) is just a goal grouping.
(defmacro
fresh
(vars &rest goals)
(quasiquote
(let
(unquote (map (fn (v) (list v (list (quote make-var)))) vars))
(mk-conj (splice-unquote goals)))))
;; call-fresh — functional alternative for code that builds goals
;; programmatically:
;; ((call-fresh (fn (x) (== x 7))) empty-s) → ({:_.N 7})
(define call-fresh (fn (f) (fn (s) ((f (make-var)) s))))

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;; lib/minikanren/goals.sx — Phase 2 piece B: core goals.
;;
;; A goal is a function (fn (s) → stream-of-substitutions).
;; Goals built here:
;; succeed — always returns (unit s)
;; fail — always returns mzero
;; == — unifies two terms; succeeds with a singleton, else fails
;; ==-check — opt-in occurs-checked equality
;; conj2 / mk-conj — sequential conjunction of goals
;; disj2 / mk-disj — interleaved disjunction of goals (raw — `conde` adds
;; the implicit-conj-per-clause sugar in a later commit)
(define succeed (fn (s) (unit s)))
(define fail (fn (s) mzero))
(define
==
(fn
(u v)
(fn
(s)
(let ((s2 (mk-unify u v s))) (if (= s2 nil) mzero (unit s2))))))
(define
==-check
(fn
(u v)
(fn
(s)
(let ((s2 (mk-unify-check u v s))) (if (= s2 nil) mzero (unit s2))))))
(define conj2 (fn (g1 g2) (fn (s) (mk-bind (g1 s) g2))))
(define disj2 (fn (g1 g2) (fn (s) (mk-mplus (g1 s) (g2 s)))))
;; Fold goals in a list. (mk-conj-list ()) ≡ succeed; (mk-disj-list ()) ≡ fail.
(define
mk-conj-list
(fn
(gs)
(cond
((empty? gs) succeed)
((empty? (rest gs)) (first gs))
(:else (conj2 (first gs) (mk-conj-list (rest gs)))))))
(define
mk-disj-list
(fn
(gs)
(cond
((empty? gs) fail)
((empty? (rest gs)) (first gs))
(:else (disj2 (first gs) (mk-disj-list (rest gs)))))))
(define mk-conj (fn (&rest gs) (mk-conj-list gs)))
(define mk-disj (fn (&rest gs) (mk-disj-list gs)))

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;; lib/minikanren/intarith.sx — fast integer arithmetic via project.
;;
;; These are ground-only escapes into host arithmetic. They run at native
;; speed (host ints) but require their arguments to walk to actual numbers
;; — they are not relational the way `pluso` (Peano) is. Use them when
;; the puzzle size makes Peano impractical.
;;
;; Naming: `-i` suffix marks "integer-only" goals.
(define
pluso-i
(fn
(a b c)
(project
(a b)
(if (and (number? a) (number? b)) (== c (+ a b)) fail))))
(define
minuso-i
(fn
(a b c)
(project
(a b)
(if (and (number? a) (number? b)) (== c (- a b)) fail))))
(define
*o-i
(fn
(a b c)
(project
(a b)
(if (and (number? a) (number? b)) (== c (* a b)) fail))))
(define
lto-i
(fn
(a b)
(project
(a b)
(if (and (number? a) (and (number? b) (< a b))) succeed fail))))
(define
lteo-i
(fn
(a b)
(project
(a b)
(if (and (number? a) (and (number? b) (<= a b))) succeed fail))))
(define
neqo-i
(fn
(a b)
(project
(a b)
(if (and (number? a) (and (number? b) (not (= a b)))) succeed fail))))
(define numbero (fn (x) (project (x) (if (number? x) succeed fail))))
(define stringo (fn (x) (project (x) (if (string? x) succeed fail))))
(define symbolo (fn (x) (project (x) (if (symbol? x) succeed fail))))
(define
even-i
(fn (n) (project (n) (if (and (number? n) (even? n)) succeed fail))))
(define
odd-i
(fn (n) (project (n) (if (and (number? n) (odd? n)) succeed fail))))
(define
sortedo
(fn
(l)
(conde
((nullo l))
((fresh (a) (== l (list a))))
((fresh (a b rest mid) (conso a mid l) (conso b rest mid) (lteo-i a b) (sortedo mid))))))
(define
mino
(fn
(l m)
(conde
((fresh (a) (== l (list a)) (== m a)))
((fresh (a d rest-min) (conso a d l) (mino d rest-min) (conde ((lteo-i a rest-min) (== m a)) ((lto-i rest-min a) (== m rest-min))))))))
(define
maxo
(fn
(l m)
(conde
((fresh (a) (== l (list a)) (== m a)))
((fresh (a d rest-max) (conso a d l) (maxo d rest-max) (conde ((lteo-i rest-max a) (== m a)) ((lto-i a rest-max) (== m rest-max))))))))
(define
sumo
(fn
(l total)
(conde
((nullo l) (== total 0))
((fresh (a d rest-sum) (conso a d l) (sumo d rest-sum) (pluso-i a rest-sum total))))))
(define
producto
(fn
(l total)
(conde
((nullo l) (== total 1))
((fresh (a d rest-prod) (conso a d l) (producto d rest-prod) (*o-i a rest-prod total))))))
(define
lengtho-i
(fn
(l n)
(conde
((nullo l) (== n 0))
((fresh (a d n-1) (conso a d l) (lengtho-i d n-1) (pluso-i 1 n-1 n))))))
(define
enumerate-from-i
(fn
(start l result)
(conde
((nullo l) (nullo result))
((fresh (a d r-rest start-prime) (conso a d l) (conso (list start a) r-rest result) (pluso-i 1 start start-prime) (enumerate-from-i start-prime d r-rest))))))
(define enumerate-i (fn (l result) (enumerate-from-i 0 l result)))
(define
counto
(fn
(x l n)
(conde
((nullo l) (== n 0))
((fresh (a d n-rest) (conso a d l) (conde ((== a x) (counto x d n-rest) (pluso-i 1 n-rest n)) ((nafc (== a x)) (counto x d n))))))))
(define
mk-arith-prog
(fn
(start step len)
(cond
((= len 0) (list))
(:else (cons start (mk-arith-prog (+ start step) step (- len 1)))))))
(define
arith-progo
(fn
(start step len result)
(project (start step len) (== result (mk-arith-prog start step len)))))

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;; lib/minikanren/matche.sx — Phase 5 piece D: pattern matching over terms.
;;
;; (matche TARGET
;; (PATTERN1 g1 g2 ...)
;; (PATTERN2 g1 ...)
;; ...)
;;
;; Pattern grammar:
;; _ wildcard — fresh anonymous var
;; x plain symbol — fresh var, bind by name
;; ATOM literal (number, string, boolean) — must equal
;; :keyword keyword literal — emitted bare (keywords self-evaluate
;; to their string name in SX, so quoting them changes
;; their type from string to keyword)
;; () empty list — must equal
;; (p1 p2 ... pn) list pattern — recurse on each element
;;
;; The macro expands to a `conde` whose clauses are
;; `((fresh (vars-in-pat) (== target pat-expr) body...))`.
;;
;; Repeated symbol names within a pattern produce the same fresh var, so
;; they unify by `==`. Fixed-length list patterns only — head/tail
;; destructuring uses `(fresh (a d) (conso a d target) body)` directly.
;;
;; Note: the macro builds the expansion via `cons` / `list` rather than a
;; quasiquote — quasiquote does not recurse into nested lambda bodies in
;; SX, so `\`(matche-clause (quote ,target) cl)` left literal
;; `(unquote target)` in the output.
(define matche-symbol-var? (fn (s) (symbol? s)))
(define
matche-collect-vars-acc
(fn
(pat acc)
(cond
((matche-symbol-var? pat)
(if (some (fn (s) (= s pat)) acc) acc (append acc (list pat))))
((and (list? pat) (not (empty? pat)))
(reduce (fn (a p) (matche-collect-vars-acc p a)) acc pat))
(:else acc))))
(define
matche-collect-vars
(fn (pat) (matche-collect-vars-acc pat (list))))
(define
matche-pattern->expr
(fn
(pat)
(cond
((matche-symbol-var? pat) pat)
((and (list? pat) (empty? pat)) (list (quote list)))
((list? pat) (cons (quote list) (map matche-pattern->expr pat)))
((keyword? pat) pat)
(:else (list (quote quote) pat)))))
(define
matche-clause
(fn
(target cl)
(let
((pat (first cl)) (body (rest cl)))
(let
((vars (matche-collect-vars pat)))
(let
((pat-expr (matche-pattern->expr pat)))
(list
(cons
(quote fresh)
(cons vars (cons (list (quote ==) target pat-expr) body)))))))))
(defmacro
matche
(target &rest clauses)
(cons (quote conde) (map (fn (cl) (matche-clause target cl)) clauses)))

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;; lib/minikanren/nafc.sx — Phase 5 piece C: negation as finite failure.
;;
;; (nafc g)
;; succeeds (yields the input substitution) if g has zero answers
;; against that substitution; fails (mzero) if g has at least one.
;;
;; Caveat: `nafc` is unsound under the open-world assumption. It only
;; makes sense for goals over fully-ground terms, or with the explicit
;; understanding that adding more facts could flip the answer. Use
;; `(project (...) ...)` to ensure the relevant vars are ground first.
;;
;; Caveat 2: stream-take forces g for at least one answer; if g is
;; infinitely-ground (say, a divergent search over an unbound list),
;; nafc itself will diverge. Standard miniKanren limitation.
(define
nafc
(fn
(g)
(fn
(s)
(let
((peek (stream-take 1 (g s))))
(if (empty? peek) (unit s) mzero)))))

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;; lib/minikanren/peano.sx — Peano-encoded natural-number relations.
;;
;; Same encoding as `lengtho`: zero is the keyword `:z`; successors are
;; `(:s n)`. So 3 = `(:s (:s (:s :z)))`. `(:z)` and `(:s ...)` are normal
;; SX values that unify positionally — no special primitives needed.
;;
;; Peano arithmetic is the canonical miniKanren way to test addition /
;; multiplication / less-than relationally without an FD constraint store.
;; (CLP(FD) integers come in Phase 6.)
(define zeroo (fn (n) (== n :z)))
(define succ-of (fn (n m) (== m (list :s n))))
(define
pluso
(fn
(a b c)
(conde
((== a :z) (== b c))
((fresh (a-1 c-1) (== a (list :s a-1)) (== c (list :s c-1)) (pluso a-1 b c-1))))))
(define minuso (fn (a b c) (pluso b c a)))
(define lteo (fn (a b) (fresh (k) (pluso a k b))))
(define lto (fn (a b) (fresh (sa) (succ-of a sa) (lteo sa b))))
(define
eveno
(fn
(n)
(conde
((== n :z))
((fresh (m) (== n (list :s (list :s m))) (eveno m))))))
(define
oddo
(fn
(n)
(conde
((== n (list :s :z)))
((fresh (m) (== n (list :s (list :s m))) (oddo m))))))
(define
*o
(fn
(a b c)
(conde
((== a :z) (== c :z))
((fresh (a-1 ab-1) (== a (list :s a-1)) (*o a-1 b ab-1) (pluso b ab-1 c))))))

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;; lib/minikanren/project.sx — Phase 5 piece B: `project`.
;;
;; (project (x y) g1 g2 ...)
;; — rebinds each named var to (mk-walk* var s) within the body's
;; lexical scope, then runs the conjunction of the body goals on
;; the same substitution. Use to escape into regular SX (arithmetic,
;; string ops, host predicates) when you need a ground value.
;;
;; If any of the projected vars is still unbound at this point, the body
;; sees the raw `(:var NAME)` term — that is intentional and lets you
;; mix project with `(== ground? var)` patterns or with conda guards.
;;
;; Hygiene: substitution parameter is gensym'd so it doesn't capture user
;; vars (`s` is a popular relation parameter name).
(defmacro
project
(vars &rest goals)
(let
((s-sym (gensym "proj-s-")))
(quasiquote
(fn
((unquote s-sym))
((let (unquote (map (fn (v) (list v (list (quote mk-walk*) v s-sym))) vars)) (mk-conj (splice-unquote goals)))
(unquote s-sym))))))

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;; lib/minikanren/queens.sx — N-queens via ino + all-distincto + project.
;;
;; Encoding: q = (c1 c2 ... cn) where ci is the column of the queen in
;; row i. Each ci ∈ {1..n}; all distinct (no two queens share a column);
;; no two queens on the same diagonal (|ci - cj| ≠ |i - j| for i ≠ j).
;;
;; The diagonal check uses `project` to escape into host arithmetic
;; once both column values are ground.
(define
safe-diag
(fn
(a b dist)
(project (a b) (if (= (abs (- a b)) dist) fail succeed))))
(define
safe-cell-vs-rest
(fn
(c c-row others next-row)
(cond
((empty? others) succeed)
(:else
(mk-conj
(safe-diag c (first others) (- next-row c-row))
(safe-cell-vs-rest c c-row (rest others) (+ next-row 1)))))))
(define
all-cells-safe
(fn
(cols start-row)
(cond
((empty? cols) succeed)
(:else
(mk-conj
(safe-cell-vs-rest
(first cols)
start-row
(rest cols)
(+ start-row 1))
(all-cells-safe (rest cols) (+ start-row 1)))))))
(define
range-1-to-n
(fn
(n)
(cond
((= n 0) (list))
(:else (append (range-1-to-n (- n 1)) (list n))))))
(define
ino-each
(fn
(cols dom)
(cond
((empty? cols) succeed)
(:else (mk-conj (ino (first cols) dom) (ino-each (rest cols) dom))))))
(define
queens-cols
(fn
(cols n)
(let
((dom (range-1-to-n n)))
(mk-conj
(ino-each cols dom)
(all-distincto cols)
(all-cells-safe cols 1)))))

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;; lib/minikanren/relations.sx — Phase 4 standard relations.
;;
;; Programs use native SX lists as data. Relations decompose lists via the
;; tagged cons-cell shape `(:cons h t)` because SX has no improper pairs;
;; the unifier treats `(:cons h t)` and the native list `(h . t)` as
;; equivalent, and `mk-walk*` flattens cons cells back to flat lists for
;; reification.
;; --- pair / list shape relations ---
(define nullo (fn (l) (== l (list))))
(define pairo (fn (p) (fresh (a d) (== p (mk-cons a d)))))
(define caro (fn (p a) (fresh (d) (== p (mk-cons a d)))))
(define cdro (fn (p d) (fresh (a) (== p (mk-cons a d)))))
(define conso (fn (a d p) (== p (mk-cons a d))))
(define firsto caro)
(define resto cdro)
(define
listo
(fn (l) (conde ((nullo l)) ((fresh (a d) (conso a d l) (listo d))))))
;; --- appendo: the canary ---
;;
;; (appendo l s ls) — `ls` is the concatenation of `l` and `s`.
;; Runs forwards (l, s known → ls), backwards (ls known → all (l, s) pairs),
;; and bidirectionally (mix of bound + unbound).
(define
appendo
(fn
(l s ls)
(conde
((nullo l) (== s ls))
((fresh (a d res) (conso a d l) (conso a res ls) (appendo d s res))))))
;; --- membero ---
;; (membero x l) — x appears (at least once) in l.
(define
appendo3
(fn
(l1 l2 l3 result)
(fresh (l12) (appendo l1 l2 l12) (appendo l12 l3 result))))
(define
partitiono
(fn
(pred l yes no)
(conde
((nullo l) (nullo yes) (nullo no))
((fresh (a d y-rest n-rest) (conso a d l) (conde ((pred a) (conso a y-rest yes) (== no n-rest) (partitiono pred d y-rest n-rest)) ((nafc (pred a)) (== yes y-rest) (conso a n-rest no) (partitiono pred d y-rest n-rest))))))))
(define
foldr-o
(fn
(rel l acc result)
(conde
((nullo l) (== result acc))
((fresh (a d r-rest) (conso a d l) (foldr-o rel d acc r-rest) (rel a r-rest result))))))
(define
foldl-o
(fn
(rel l acc result)
(conde
((nullo l) (== result acc))
((fresh (a d new-acc) (conso a d l) (rel acc a new-acc) (foldl-o rel d new-acc result))))))
(define
flat-mapo
(fn
(rel l result)
(conde
((nullo l) (nullo result))
((fresh (a d a-result rest-result) (conso a d l) (rel a a-result) (flat-mapo rel d rest-result) (appendo a-result rest-result result))))))
(define
nub-o
(fn
(l result)
(conde
((nullo l) (nullo result))
((fresh (a d r-rest) (conso a d l) (conde ((membero a d) (nub-o d result)) ((nafc (membero a d)) (conso a r-rest result) (nub-o d r-rest))))))))
(define
take-while-o
(fn
(pred l result)
(conde
((nullo l) (nullo result))
((fresh (a d r-rest) (conso a d l) (conde ((pred a) (conso a r-rest result) (take-while-o pred d r-rest)) ((nafc (pred a)) (== result (list)))))))))
(define
drop-while-o
(fn
(pred l result)
(conde
((nullo l) (nullo result))
((fresh (a d) (conso a d l) (conde ((pred a) (drop-while-o pred d result)) ((nafc (pred a)) (== result l))))))))
(define
membero
(fn
(x l)
(conde
((fresh (d) (conso x d l)))
((fresh (a d) (conso a d l) (membero x d))))))
(define
not-membero
(fn
(x l)
(conde
((nullo l))
((fresh (a d) (conso a d l) (nafc (== a x)) (not-membero x d))))))
(define
subseto
(fn
(l1 l2)
(conde
((nullo l1))
((fresh (a d) (conso a d l1) (membero a l2) (subseto d l2))))))
(define
reverseo
(fn
(l r)
(conde
((nullo l) (nullo r))
((fresh (a d res-rev) (conso a d l) (reverseo d res-rev) (appendo res-rev (list a) r))))))
(define
rev-acco
(fn
(l acc result)
(conde
((nullo l) (== result acc))
((fresh (a d acc-prime) (conso a d l) (conso a acc acc-prime) (rev-acco d acc-prime result))))))
(define rev-2o (fn (l result) (rev-acco l (list) result)))
(define palindromeo (fn (l) (fresh (rev) (reverseo l rev) (== l rev))))
(define prefixo (fn (p l) (fresh (rest) (appendo p rest l))))
(define suffixo (fn (s l) (fresh (front) (appendo front s l))))
(define
subo
(fn
(s l)
(fresh
(front-and-s back front)
(appendo front-and-s back l)
(appendo front s front-and-s))))
(define
selecto
(fn
(x rest l)
(conde
((conso x rest l))
((fresh (a d r) (conso a d l) (conso a r rest) (selecto x r d))))))
(define
lengtho
(fn
(l n)
(conde
((nullo l) (== n :z))
((fresh (a d n-1) (conso a d l) (== n (list :s n-1)) (lengtho d n-1))))))
(define
inserto
(fn
(a l p)
(conde
((conso a l p))
((fresh (h t pt) (conso h t l) (conso h pt p) (inserto a t pt))))))
(define
permuteo
(fn
(l p)
(conde
((nullo l) (nullo p))
((fresh (a d perm-d) (conso a d l) (permuteo d perm-d) (inserto a perm-d p))))))
(define
flatteno
(fn
(tree flat)
(conde
((nullo tree) (nullo flat))
((pairo tree)
(fresh
(h t hf tf)
(conso h t tree)
(flatteno h hf)
(flatteno t tf)
(appendo hf tf flat)))
((nafc (nullo tree)) (nafc (pairo tree)) (== flat (list tree))))))
(define
rembero
(fn
(x l out)
(conde
((nullo l) (nullo out))
((fresh (a d) (conso a d l) (== a x) (== out d)))
((fresh (a d res) (conso a d l) (nafc (== a x)) (conso a res out) (rembero x d res))))))
(define
removeo-allo
(fn
(x l result)
(conde
((nullo l) (nullo result))
((fresh (a d) (conso a d l) (== a x) (removeo-allo x d result)))
((fresh (a d r-rest) (conso a d l) (nafc (== a x)) (conso a r-rest result) (removeo-allo x d r-rest))))))
(define
assoco
(fn
(key pairs val)
(fresh
(rest)
(conde
((conso (list key val) rest pairs))
((fresh (other) (conso other rest pairs) (assoco key rest val)))))))
(define
nth-o
(fn
(n l elem)
(conde
((== n :z) (fresh (d) (conso elem d l)))
((fresh (n-1 a d) (== n (list :s n-1)) (conso a d l) (nth-o n-1 d elem))))))
(define
samelengtho
(fn
(l1 l2)
(conde
((nullo l1) (nullo l2))
((fresh (a d a-prime d-prime) (conso a d l1) (conso a-prime d-prime l2) (samelengtho d d-prime))))))
(define
mapo
(fn
(rel l1 l2)
(conde
((nullo l1) (nullo l2))
((fresh (a d a-prime d-prime) (conso a d l1) (conso a-prime d-prime l2) (rel a a-prime) (mapo rel d d-prime))))))
(define
iterate-no
(fn
(rel n x result)
(conde
((== n :z) (== result x))
((fresh (n-1 mid) (== n (list :s n-1)) (rel x mid) (iterate-no rel n-1 mid result))))))
(define
pairlisto
(fn
(l1 l2 pairs)
(conde
((nullo l1) (nullo l2) (nullo pairs))
((fresh (a1 d1 a2 d2 d-pairs) (conso a1 d1 l1) (conso a2 d2 l2) (conso (list a1 a2) d-pairs pairs) (pairlisto d1 d2 d-pairs))))))
(define
zip-with-o
(fn
(rel l1 l2 result)
(conde
((nullo l1) (nullo l2) (nullo result))
((fresh (a1 d1 a2 d2 a-result d-result) (conso a1 d1 l1) (conso a2 d2 l2) (rel a1 a2 a-result) (conso a-result d-result result) (zip-with-o rel d1 d2 d-result))))))
(define
swap-firsto
(fn
(l result)
(fresh
(a b rest mid-l mid-r)
(conso a mid-l l)
(conso b rest mid-l)
(conso b mid-r result)
(conso a rest mid-r))))
(define
everyo
(fn
(rel l)
(conde
((nullo l))
((fresh (a d) (conso a d l) (rel a) (everyo rel d))))))
(define
someo
(fn
(rel l)
(conde
((fresh (a d) (conso a d l) (rel a)))
((fresh (a d) (conso a d l) (someo rel d))))))
(define
lasto
(fn
(l x)
(conde
((conso x (list) l))
((fresh (a d) (conso a d l) (lasto d x))))))
(define
init-o
(fn
(l init)
(conde
((fresh (x) (conso x (list) l) (== init (list))))
((fresh (a d d-init) (conso a d l) (conso a d-init init) (init-o d d-init))))))
(define
tako
(fn
(n l prefix)
(conde
((== n :z) (== prefix (list)))
((fresh (n-1 a d p-rest) (== n (list :s n-1)) (conso a d l) (conso a p-rest prefix) (tako n-1 d p-rest))))))
(define
dropo
(fn
(n l suffix)
(conde
((== n :z) (== suffix l))
((fresh (n-1 a d) (== n (list :s n-1)) (conso a d l) (dropo n-1 d suffix))))))
(define
repeato
(fn
(x n result)
(conde
((== n :z) (== result (list)))
((fresh (n-1 r-rest) (== n (list :s n-1)) (conso x r-rest result) (repeato x n-1 r-rest))))))
(define
concato
(fn
(lists result)
(conde
((nullo lists) (nullo result))
((fresh (h t r-rest) (conso h t lists) (appendo h r-rest result) (concato t r-rest))))))

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;; lib/minikanren/run.sx — Phase 3: drive a goal + reify the query var.
;;
;; reify-name N — make the canonical "_.N" reified symbol.
;; reify-s term rs — walk term in rs, add a mapping from each fresh
;; unbound var to its _.N name (left-to-right order).
;; reify q s — walk* q in s, build reify-s, walk* again to
;; substitute reified names in.
;; run-n n q-name g... — defmacro: bind q-name to a fresh var, conj goals,
;; take ≤ n answers from the stream, reify each
;; through q-name. n = -1 takes all (used by run*).
;; run* — defmacro: (run* q g...) ≡ (run-n -1 q g...)
;; run — defmacro: (run n q g...) ≡ (run-n n q g...)
;; The two-segment form is the standard TRS API.
(define reify-name (fn (n) (make-symbol (str "_." n))))
(define
reify-s
(fn
(term rs)
(let
((w (mk-walk term rs)))
(cond
((is-var? w) (extend (var-name w) (reify-name (len rs)) rs))
((mk-list-pair? w) (reduce (fn (acc a) (reify-s a acc)) rs w))
(:else rs)))))
(define
reify
(fn
(term s)
(let
((w (mk-walk* term s)))
(let ((rs (reify-s w (empty-subst)))) (mk-walk* w rs)))))
(defmacro
run-n
(n q-name &rest goals)
(quasiquote
(let
(((unquote q-name) (make-var)))
(map
(fn (s) (reify (unquote q-name) s))
(stream-take
(unquote n)
((mk-conj (splice-unquote goals)) empty-s))))))
(defmacro
run*
(q-name &rest goals)
(quasiquote (run-n -1 (unquote q-name) (splice-unquote goals))))
(defmacro
run
(n q-name &rest goals)
(quasiquote (run-n (unquote n) (unquote q-name) (splice-unquote goals))))

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;; lib/minikanren/stream.sx — Phase 2 piece A: lazy streams of substitutions.
;;
;; SX has no improper pairs (cons requires a list cdr), so we use a
;; tagged stream-cell shape for mature stream elements:
;;
;; stream ::= mzero empty (the SX empty list)
;; | (:s HEAD TAIL) mature cell, TAIL is a stream
;; | thunk (fn () ...) → stream when forced
;;
;; HEAD is a substitution dict. TAIL is again a stream (possibly a thunk),
;; which is what gives us laziness — mk-mplus can return a mature head with
;; a thunk in the tail, deferring the rest of the search.
(define mzero (list))
(define s-cons (fn (h t) (list :s h t)))
(define
s-cons?
(fn (s) (and (list? s) (not (empty? s)) (= (first s) :s))))
(define s-car (fn (s) (nth s 1)))
(define s-cdr (fn (s) (nth s 2)))
(define unit (fn (s) (s-cons s mzero)))
(define stream-pause? (fn (s) (and (not (list? s)) (callable? s))))
;; mk-mplus — interleave two streams. If s1 is paused we suspend and
;; swap (Reasoned Schemer "interleave"); otherwise mature-cons head with
;; mk-mplus of the rest.
(define
mk-mplus
(fn
(s1 s2)
(cond
((empty? s1) s2)
((stream-pause? s1) (fn () (mk-mplus s2 (s1))))
(:else (s-cons (s-car s1) (mk-mplus (s-cdr s1) s2))))))
;; mk-bind — apply goal g to every substitution in stream s, mk-mplus-ing.
(define
mk-bind
(fn
(s g)
(cond
((empty? s) mzero)
((stream-pause? s) (fn () (mk-bind (s) g)))
(:else (mk-mplus (g (s-car s)) (mk-bind (s-cdr s) g))))))
;; stream-take — force up to n results out of a (possibly lazy) stream
;; into a flat SX list of substitutions. n = -1 means take all.
(define
stream-take
(fn
(n s)
(cond
((= n 0) (list))
((empty? s) (list))
((stream-pause? s) (stream-take n (s)))
(:else
(cons
(s-car s)
(stream-take
(if (= n -1) -1 (- n 1))
(s-cdr s)))))))

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;; lib/minikanren/tabling.sx — Phase 7 piece A: naive memoization.
;;
;; A `table-2` wrapper for 2-arg relations (input, output). Caches by
;; ground input (walked at call time). On hit, replays the cached output
;; values; on miss, runs the relation, collects all output values from
;; the answer stream, stores, then replays.
;;
;; Limitations of naive memoization (vs proper SLG / producer-consumer
;; tabling):
;; - Each call must terminate before its result enters the cache —
;; so cyclic recursive calls with the SAME ground input would still
;; diverge (not addressed here).
;; - Caching by full ground walk only; partially-ground args fall
;; through to the underlying relation.
;;
;; Despite the limitations, naive memoization is enough for the
;; canonical demo: Fibonacci goes from exponential to linear because
;; each fib(k) result is computed at most once.
;;
;; Cache lifetime: a single global mk-tab-cache. Use `(mk-tab-clear!)`
;; between independent queries.
(define mk-tab-cache {})
(define mk-tab-clear! (fn () (set! mk-tab-cache {})))
(define
mk-tab-lookup
(fn
(key)
(cond
((has-key? mk-tab-cache key) (get mk-tab-cache key))
(:else :miss))))
(define
mk-tab-store!
(fn (key vals) (set! mk-tab-cache (assoc mk-tab-cache key vals))))
(define
mk-tab-ground-term?
(fn
(t)
(cond
((is-var? t) false)
((mk-cons-cell? t)
(and
(mk-tab-ground-term? (mk-cons-head t))
(mk-tab-ground-term? (mk-cons-tail t))))
((mk-list-pair? t) (every? mk-tab-ground-term? t))
(:else true))))
(define
mk-tab-replay-vals
(fn
(vals output s)
(cond
((empty? vals) mzero)
(:else
(let
((sp (mk-unify output (first vals) s)))
(let
((this-stream (cond ((= sp nil) mzero) (:else (unit sp)))))
(mk-mplus this-stream (mk-tab-replay-vals (rest vals) output s))))))))
(define
table-2
(fn
(name rel-fn)
(fn
(input output)
(fn
(s)
(let
((winput (mk-walk* input s)))
(cond
((mk-tab-ground-term? winput)
(let
((key (str name "@" winput)))
(let
((cached (mk-tab-lookup key)))
(cond
((= cached :miss)
(let
((all-substs (stream-take -1 ((rel-fn input output) s))))
(let
((vals (map (fn (s2) (mk-walk* output s2)) all-substs)))
(begin
(mk-tab-store! key vals)
(mk-tab-replay-vals vals output s)))))
(:else (mk-tab-replay-vals cached output s))))))
(:else ((rel-fn input output) s))))))))
;; --- table-1: 1-arg relation (one input, no output to cache) ---
;; The relation is a predicate `(p input)` that succeeds or fails.
;; Cache stores either :ok or :no.
(define
table-1
(fn
(name rel-fn)
(fn
(input)
(fn
(s)
(let
((winput (mk-walk* input s)))
(cond
((mk-tab-ground-term? winput)
(let
((key (str name "@1@" winput)))
(let
((cached (mk-tab-lookup key)))
(cond
((= cached :miss)
(let
((stream ((rel-fn input) s)))
(let
((peek (stream-take 1 stream)))
(cond
((empty? peek)
(begin (mk-tab-store! key :no) mzero))
(:else (begin (mk-tab-store! key :ok) stream))))))
((= cached :ok) (unit s))
((= cached :no) mzero)
(:else mzero)))))
(:else ((rel-fn input) s))))))))
;; --- table-3: 3-arg relation (input1 input2 output) ---
;; Cache keyed by (input1, input2). Output values cached as a list.
(define
table-3
(fn
(name rel-fn)
(fn
(i1 i2 output)
(fn
(s)
(let
((wi1 (mk-walk* i1 s)) (wi2 (mk-walk* i2 s)))
(cond
((and (mk-tab-ground-term? wi1) (mk-tab-ground-term? wi2))
(let
((key (str name "@3@" wi1 "/" wi2)))
(let
((cached (mk-tab-lookup key)))
(cond
((= cached :miss)
(let
((all-substs (stream-take -1 ((rel-fn i1 i2 output) s))))
(let
((vals (map (fn (s2) (mk-walk* output s2)) all-substs)))
(begin
(mk-tab-store! key vals)
(mk-tab-replay-vals vals output s)))))
(:else (mk-tab-replay-vals cached output s))))))
(:else ((rel-fn i1 i2 output) s))))))))

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;; lib/minikanren/tests/appendo3.sx — 3-list append.
(mk-test
"appendo3-forward"
(run*
q
(appendo3
(list 1 2)
(list 3 4)
(list 5 6)
q))
(list
(list 1 2 3 4 5 6)))
(mk-test
"appendo3-empty-everything"
(run* q (appendo3 (list) (list) (list) q))
(list (list)))
(mk-test
"appendo3-recover-middle"
(run*
q
(appendo3
(list 1 2)
q
(list 5 6)
(list 1 2 3 4 5 6)))
(list (list 3 4)))
(mk-test
"appendo3-empty-middle"
(run*
q
(appendo3
(list 1 2)
(list)
(list 3 4)
q))
(list (list 1 2 3 4)))
(mk-test
"appendo3-empty-first-and-last"
(run*
q
(appendo3 (list) (list 1 2 3) (list) q))
(list (list 1 2 3)))
(mk-tests-run!)

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;; lib/minikanren/tests/arith-prog.sx — arithmetic progression generation.
(mk-test
"arith-progo-zero-len"
(run* q (arith-progo 5 1 0 q))
(list (list)))
(mk-test
"arith-progo-1-to-5"
(run* q (arith-progo 1 1 5 q))
(list (list 1 2 3 4 5)))
(mk-test
"arith-progo-evens-from-0"
(run* q (arith-progo 0 2 5 q))
(list (list 0 2 4 6 8)))
(mk-test
"arith-progo-descending"
(run* q (arith-progo 10 -1 4 q))
(list (list 10 9 8 7)))
(mk-test
"arith-progo-zero-step"
(run* q (arith-progo 7 0 3 q))
(list (list 7 7 7)))
(mk-test
"arith-progo-negative-start"
(run* q (arith-progo -3 2 4 q))
(list (list -3 -1 1 3)))
(mk-tests-run!)

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;; lib/minikanren/tests/btree-walko.sx — walk a leaves-of-binary-tree relation
;; using matche dispatch on (:leaf v) and (:node left right) patterns.
(define
btree-walko
(fn
(tree v)
(matche
tree
((:leaf x) (== v x))
((:node l r) (conde ((btree-walko l v)) ((btree-walko r v)))))))
;; A small test tree: ((1 2) (3 (4 5))).
(define
test-btree
(list
:node (list :node (list :leaf 1) (list :leaf 2))
(list
:node (list :leaf 3)
(list :node (list :leaf 4) (list :leaf 5)))))
(mk-test
"btree-walko-enumerates-all-leaves"
(let
((leaves (run* q (btree-walko test-btree q))))
(and
(= (len leaves) 5)
(and
(some (fn (l) (= l 1)) leaves)
(and
(some (fn (l) (= l 2)) leaves)
(and
(some (fn (l) (= l 3)) leaves)
(and
(some (fn (l) (= l 4)) leaves)
(some (fn (l) (= l 5)) leaves)))))))
true)
(mk-test
"btree-walko-find-3-membership"
(run 1 q (btree-walko test-btree 3))
(list (make-symbol "_.0")))
(mk-test
"btree-walko-find-99-not-present"
(run* q (btree-walko test-btree 99))
(list))
(mk-test
"btree-walko-leaf-only"
(run* q (btree-walko (list :leaf 42) q))
(list 42))
(mk-tests-run!)

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;; lib/minikanren/tests/classics.sx — small classic-style puzzles that
;; exercise the full system end to end (relations + conde + matche +
;; fresh + run*). Each test is a self-contained miniKanren program.
;; -----------------------------------------------------------------------
;; Pet puzzle (3 friends, 3 pets, 1-each).
;; -----------------------------------------------------------------------
(mk-test
"classics-pet-puzzle"
(run*
q
(fresh
(a b c)
(== q (list a b c))
(permuteo (list :dog :cat :fish) (list a b c))
(== b :fish)
(conde ((== a :cat)) ((== a :fish)))))
(list (list :cat :fish :dog)))
;; -----------------------------------------------------------------------
;; Family-relations puzzle (uses membero on a fact list).
;; -----------------------------------------------------------------------
(define
parent-facts
(list
(list "alice" "bob")
(list "alice" "carol")
(list "bob" "dave")
(list "carol" "eve")
(list "dave" "frank")))
(define parento (fn (x y) (membero (list x y) parent-facts)))
(define grandparento (fn (x z) (fresh (y) (parento x y) (parento y z))))
(mk-test
"classics-grandparents-of-frank"
(run* q (grandparento q "frank"))
(list "bob"))
(mk-test
"classics-grandchildren-of-alice"
(run* q (grandparento "alice" q))
(list "dave" "eve"))
;; -----------------------------------------------------------------------
;; Symbolic differentiation, matche-driven.
;; Variable :x: d/dx x = 1
;; Sum (:+ a b): d/dx (a+b) = (da + db)
;; Product (:* a b): d/dx (a*b) = (da*b + a*db)
;; -----------------------------------------------------------------------
(define
diffo
(fn
(expr var d)
(matche
expr
(:x (== d 1))
((:+ a b)
(fresh
(da db)
(== d (list :+ da db))
(diffo a var da)
(diffo b var db)))
((:* a b)
(fresh
(da db)
(== d (list :+ (list :* da b) (list :* a db)))
(diffo a var da)
(diffo b var db))))))
(mk-test "classics-diff-of-x" (run* q (diffo :x :x q)) (list 1))
(mk-test
"classics-diff-of-x-plus-x"
(run* q (diffo (list :+ :x :x) :x q))
(list (list :+ 1 1)))
(mk-test
"classics-diff-of-x-times-x"
(run* q (diffo (list :* :x :x) :x q))
(list (list :+ (list :* 1 :x) (list :* :x 1))))
(mk-tests-run!)

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;; lib/minikanren/tests/clpfd-distinct.sx — fd-distinct (alldifferent).
(mk-test
"fd-distinct-empty"
(run* q (fd-distinct (list)))
(list (make-symbol "_.0")))
(mk-test
"fd-distinct-singleton"
(run* q (fd-distinct (list 5)))
(list (make-symbol "_.0")))
(mk-test
"fd-distinct-pair-distinct"
(run* q (fd-distinct (list 1 2)))
(list (make-symbol "_.0")))
(mk-test
"fd-distinct-pair-equal-fails"
(run* q (fd-distinct (list 5 5)))
(list))
(mk-test
"fd-distinct-3-perms-of-3"
(let
((res (run* q (fresh (a b c) (fd-in a (list 1 2 3)) (fd-in b (list 1 2 3)) (fd-in c (list 1 2 3)) (fd-distinct (list a b c)) (fd-label (list a b c)) (== q (list a b c))))))
(= (len res) 6))
true)
(mk-test
"fd-distinct-4-perms-of-4-count"
(let
((res (run* q (fresh (a b c d) (fd-in a (list 1 2 3 4)) (fd-in b (list 1 2 3 4)) (fd-in c (list 1 2 3 4)) (fd-in d (list 1 2 3 4)) (fd-distinct (list a b c d)) (fd-label (list a b c d)) (== q (list a b c d))))))
(= (len res) 24))
true)
(mk-test
"fd-distinct-pigeonhole-fails"
(run*
q
(fresh
(a b c d)
(fd-in a (list 1 2 3))
(fd-in b (list 1 2 3))
(fd-in c (list 1 2 3))
(fd-in d (list 1 2 3))
(fd-distinct (list a b c d))
(fd-label (list a b c d))
(== q (list a b c d))))
(list))
(mk-tests-run!)

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;; lib/minikanren/tests/clpfd-domains.sx — Phase 6 piece B: domain primitives.
;; --- domain construction ---
(mk-test
"fd-dom-from-list-sorts"
(fd-dom-from-list
(list 3 1 2 1 5))
(list 1 2 3 5))
(mk-test "fd-dom-from-list-empty" (fd-dom-from-list (list)) (list))
(mk-test
"fd-dom-from-list-single"
(fd-dom-from-list (list 7))
(list 7))
(mk-test
"fd-dom-range-1-5"
(fd-dom-range 1 5)
(list 1 2 3 4 5))
(mk-test "fd-dom-range-empty" (fd-dom-range 5 1) (list))
;; --- predicates ---
(mk-test "fd-dom-empty-yes" (fd-dom-empty? (list)) true)
(mk-test "fd-dom-empty-no" (fd-dom-empty? (list 1)) false)
(mk-test "fd-dom-singleton-yes" (fd-dom-singleton? (list 5)) true)
(mk-test
"fd-dom-singleton-multi"
(fd-dom-singleton? (list 1 2))
false)
(mk-test "fd-dom-singleton-empty" (fd-dom-singleton? (list)) false)
(mk-test
"fd-dom-min"
(fd-dom-min (list 3 7 9))
3)
(mk-test
"fd-dom-max"
(fd-dom-max (list 3 7 9))
9)
(mk-test
"fd-dom-member-yes"
(fd-dom-member?
3
(list 1 2 3 4))
true)
(mk-test
"fd-dom-member-no"
(fd-dom-member?
9
(list 1 2 3 4))
false)
;; --- intersect / without ---
(mk-test
"fd-dom-intersect"
(fd-dom-intersect
(list 1 2 3 4 5)
(list 2 4 6))
(list 2 4))
(mk-test
"fd-dom-intersect-disjoint"
(fd-dom-intersect
(list 1 2 3)
(list 4 5 6))
(list))
(mk-test
"fd-dom-intersect-empty"
(fd-dom-intersect (list) (list 1 2 3))
(list))
(mk-test
"fd-dom-intersect-equal"
(fd-dom-intersect
(list 1 2 3)
(list 1 2 3))
(list 1 2 3))
(mk-test
"fd-dom-without-mid"
(fd-dom-without
3
(list 1 2 3 4 5))
(list 1 2 4 5))
(mk-test
"fd-dom-without-missing"
(fd-dom-without 9 (list 1 2 3))
(list 1 2 3))
(mk-test
"fd-dom-without-min"
(fd-dom-without 1 (list 1 2 3))
(list 2 3))
;; --- store accessors ---
(mk-test "fd-domain-of-unset" (fd-domain-of {} "x") nil)
(mk-test
"fd-domain-of-set"
(let
((s (fd-set-domain {} "x" (list 1 2 3))))
(fd-domain-of s "x"))
(list 1 2 3))
(mk-test
"fd-set-domain-empty-fails"
(fd-set-domain {} "x" (list))
nil)
(mk-test
"fd-set-domain-overrides"
(let
((s (fd-set-domain {} "x" (list 1 2 3))))
(fd-domain-of (fd-set-domain s "x" (list 5)) "x"))
(list 5))
(mk-test
"fd-set-domain-multiple-vars"
(let
((s (fd-set-domain (fd-set-domain {} "x" (list 1)) "y" (list 2 3))))
(list (fd-domain-of s "x") (fd-domain-of s "y")))
(list (list 1) (list 2 3)))
(mk-tests-run!)

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;; lib/minikanren/tests/clpfd-in-label.sx — fd-in (domain narrowing) + fd-label.
;; --- fd-in: domain narrowing ---
(mk-test
"fd-in-bare-label"
(run*
q
(fresh
(x)
(fd-in x (list 1 2 3 4 5))
(fd-label (list x))
(== q x)))
(list 1 2 3 4 5))
(mk-test
"fd-in-intersection"
(run*
q
(fresh
(x)
(fd-in x (list 1 2 3 4 5))
(fd-in x (list 3 4 5 6 7))
(fd-label (list x))
(== q x)))
(list 3 4 5))
(mk-test
"fd-in-disjoint-empty"
(run*
q
(fresh
(x)
(fd-in x (list 1 2 3))
(fd-in x (list 7 8 9))
(fd-label (list x))
(== q x)))
(list))
(mk-test
"fd-in-singleton-domain"
(run*
q
(fresh (x) (fd-in x (list 5)) (fd-label (list x)) (== q x)))
(list 5))
;; --- ground value checks the domain ---
(mk-test
"fd-in-ground-in-domain"
(run*
q
(fresh
(x)
(== x 3)
(fd-in x (list 1 2 3 4 5))
(== q x)))
(list 3))
(mk-test
"fd-in-ground-not-in-domain"
(run*
q
(fresh
(x)
(== x 9)
(fd-in x (list 1 2 3 4 5))
(== q x)))
(list))
;; --- fd-label across multiple vars ---
(mk-test
"fd-label-multiple-vars"
(let
((res (run* q (fresh (a b) (fd-in a (list 1 2 3)) (fd-in b (list 10 20)) (fd-label (list a b)) (== q (list a b))))))
(= (len res) 6))
true)
(mk-test
"fd-label-empty-vars"
(run* q (fd-label (list)))
(list (make-symbol "_.0")))
;; --- composition with regular goals ---
(mk-test
"fd-in-with-membero-style-filtering"
(run*
q
(fresh
(x)
(fd-in
x
(list
1
2
3
4
5
6
7
8
9
10))
(fd-label (list x))
(== q x)))
(list
1
2
3
4
5
6
7
8
9
10))
(mk-tests-run!)

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;; lib/minikanren/tests/clpfd-neq.sx — fd-neq with constraint propagation.
;; --- ground / domain interaction ---
(mk-test
"fd-neq-ground-distinct"
(run*
q
(fresh
(x)
(fd-neq x 5)
(fd-in x (list 4 5 6))
(fd-label (list x))
(== q x)))
(list 4 6))
(mk-test
"fd-neq-ground-equal-fails"
(run* q (fresh (x) (== x 5) (fd-neq x 5) (== q x)))
(list))
(mk-test
"fd-neq-symmetric"
(run*
q
(fresh
(x)
(fd-neq 7 x)
(fd-in x (list 5 6 7 8 9))
(fd-label (list x))
(== q x)))
(list 5 6 8 9))
;; --- two vars with overlapping domains ---
(mk-test
"fd-neq-pair-from-3"
(let
((res (run* q (fresh (x y) (fd-in x (list 1 2 3)) (fd-in y (list 1 2 3)) (fd-neq x y) (fd-label (list x y)) (== q (list x y))))))
(= (len res) 6))
true)
(mk-test
"fd-all-distinct-3-of-3"
(let
((res (run* q (fresh (a b c) (fd-in a (list 1 2 3)) (fd-in b (list 1 2 3)) (fd-in c (list 1 2 3)) (fd-neq a b) (fd-neq a c) (fd-neq b c) (fd-label (list a b c)) (== q (list a b c))))))
(= (len res) 6))
true)
(mk-test
"fd-pigeonhole-fails"
(run*
q
(fresh
(a b c)
(fd-in a (list 1 2))
(fd-in b (list 1 2))
(fd-in c (list 1 2))
(fd-neq a b)
(fd-neq a c)
(fd-neq b c)
(fd-label (list a b c))
(== q (list a b c))))
(list))
;; --- propagation when one side becomes ground ---
(mk-test
"fd-neq-propagates-after-ground"
(run*
q
(fresh
(x y)
(fd-in x (list 1 2 3))
(fd-in y (list 1 2 3))
(fd-neq x y)
(== x 2)
(fd-label (list y))
(== q y)))
(list 1 3))
(mk-tests-run!)

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;; lib/minikanren/tests/clpfd-ord.sx — fd-lt / fd-lte / fd-eq.
;; --- fd-lt ---
(mk-test
"fd-lt-narrows-x-against-num"
(run*
q
(fresh
(x)
(fd-in x (list 1 2 3 4 5))
(fd-lt x 3)
(fd-label (list x))
(== q x)))
(list 1 2))
(mk-test
"fd-lt-narrows-x-against-num-symmetric"
(run*
q
(fresh
(x)
(fd-in x (list 1 2 3 4 5))
(fd-lt 3 x)
(fd-label (list x))
(== q x)))
(list 4 5))
(mk-test
"fd-lt-pair-ordered"
(let
((res (run* q (fresh (x y) (fd-in x (list 1 2 3 4)) (fd-in y (list 1 2 3 4)) (fd-lt x y) (fd-label (list x y)) (== q (list x y))))))
(= (len res) 6))
true)
(mk-test
"fd-lt-impossible-fails"
(run*
q
(fresh
(x)
(fd-in x (list 5 6 7))
(fd-lt x 3)
(fd-label (list x))
(== q x)))
(list))
;; --- fd-lte ---
(mk-test
"fd-lte-includes-equal"
(run*
q
(fresh
(x)
(fd-in x (list 1 2 3 4 5))
(fd-lte x 3)
(fd-label (list x))
(== q x)))
(list 1 2 3))
(mk-test
"fd-lte-equal-bound"
(run*
q
(fresh
(x)
(fd-in x (list 1 2 3 4 5))
(fd-lte 3 x)
(fd-label (list x))
(== q x)))
(list 3 4 5))
;; --- fd-eq ---
(mk-test
"fd-eq-bind"
(run*
q
(fresh
(x)
(fd-in x (list 1 2 3 4 5))
(fd-eq x 3)
(== q x)))
(list 3))
(mk-test
"fd-eq-out-of-domain-fails"
(run*
q
(fresh
(x)
(fd-in x (list 1 2 3))
(fd-eq x 5)
(== q x)))
(list))
(mk-test
"fd-eq-two-vars-share-domain"
(run*
q
(fresh
(x y)
(fd-in x (list 1 2 3))
(fd-in y (list 2 3 4))
(fd-eq x y)
(fd-label (list x y))
(== q (list x y))))
(list (list 2 2) (list 3 3)))
;; --- combine fd-lt + fd-neq for "between" puzzle ---
(mk-test
"fd-lt-neq-combined"
(run*
q
(fresh
(x y z)
(fd-in x (list 1 2 3))
(fd-in y (list 1 2 3))
(fd-in z (list 1 2 3))
(fd-lt x y)
(fd-lt y z)
(fd-label (list x y z))
(== q (list x y z))))
(list (list 1 2 3)))
(mk-tests-run!)

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;; lib/minikanren/tests/clpfd-plus.sx — fd-plus (x + y = z).
(mk-test
"fd-plus-all-ground"
(run* q (fresh (z) (fd-plus 2 3 z) (== q z)))
(list 5))
(mk-test
"fd-plus-recover-x"
(run* q (fresh (x) (fd-plus x 3 5) (== q x)))
(list 2))
(mk-test
"fd-plus-recover-y"
(run* q (fresh (y) (fd-plus 2 y 5) (== q y)))
(list 3))
(mk-test
"fd-plus-impossible-fails"
(run*
q
(fresh
(z)
(fd-plus 2 3 z)
(== z 99)
(== q z)))
(list))
(mk-test
"fd-plus-domain-check"
(run*
q
(fresh
(x)
(fd-in x (list 3 4 5))
(fd-plus x 3 5)
(== q x)))
(list))
(mk-test
"fd-plus-pairs-summing-to-5"
(run*
q
(fresh
(x y)
(fd-in x (list 1 2 3 4))
(fd-in y (list 1 2 3 4))
(fd-plus x y 5)
(fd-label (list x y))
(== q (list x y))))
(list
(list 1 4)
(list 2 3)
(list 3 2)
(list 4 1)))
(mk-test
"fd-plus-z-derived"
(run* q (fresh (z) (fd-plus 7 8 z) (== q z)))
(list 15))
(mk-tests-run!)

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;; lib/minikanren/tests/clpfd-times.sx — fd-times (x * y = z).
(mk-test
"fd-times-3-4"
(run* q (fresh (z) (fd-times 3 4 z) (== q z)))
(list 12))
(mk-test
"fd-times-recover-divisor"
(run* q (fresh (x) (fd-times x 5 30) (== q x)))
(list 6))
(mk-test
"fd-times-non-divisible-fails"
(run* q (fresh (x) (fd-times x 5 31) (== q x)))
(list))
(mk-test
"fd-times-by-zero"
(run* q (fresh (z) (fd-times 0 99 z) (== q z)))
(list 0))
(mk-test
"fd-times-zero-by-anything-zero"
(run*
q
(fresh
(x)
(fd-in x (list 1 2 3))
(fd-times x 0 0)
(fd-label (list x))
(== q x)))
(list 1 2 3))
(mk-test
"fd-times-12-divisor-pairs"
(run*
q
(fresh
(x y)
(fd-in
x
(list
1
2
3
4
5
6))
(fd-in
y
(list
1
2
3
4
5
6))
(fd-times x y 12)
(fd-label (list x y))
(== q (list x y))))
(list
(list 2 6)
(list 3 4)
(list 4 3)
(list 6 2)))
(mk-test
"fd-times-square-of-each"
(run*
q
(fresh
(x z)
(fd-in x (list 1 2 3 4 5))
(fd-times x x z)
(fd-label (list x))
(== q (list x z))))
(list
(list 1 1)
(list 2 4)
(list 3 9)
(list 4 16)
(list 5 25)))
(mk-tests-run!)

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;; lib/minikanren/tests/conda.sx — Phase 5 piece A tests for `conda`.
;; --- conda commits to first non-failing head, keeps ALL its answers ---
(mk-test
"conda-first-clause-keeps-all"
(run*
q
(conda
((mk-disj (== q 1) (== q 2)))
((== q 100))))
(list 1 2))
(mk-test
"conda-skips-failing-head"
(run*
q
(conda
((== 1 2))
((mk-disj (== q 10) (== q 20)))))
(list 10 20))
(mk-test
"conda-all-fail"
(run*
q
(conda ((== 1 2)) ((== 3 4))))
(list))
(mk-test "conda-no-clauses" (run* q (conda)) (list))
;; --- conda DIFFERS from condu: conda keeps all head answers ---
(mk-test
"conda-vs-condu-divergence"
(list
(run*
q
(conda
((mk-disj (== q 1) (== q 2)))
((== q 100))))
(run*
q
(condu
((mk-disj (== q 1) (== q 2)))
((== q 100)))))
(list (list 1 2) (list 1)))
;; --- conda head's rest-goals run on every head answer ---
(mk-test
"conda-rest-goals-run-on-all-answers"
(run*
q
(fresh
(x r)
(conda
((mk-disj (== x 1) (== x 2))
(== r (list :tag x))))
(== q r)))
(list (list :tag 1) (list :tag 2)))
;; --- if rest-goals fail on a head answer, that head answer is filtered;
;; the clause does not fall through to next clauses (per soft-cut). ---
(mk-test
"conda-rest-fails-no-fallthrough"
(run*
q
(conda
((mk-disj (== q 1) (== q 2)) (== q 99))
((== q 200))))
(list))
(mk-tests-run!)

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;; lib/minikanren/tests/conde.sx — Phase 2 piece C tests for `conde`.
;;
;; Note on ordering: conde clauses are wrapped in Zzz (inverse-eta delay),
;; so applying the conde goal to a substitution returns thunks. mk-mplus
;; suspends-and-swaps when its left operand is paused, giving fair
;; interleaving — this is exactly what makes recursive relations work,
;; but it does mean conde answers can interleave rather than appear in
;; strict left-to-right clause order.
;; --- single-clause conde ≡ conj of clause body ---
(mk-test
"conde-one-clause"
(let ((q (mk-var "q"))) (run* q (conde ((== q 7)))))
(list 7))
(mk-test
"conde-one-clause-multi-goals"
(let
((q (mk-var "q")))
(run* q (conde ((fresh (x) (== x 5) (== q (list x x)))))))
(list (list 5 5)))
;; --- multi-clause: produces one row per clause (interleaved) ---
(mk-test
"conde-three-clauses-as-set"
(let
((qs (run* q (conde ((== q 1)) ((== q 2)) ((== q 3))))))
(and
(= (len qs) 3)
(and
(some (fn (x) (= x 1)) qs)
(and
(some (fn (x) (= x 2)) qs)
(some (fn (x) (= x 3)) qs)))))
true)
(mk-test
"conde-mixed-success-failure-as-set"
(let
((qs (run* q (conde ((== q "a")) ((== 1 2)) ((== q "b"))))))
(and
(= (len qs) 2)
(and (some (fn (x) (= x "a")) qs) (some (fn (x) (= x "b")) qs))))
true)
;; --- conde with conjuncts inside clauses ---
(mk-test
"conde-clause-conj-as-set"
(let
((rows (run* q (fresh (x y) (conde ((== x 1) (== y 10)) ((== x 2) (== y 20))) (== q (list x y))))))
(and
(= (len rows) 2)
(and
(some (fn (r) (= r (list 1 10))) rows)
(some (fn (r) (= r (list 2 20))) rows))))
true)
;; --- nested conde ---
(mk-test
"conde-nested-yields-three"
(let
((qs (run* q (conde ((conde ((== q 1)) ((== q 2)))) ((== q 3))))))
(and
(= (len qs) 3)
(and
(some (fn (x) (= x 1)) qs)
(and
(some (fn (x) (= x 2)) qs)
(some (fn (x) (= x 3)) qs)))))
true)
;; --- conde all clauses fail → empty stream ---
(mk-test
"conde-all-fail"
(run*
q
(conde ((== 1 2)) ((== 3 4))))
(list))
;; --- empty conde: no clauses ⇒ fail ---
(mk-test "conde-no-clauses" (run* q (conde)) (list))
(mk-tests-run!)

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;; lib/minikanren/tests/condu.sx — Phase 2 piece D tests for `onceo` and `condu`.
;; --- onceo: at most one answer ---
(mk-test
"onceo-single-success-passes-through"
(let
((q (mk-var "q")))
(let
((res (stream-take 5 ((onceo (== q 7)) empty-s))))
(map (fn (s) (mk-walk q s)) res)))
(list 7))
(mk-test
"onceo-multi-success-trimmed-to-one"
(let
((q (mk-var "q")))
(let
((res (stream-take 5 ((onceo (mk-disj (== q 1) (== q 2) (== q 3))) empty-s))))
(map (fn (s) (mk-walk q s)) res)))
(list 1))
(mk-test
"onceo-failure-stays-failure"
((onceo (== 1 2)) empty-s)
(list))
(mk-test
"onceo-conde-trimmed"
(let
((q (mk-var "q")))
(let
((res (stream-take 5 ((onceo (conde ((== q "a")) ((== q "b")))) empty-s))))
(map (fn (s) (mk-walk q s)) res)))
(list "a"))
;; --- condu: first clause with successful head wins ---
(mk-test
"condu-first-clause-wins"
(let
((q (mk-var "q")))
(let
((res (stream-take 10 ((condu ((== q 1)) ((== q 2))) empty-s))))
(map (fn (s) (mk-walk q s)) res)))
(list 1))
(mk-test
"condu-skips-failing-head"
(let
((q (mk-var "q")))
(let
((res (stream-take 10 ((condu ((== 1 2)) ((== q 100)) ((== q 200))) empty-s))))
(map (fn (s) (mk-walk q s)) res)))
(list 100))
(mk-test
"condu-all-fail-empty"
((condu ((== 1 2)) ((== 3 4)))
empty-s)
(list))
(mk-test "condu-empty-clauses-fail" ((condu) empty-s) (list))
;; --- condu commits head's first answer; rest-goals can still backtrack
;; within that committed substitution but cannot revisit other heads. ---
(mk-test
"condu-head-onceo-rest-runs"
(let
((q (mk-var "q")) (r (mk-var "r")))
(let
((res (stream-take 10 ((condu ((mk-disj (== q 1) (== q 2)) (== r 99))) empty-s))))
(map (fn (s) (list (mk-walk q s) (mk-walk r s))) res)))
(list (list 1 99)))
(mk-test
"condu-rest-goals-can-fail-the-clause"
(let
((q (mk-var "q")))
(let
((res (stream-take 10 ((condu ((== q 1) (== 2 3)) ((== q 99))) empty-s))))
(map (fn (s) (mk-walk q s)) res)))
(list))
(mk-tests-run!)

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;; lib/minikanren/tests/counto.sx — count occurrences of x in l (intarith).
(mk-test
"counto-empty"
(run* q (counto 1 (list) q))
(list 0))
(mk-test
"counto-not-found"
(run* q (counto 99 (list 1 2 3) q))
(list 0))
(mk-test
"counto-once"
(run* q (counto 2 (list 1 2 3) q))
(list 1))
(mk-test
"counto-thrice"
(run*
q
(counto
1
(list 1 2 1 3 1)
q))
(list 3))
(mk-test
"counto-all-same"
(run*
q
(counto 7 (list 7 7 7 7) q))
(list 4))
(mk-test
"counto-string"
(run* q (counto "x" (list "x" "y" "x") q))
(list 2))
(mk-tests-run!)

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;; lib/minikanren/tests/cyclic-graph.sx — demonstrates the naive-patho
;; behaviour on a cyclic graph. Without Phase-7 tabling/SLG, the search
;; produces ever-longer paths revisiting the cycle. `run n` truncates;
;; `run*` would diverge.
(define cyclic-edges (list (list :a :b) (list :b :a) (list :b :c)))
(define cyclic-edgeo (fn (x y) (membero (list x y) cyclic-edges)))
(define
cyclic-patho
(fn
(x y path)
(conde
((cyclic-edgeo x y) (== path (list x y)))
((fresh (z mid) (cyclic-edgeo x z) (cyclic-patho z y mid) (conso x mid path))))))
;; --- direct edge ---
(mk-test
"cyclic-direct"
(run 1 q (cyclic-patho :a :b q))
(list (list :a :b)))
;; --- runs first 5 paths from a to b: bare edge, then increasing
;; numbers of cycle traversals (a->b->a->b, etc.) ---
(mk-test
"cyclic-enumerates-prefix-via-run-n"
(let
((paths (run 5 q (cyclic-patho :a :b q))))
(and
(= (len paths) 5)
(and
(every? (fn (p) (= (first p) :a)) paths)
(every? (fn (p) (= (last p) :b)) paths))))
true)
(mk-test
"cyclic-finds-c-via-cycle-or-direct"
(let
((paths (run 3 q (cyclic-patho :a :c q))))
(and
(>= (len paths) 1)
(some (fn (p) (= p (list :a :b :c))) paths)))
true)
(mk-tests-run!)

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;; lib/minikanren/tests/defrel.sx — Prolog-style relation definition macro.
(defrel
(my-membero x l)
((fresh (d) (conso x d l)))
((fresh (a d) (conso a d l) (my-membero x d))))
(mk-test
"defrel-defines-membero"
(run* q (my-membero q (list 1 2 3)))
(list 1 2 3))
(defrel
(my-listo l)
((nullo l))
((fresh (a d) (conso a d l) (my-listo d))))
(mk-test
"defrel-listo-bounded"
(run 3 q (my-listo q))
(list
(list)
(list (make-symbol "_.0"))
(list (make-symbol "_.0") (make-symbol "_.1"))))
;; Multi-arg relation with arithmetic.
(defrel
(my-pluso a b c)
((== a :z) (== b c))
((fresh (a-1 c-1) (== a (list :s a-1)) (== c (list :s c-1)) (my-pluso a-1 b c-1))))
(mk-test
"defrel-pluso-2-3"
(run*
q
(my-pluso (list :s (list :s :z)) (list :s (list :s (list :s :z))) q))
(list (list :s (list :s (list :s (list :s (list :s :z)))))))
(mk-tests-run!)

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;; lib/minikanren/tests/enumerate.sx — index-each-element relation.
(mk-test
"enumerate-i-empty"
(run* q (enumerate-i (list) q))
(list (list)))
(mk-test
"enumerate-i-three"
(run* q (enumerate-i (list :a :b :c) q))
(list
(list (list 0 :a) (list 1 :b) (list 2 :c))))
(mk-test
"enumerate-i-strings"
(run* q (enumerate-i (list "x" "y" "z") q))
(list
(list (list 0 "x") (list 1 "y") (list 2 "z"))))
(mk-test
"enumerate-from-i-100"
(run* q (enumerate-from-i 100 (list :x :y :z) q))
(list
(list (list 100 :x) (list 101 :y) (list 102 :z))))
(mk-test
"enumerate-from-i-singleton"
(run* q (enumerate-from-i 0 (list :only) q))
(list (list (list 0 :only))))
(mk-tests-run!)

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;; lib/minikanren/tests/fd.sx — Phase 6 piece A: ino + all-distincto.
;; --- ino ---
(mk-test
"ino-element-in-domain"
(run* q (ino q (list 1 2 3)))
(list 1 2 3))
(mk-test "ino-empty-domain" (run* q (ino q (list))) (list))
(mk-test
"ino-singleton-domain"
(run* q (ino q (list 42)))
(list 42))
;; --- all-distincto ---
(mk-test
"all-distincto-empty"
(run* q (all-distincto (list)))
(list (make-symbol "_.0")))
(mk-test
"all-distincto-singleton"
(run* q (all-distincto (list 1)))
(list (make-symbol "_.0")))
(mk-test
"all-distincto-distinct-three"
(run* q (all-distincto (list 1 2 3)))
(list (make-symbol "_.0")))
(mk-test
"all-distincto-duplicate-fails"
(run* q (all-distincto (list 1 2 1)))
(list))
(mk-test
"all-distincto-adjacent-duplicate-fails"
(run* q (all-distincto (list 1 1 2)))
(list))
;; --- ino + all-distincto: classic enumerate-all-permutations ---
(mk-test
"fd-puzzle-three-distinct-from-domain"
(let
((perms (run* q (fresh (a b c) (== q (list a b c)) (ino a (list 1 2 3)) (ino b (list 1 2 3)) (ino c (list 1 2 3)) (all-distincto (list a b c))))))
(and
(= (len perms) 6)
(and
(some (fn (p) (= p (list 1 2 3))) perms)
(and
(some
(fn (p) (= p (list 1 3 2)))
perms)
(and
(some
(fn (p) (= p (list 2 1 3)))
perms)
(and
(some
(fn (p) (= p (list 2 3 1)))
perms)
(and
(some
(fn (p) (= p (list 3 1 2)))
perms)
(some
(fn (p) (= p (list 3 2 1)))
perms))))))))
true)
(mk-tests-run!)

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;; lib/minikanren/tests/flat-mapo.sx — concatMap-style relation.
(mk-test
"flat-mapo-empty"
(run* q (flat-mapo (fn (x r) (== r (list x x))) (list) q))
(list (list)))
(mk-test
"flat-mapo-duplicate-each"
(run*
q
(flat-mapo
(fn (x r) (== r (list x x)))
(list 1 2 3)
q))
(list
(list 1 1 2 2 3 3)))
(mk-test
"flat-mapo-empty-from-each"
(run* q (flat-mapo (fn (x r) (== r (list))) (list :a :b :c) q))
(list (list)))
(mk-test
"flat-mapo-singleton-from-each-is-identity"
(run* q (flat-mapo (fn (x r) (== r (list x))) (list :a :b :c) q))
(list (list :a :b :c)))
(mk-test
"flat-mapo-tag-each"
(run*
q
(flat-mapo
(fn (x r) (== r (list :tag x)))
(list 1 2)
q))
(list (list :tag 1 :tag 2)))
(mk-tests-run!)

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(mk-test "flatteno-empty" (run* q (flatteno (list) q)) (list (list)))
(mk-test
"flatteno-atom"
(run* q (flatteno 5 q))
(list (list 5)))
(mk-test
"flatteno-flat-list"
(run* q (flatteno (list 1 2 3) q))
(list (list 1 2 3)))
(mk-test
"flatteno-singleton"
(run* q (flatteno (list 1) q))
(list (list 1)))
(mk-test
"flatteno-nested-once"
(run*
q
(flatteno (list 1 (list 2 3) 4) q))
(list (list 1 2 3 4)))
(mk-test
"flatteno-nested-twice"
(run*
q
(flatteno
(list
1
(list 2 (list 3 4))
5)
q))
(list (list 1 2 3 4 5)))
(mk-test
"flatteno-keywords"
(run* q (flatteno (list :a (list :b :c) :d) q))
(list (list :a :b :c :d)))
(mk-tests-run!)

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;; lib/minikanren/tests/foldl-o.sx — relational left fold.
(mk-test
"foldl-o-empty"
(run* q (foldl-o pluso-i (list) 42 q))
(list 42))
(mk-test
"foldl-o-sum"
(run*
q
(foldl-o
pluso-i
(list 1 2 3 4 5)
0
q))
(list 15))
(mk-test
"foldl-o-product"
(run*
q
(foldl-o
*o-i
(list 1 2 3 4)
1
q))
(list 24))
(mk-test
"foldl-o-reverse-via-flip-conso"
(run*
q
(foldl-o
(fn (acc x r) (conso x acc r))
(list 1 2 3 4)
(list)
q))
(list (list 4 3 2 1)))
(mk-test
"foldl-o-with-init"
(run*
q
(foldl-o pluso-i (list 1 2 3) 100 q))
(list 106))
(mk-tests-run!)

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;; lib/minikanren/tests/foldr-o.sx — relational right fold.
(mk-test
"foldr-o-empty"
(run* q (foldr-o conso (list) (list 99) q))
(list (list 99)))
(mk-test
"foldr-o-conso-rebuilds-list"
(run* q (foldr-o conso (list 1 2 3) (list) q))
(list (list 1 2 3)))
(mk-test
"foldr-o-appendo-flattens"
(run*
q
(foldr-o
appendo
(list
(list 1 2)
(list 3)
(list 4 5))
(list)
q))
(list (list 1 2 3 4 5)))
(mk-test
"foldr-o-with-acc-init"
(run*
q
(foldr-o
conso
(list 1 2)
(list 9 9)
q))
(list (list 1 2 9 9)))
(mk-tests-run!)

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;; lib/minikanren/tests/fresh.sx — Phase 2 piece B tests for `fresh`.
;; --- empty fresh: pure goal grouping ---
(mk-test
"fresh-empty-vars-equiv-conj"
(stream-take 5 ((fresh () (== 1 1)) empty-s))
(list empty-s))
(mk-test
"fresh-empty-vars-no-goals-is-succeed"
(stream-take 5 ((fresh ()) empty-s))
(list empty-s))
;; --- single var ---
(mk-test
"fresh-one-var-bound"
(let
((s (first (stream-take 5 ((fresh (x) (== x 7)) empty-s)))))
(first (vals s)))
7)
;; --- multiple vars + multiple goals ---
(mk-test
"fresh-two-vars-three-goals"
(let
((q (mk-var "q"))
(g
(fresh
(x y)
(== x 10)
(== y 20)
(== q (list x y)))))
(mk-walk* q (first (stream-take 5 (g empty-s)))))
(list 10 20))
(mk-test
"fresh-three-vars"
(let
((q (mk-var "q"))
(g
(fresh
(a b c)
(== a 1)
(== b 2)
(== c 3)
(== q (list a b c)))))
(mk-walk* q (first (stream-take 5 (g empty-s)))))
(list 1 2 3))
;; --- fresh interacts with disj ---
(mk-test
"fresh-with-disj"
(let
((q (mk-var "q")))
(let
((g (fresh (x) (mk-disj (== x 1) (== x 2)) (== q x))))
(let
((res (stream-take 5 (g empty-s))))
(map (fn (s) (mk-walk q s)) res))))
(list 1 2))
;; --- nested fresh ---
(mk-test
"fresh-nested"
(let
((q (mk-var "q"))
(g
(fresh
(x)
(fresh
(y)
(== x 1)
(== y 2)
(== q (list x y))))))
(mk-walk* q (first (stream-take 5 (g empty-s)))))
(list 1 2))
;; --- call-fresh (functional alternative) ---
(mk-test
"call-fresh-binds-and-walks"
(let
((s (first (stream-take 5 ((call-fresh (fn (x) (== x 99))) empty-s)))))
(first (vals s)))
99)
(mk-test
"call-fresh-distinct-from-outer-vars"
(let
((q (mk-var "q")))
(let
((g (call-fresh (fn (x) (mk-conj (== x 5) (== q (list x x)))))))
(mk-walk* q (first (stream-take 5 (g empty-s))))))
(list 5 5))
(mk-tests-run!)

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;; lib/minikanren/tests/goals.sx — Phase 2 tests for stream.sx + goals.sx.
;;
;; Streams use a tagged shape internally (`(:s head tail)`) so that mature
;; cells can have thunk tails — SX has no improper pairs. Test assertions
;; therefore stream-take into a plain SX list, or check goal effects via
;; mk-walk on the resulting subst, instead of inspecting raw streams.
;; --- stream-take base cases (input streams use s-cons / mzero) ---
(mk-test
"stream-take-zero-from-mature"
(stream-take 0 (s-cons (empty-subst) mzero))
(list))
(mk-test "stream-take-from-mzero" (stream-take 5 mzero) (list))
(mk-test
"stream-take-mature-pair"
(stream-take 5 (s-cons :a (s-cons :b mzero)))
(list :a :b))
(mk-test
"stream-take-fewer-than-available"
(stream-take 1 (s-cons :a (s-cons :b mzero)))
(list :a))
(mk-test
"stream-take-all-with-neg-1"
(stream-take -1 (s-cons :a (s-cons :b (s-cons :c mzero))))
(list :a :b :c))
;; --- stream-take forces immature thunks ---
(mk-test
"stream-take-forces-thunk"
(stream-take 5 (fn () (s-cons :x mzero)))
(list :x))
(mk-test
"stream-take-forces-nested-thunks"
(stream-take 5 (fn () (fn () (s-cons :y mzero))))
(list :y))
;; --- mk-mplus interleaves ---
(mk-test
"mplus-empty-left"
(stream-take 5 (mk-mplus mzero (s-cons :r mzero)))
(list :r))
(mk-test
"mplus-empty-right"
(stream-take 5 (mk-mplus (s-cons :l mzero) mzero))
(list :l))
(mk-test
"mplus-mature-mature"
(stream-take
5
(mk-mplus (s-cons :a (s-cons :b mzero)) (s-cons :c (s-cons :d mzero))))
(list :a :b :c :d))
(mk-test
"mplus-with-paused-left-swaps"
(stream-take
5
(mk-mplus
(fn () (s-cons :a (s-cons :b mzero)))
(s-cons :c (s-cons :d mzero))))
(list :c :d :a :b))
;; --- mk-bind ---
(mk-test
"bind-empty-stream"
(stream-take 5 (mk-bind mzero (fn (s) (unit s))))
(list))
(mk-test
"bind-singleton-identity"
(stream-take
5
(mk-bind (s-cons 5 mzero) (fn (x) (unit x))))
(list 5))
(mk-test
"bind-flat-multi"
(stream-take
10
(mk-bind
(s-cons 1 (s-cons 2 mzero))
(fn (x) (s-cons x (s-cons (* x 10) mzero)))))
(list 1 10 2 20))
(mk-test
"bind-fail-prunes-some"
(stream-take
10
(mk-bind
(s-cons 1 (s-cons 2 (s-cons 3 mzero)))
(fn (x) (if (= x 2) mzero (unit x)))))
(list 1 3))
;; --- core goals: succeed / fail ---
(mk-test
"succeed-yields-singleton"
(stream-take 5 (succeed empty-s))
(list empty-s))
(mk-test "fail-yields-mzero" (stream-take 5 (fail empty-s)) (list))
;; --- == ---
(mk-test
"eq-ground-success"
(stream-take 5 ((== 1 1) empty-s))
(list empty-s))
(mk-test
"eq-ground-failure"
(stream-take 5 ((== 1 2) empty-s))
(list))
(mk-test
"eq-binds-var"
(let
((x (mk-var "x")))
(mk-walk
x
(first (stream-take 5 ((== x 7) empty-s)))))
7)
(mk-test
"eq-list-success"
(let
((x (mk-var "x")))
(mk-walk
x
(first
(stream-take
5
((== x (list 1 2)) empty-s)))))
(list 1 2))
(mk-test
"eq-list-mismatch-fails"
(stream-take
5
((== (list 1 2) (list 1 3)) empty-s))
(list))
;; --- conj2 / mk-conj ---
(mk-test
"conj2-both-bind"
(let
((x (mk-var "x")) (y (mk-var "y")))
(let
((s (first (stream-take 5 ((conj2 (== x 1) (== y 2)) empty-s)))))
(list (mk-walk x s) (mk-walk y s))))
(list 1 2))
(mk-test
"conj2-conflict-empty"
(let
((x (mk-var "x")))
(stream-take
5
((conj2 (== x 1) (== x 2)) empty-s)))
(list))
(mk-test
"conj-empty-is-succeed"
(stream-take 5 ((mk-conj) empty-s))
(list empty-s))
(mk-test
"conj-single-is-goal"
(let
((x (mk-var "x")))
(mk-walk
x
(first
(stream-take 5 ((mk-conj (== x 99)) empty-s)))))
99)
(mk-test
"conj-three-bindings"
(let
((x (mk-var "x")) (y (mk-var "y")) (z (mk-var "z")))
(let
((s (first (stream-take 5 ((mk-conj (== x 1) (== y 2) (== z 3)) empty-s)))))
(list (mk-walk x s) (mk-walk y s) (mk-walk z s))))
(list 1 2 3))
;; --- disj2 / mk-disj ---
(mk-test
"disj2-both-succeed"
(let
((q (mk-var "q")))
(let
((res (stream-take 5 ((disj2 (== q 1) (== q 2)) empty-s))))
(map (fn (s) (mk-walk q s)) res)))
(list 1 2))
(mk-test
"disj2-fail-or-succeed"
(let
((q (mk-var "q")))
(let
((res (stream-take 5 ((disj2 fail (== q 5)) empty-s))))
(map (fn (s) (mk-walk q s)) res)))
(list 5))
(mk-test
"disj-empty-is-fail"
(stream-take 5 ((mk-disj) empty-s))
(list))
(mk-test
"disj-three-clauses"
(let
((q (mk-var "q")))
(let
((res (stream-take 5 ((mk-disj (== q "a") (== q "b") (== q "c")) empty-s))))
(map (fn (s) (mk-walk q s)) res)))
(list "a" "b" "c"))
;; --- conj/disj nesting ---
(mk-test
"disj-of-conj"
(let
((x (mk-var "x")) (y (mk-var "y")))
(let
((res (stream-take 5 ((mk-disj (mk-conj (== x 1) (== y 2)) (mk-conj (== x 3) (== y 4))) empty-s))))
(map (fn (s) (list (mk-walk x s) (mk-walk y s))) res)))
(list (list 1 2) (list 3 4)))
;; --- ==-check ---
(mk-test
"eq-check-no-occurs-fails"
(let
((x (mk-var "x")))
(stream-take 5 ((==-check x (list 1 x)) empty-s)))
(list))
(mk-test
"eq-check-no-occurs-non-occurring-succeeds"
(let
((x (mk-var "x")))
(mk-walk
x
(first (stream-take 5 ((==-check x 5) empty-s)))))
5)
(mk-tests-run!)

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;; lib/minikanren/tests/graph.sx — directed-graph reachability via patho.
(define
test-edges
(list (list :a :b) (list :b :c) (list :c :d) (list :a :c) (list :d :e)))
(define edgeo (fn (from to) (membero (list from to) test-edges)))
(define
patho
(fn
(x y path)
(conde
((edgeo x y) (== path (list x y)))
((fresh (z mid-path) (edgeo x z) (patho z y mid-path) (conso x mid-path path))))))
;; --- direct edges ---
(mk-test "patho-direct" (run* q (patho :a :b q)) (list (list :a :b)))
(mk-test "patho-no-direct-edge" (run* q (patho :e :a q)) (list))
;; --- indirect ---
(mk-test
"patho-multi-hop"
(let
((paths (run* q (patho :a :d q))))
(and
(= (len paths) 2)
(and
(some (fn (p) (= p (list :a :b :c :d))) paths)
(some (fn (p) (= p (list :a :c :d))) paths))))
true)
(mk-test
"patho-to-leaf"
(let
((paths (run* q (patho :a :e q))))
(and
(= (len paths) 2)
(and
(some (fn (p) (= p (list :a :b :c :d :e))) paths)
(some (fn (p) (= p (list :a :c :d :e))) paths))))
true)
;; --- enumeration with multiplicity ---
;; Each path contributes one tuple, so reachable nodes can repeat. Here
;; targets are: b (1 path), c (2 paths), d (2 paths), e (2 paths) = 7.
(mk-test
"patho-enumerate-from-a-with-multiplicity"
(let
((targets (run* q (fresh (path) (patho :a q path)))))
(and
(= (len targets) 7)
(and
(some (fn (t) (= t :b)) targets)
(and
(some (fn (t) (= t :c)) targets)
(and
(some (fn (t) (= t :d)) targets)
(some (fn (t) (= t :e)) targets))))))
true)
;; --- unreachable target ---
(mk-test "patho-unreachable" (run* q (patho :a :z q)) (list))
(mk-tests-run!)

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;; lib/minikanren/tests/intarith.sx — ground-only integer arithmetic
;; goals that escape into host operations via project.
;; --- pluso-i ---
(mk-test
"pluso-i-forward"
(run* q (pluso-i 7 8 q))
(list 15))
(mk-test
"pluso-i-zero"
(run* q (pluso-i 0 0 q))
(list 0))
(mk-test
"pluso-i-negatives"
(run* q (pluso-i -5 3 q))
(list -2))
(mk-test
"pluso-i-non-ground-fails"
(run* q (fresh (a) (pluso-i a 3 5)))
(list))
;; --- minuso-i ---
(mk-test
"minuso-i-forward"
(run* q (minuso-i 10 4 q))
(list 6))
(mk-test
"minuso-i-zero"
(run* q (minuso-i 5 5 q))
(list 0))
;; --- *o-i ---
(mk-test
"times-i-forward"
(run* q (*o-i 6 7 q))
(list 42))
(mk-test
"times-i-by-zero"
(run* q (*o-i 0 99 q))
(list 0))
(mk-test
"times-i-by-one"
(run* q (*o-i 1 17 q))
(list 17))
;; --- comparisons ---
(mk-test
"lto-i-true"
(run 1 q (lto-i 2 5))
(list (make-symbol "_.0")))
(mk-test "lto-i-false" (run* q (lto-i 5 2)) (list))
(mk-test "lto-i-equal-false" (run* q (lto-i 3 3)) (list))
(mk-test
"lteo-i-equal"
(run 1 q (lteo-i 4 4))
(list (make-symbol "_.0")))
(mk-test
"lteo-i-less"
(run 1 q (lteo-i 1 4))
(list (make-symbol "_.0")))
(mk-test "lteo-i-more" (run* q (lteo-i 9 4)) (list))
(mk-test
"neqo-i-different"
(run 1 q (neqo-i 3 5))
(list (make-symbol "_.0")))
(mk-test "neqo-i-same" (run* q (neqo-i 3 3)) (list))
;; --- composition with relational vars ---
(mk-test
"intarith-with-membero"
(run*
q
(fresh
(x)
(membero
x
(list 1 2 3 4 5))
(lto-i x 3)
(== q x)))
(list 1 2))
(mk-test "even-i-pos" (run* q (even-i 4)) (list (make-symbol "_.0")))
(mk-test "even-i-neg" (run* q (even-i 5)) (list))
(mk-test "odd-i-pos" (run* q (odd-i 7)) (list (make-symbol "_.0")))
(mk-test "odd-i-neg" (run* q (odd-i 4)) (list))
(mk-test
"even-i-filter"
(run* q (fresh (x) (membero x (list 1 2 3 4 5 6)) (even-i x) (== q x)))
(list 2 4 6))
(mk-tests-run!)

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;; lib/minikanren/tests/iterate-no.sx — iterated relation application.
(define
mk-nat
(fn (n) (if (= n 0) :z (list :s (mk-nat (- n 1))))))
(mk-test
"iterate-no-zero"
(run*
q
(iterate-no
(fn (a b) (== b (list :wrap a)))
(mk-nat 0)
:seed q))
(list :seed))
(mk-test
"iterate-no-three-wraps"
(run*
q
(iterate-no (fn (a b) (== b (list :wrap a))) (mk-nat 3) :x q))
(list (list :wrap (list :wrap (list :wrap :x)))))
(mk-test
"iterate-no-succ-three-times"
(run*
q
(iterate-no (fn (a b) (== b (list :s a))) (mk-nat 3) :z q))
(list (mk-nat 3)))
(mk-test
"iterate-no-with-list-cons"
(run*
q
(iterate-no (fn (a b) (conso :a a b)) (mk-nat 4) (list) q))
(list (list :a :a :a :a)))
(mk-tests-run!)

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;; lib/minikanren/tests/lasto.sx — last-element + init-without-last.
(mk-test
"lasto-singleton"
(run* q (lasto (list 5) q))
(list 5))
(mk-test
"lasto-multi"
(run* q (lasto (list 1 2 3 4) q))
(list 4))
(mk-test "lasto-empty" (run* q (lasto (list) q)) (list))
(mk-test "lasto-strings" (run* q (lasto (list "a" "b" "c") q)) (list "c"))
(mk-test
"init-o-multi"
(run* q (init-o (list 1 2 3 4) q))
(list (list 1 2 3)))
(mk-test
"init-o-singleton"
(run* q (init-o (list 7) q))
(list (list)))
(mk-test "init-o-empty" (run* q (init-o (list) q)) (list))
(mk-test
"lasto-init-o-roundtrip"
(run*
q
(fresh
(init last)
(lasto (list 1 2 3 4) last)
(init-o (list 1 2 3 4) init)
(appendo init (list last) q)))
(list (list 1 2 3 4)))
(mk-tests-run!)

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;; lib/minikanren/tests/latin.sx — 2x2 Latin square via ino + all-distincto.
;;
;; A 2x2 Latin square has 2 distinct fillings:
;; ((1 2) (2 1)) and ((2 1) (1 2)).
;; The 3x3 version has 12 fillings but takes minutes under naive search;
;; full CLP(FD) (Phase 6 proper) would handle it in milliseconds.
(define
latin-2x2
(fn
(cells)
(let
((c11 (nth cells 0))
(c12 (nth cells 1))
(c21 (nth cells 2))
(c22 (nth cells 3))
(dom (list 1 2)))
(mk-conj
(ino c11 dom)
(ino c12 dom)
(ino c21 dom)
(ino c22 dom)
(all-distincto (list c11 c12))
(all-distincto (list c21 c22))
(all-distincto (list c11 c21))
(all-distincto (list c12 c22)))))) ;; col 2
(mk-test
"latin-2x2-count"
(let
((squares (run* q (fresh (a b c d) (== q (list a b c d)) (latin-2x2 (list a b c d))))))
(len squares))
2)
(mk-test
"latin-2x2-as-set"
(let
((squares (run* q (fresh (a b c d) (== q (list a b c d)) (latin-2x2 (list a b c d))))))
(and
(= (len squares) 2)
(and
(some
(fn (s) (= s (list 1 2 2 1)))
squares)
(some
(fn (s) (= s (list 2 1 1 2)))
squares))))
true)
(mk-test
"latin-2x2-with-clue"
(run*
q
(fresh
(a b c d)
(== a 1)
(== q (list a b c d))
(latin-2x2 (list a b c d))))
(list (list 1 2 2 1)))
(mk-tests-run!)

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;; lib/minikanren/tests/laziness.sx — verify Zzz wrapping (in conde)
;; lets infinitely-recursive relations produce finite prefixes via run-n.
;; --- a relation that has no base case but conde-protects via Zzz ---
(define
listo-aux
(fn
(l)
(conde ((nullo l)) ((fresh (a d) (conso a d l) (listo-aux d))))))
(mk-test
"infinite-relation-truncates-via-run-n"
(run 4 q (listo-aux q))
(list
(list)
(list (make-symbol "_.0"))
(list (make-symbol "_.0") (make-symbol "_.1"))
(list (make-symbol "_.0") (make-symbol "_.1") (make-symbol "_.2"))))
;; --- two infinite generators interleaved via mk-disj must both produce
;; answers (no starvation) — the fairness test ---
(define
ones-gen
(fn
(l)
(conde
((== l (list)))
((fresh (d) (conso 1 d l) (ones-gen d))))))
(define
twos-gen
(fn
(l)
(conde
((== l (list)))
((fresh (d) (conso 2 d l) (twos-gen d))))))
(mk-test
"interleaving-keeps-both-streams-alive"
(let
((res (run 4 q (mk-disj (ones-gen q) (twos-gen q)))))
(and
(= (len res) 4)
(and
(some
(fn
(x)
(and
(list? x)
(and (not (empty? x)) (= (first x) 1))))
res)
(some
(fn
(x)
(and
(list? x)
(and (not (empty? x)) (= (first x) 2))))
res))))
true)
;; --- run* terminates on a relation whose conde has finite base case
;; reached from any starting point ---
(mk-test
"run-star-terminates-on-bounded-relation"
(run*
q
(fresh
(l)
(== l (list 1 2 3))
(listo l)
(== q :ok)))
(list :ok))
(mk-tests-run!)

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;; lib/minikanren/tests/lengtho-i.sx — integer-indexed length (fast).
(mk-test "lengtho-i-empty" (run* q (lengtho-i (list) q)) (list 0))
(mk-test
"lengtho-i-singleton"
(run* q (lengtho-i (list :a) q))
(list 1))
(mk-test
"lengtho-i-three"
(run* q (lengtho-i (list 1 2 3) q))
(list 3))
(mk-test
"lengtho-i-five"
(run*
q
(lengtho-i
(list 1 2 3 4 5)
q))
(list 5))
(mk-test
"lengtho-i-mixed-types"
(run*
q
(lengtho-i (list 1 "two" :three (list 4 5)) q))
(list 4))
(mk-tests-run!)

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;; lib/minikanren/tests/list-relations.sx — rembero, assoco, nth-o, samelengtho.
;; --- rembero (remove first occurrence) ---
(mk-test
"rembero-element-present"
(run*
q
(rembero 2 (list 1 2 3 2) q))
(list (list 1 3 2)))
(mk-test
"rembero-element-not-present"
(run* q (rembero 99 (list 1 2 3) q))
(list (list 1 2 3)))
(mk-test
"rembero-empty"
(run* q (rembero 1 (list) q))
(list (list)))
(mk-test
"rembero-only-element"
(run* q (rembero 5 (list 5) q))
(list (list)))
(mk-test
"rembero-first-of-many"
(run*
q
(rembero 1 (list 1 2 3 4) q))
(list (list 2 3 4)))
;; --- assoco (alist lookup) ---
(define
test-pairs
(list
(list "alice" 30)
(list "bob" 25)
(list "carol" 35)))
(mk-test
"assoco-found"
(run* q (assoco "bob" test-pairs q))
(list 25))
(mk-test
"assoco-first"
(run* q (assoco "alice" test-pairs q))
(list 30))
(mk-test "assoco-missing" (run* q (assoco "dave" test-pairs q)) (list))
(mk-test
"assoco-find-keys-with-value"
(run* q (assoco q test-pairs 25))
(list "bob"))
;; --- nth-o (Peano-indexed access) ---
(mk-test
"nth-o-zero"
(run* q (nth-o :z (list 10 20 30) q))
(list 10))
(mk-test
"nth-o-one"
(run* q (nth-o (list :s :z) (list 10 20 30) q))
(list 20))
(mk-test
"nth-o-two"
(run*
q
(nth-o (list :s (list :s :z)) (list 10 20 30) q))
(list 30))
(mk-test
"nth-o-out-of-range"
(run*
q
(nth-o
(list :s (list :s (list :s :z)))
(list 10 20 30)
q))
(list))
;; --- samelengtho ---
(mk-test
"samelengtho-equal"
(run*
q
(samelengtho (list 1 2 3) (list :a :b :c)))
(list (make-symbol "_.0")))
(mk-test
"samelengtho-different-fails"
(run* q (samelengtho (list 1 2) (list :a :b :c)))
(list))
(mk-test
"samelengtho-empty-equal"
(run* q (samelengtho (list) (list)))
(list (make-symbol "_.0")))
(mk-test
"samelengtho-builds-vars"
(run 1 q (samelengtho (list 1 2 3) q))
(list (list (make-symbol "_.0") (make-symbol "_.1") (make-symbol "_.2"))))
(mk-test
"samelengtho-enumerates-pairs"
(run
3
q
(fresh (l1 l2) (samelengtho l1 l2) (== q (list l1 l2))))
(list
(list (list) (list))
(list (list (make-symbol "_.0")) (list (make-symbol "_.1")))
(list
(list (make-symbol "_.0") (make-symbol "_.1"))
(list (make-symbol "_.2") (make-symbol "_.3")))))
(mk-tests-run!)

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;; lib/minikanren/tests/mapo.sx — relational map.
(mk-test
"mapo-identity"
(run*
q
(mapo (fn (a b) (== a b)) (list 1 2 3) q))
(list (list 1 2 3)))
(mk-test
"mapo-tag-each"
(run*
q
(mapo
(fn (a b) (== b (list :tag a)))
(list 1 2 3)
q))
(list
(list
(list :tag 1)
(list :tag 2)
(list :tag 3))))
(mk-test
"mapo-backward"
(run*
q
(mapo (fn (a b) (== a b)) q (list 1 2 3)))
(list (list 1 2 3)))
(mk-test
"mapo-empty"
(run* q (mapo (fn (a b) (== a b)) (list) q))
(list (list)))
(mk-test
"mapo-duplicate"
(run* q (mapo (fn (a b) (== b (list a a))) (list :x :y) q))
(list (list (list :x :x) (list :y :y))))
(mk-test
"mapo-different-length-fails"
(run*
q
(mapo
(fn (a b) (== a b))
(list 1 2)
(list 1 2 3)))
(list))
;; mapo + arithmetic via intarith
(mk-test
"mapo-square-each"
(run*
q
(mapo
(fn (a b) (*o-i a a b))
(list 1 2 3 4)
q))
(list (list 1 4 9 16)))
(mk-tests-run!)

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;; lib/minikanren/tests/matche.sx — Phase 5 piece D tests for `matche`.
;; --- literal patterns ---
(mk-test
"matche-literal-number"
(run* q (matche q (1 (== q 1))))
(list 1))
(mk-test
"matche-literal-string"
(run* q (matche q ("hello" (== q "hello"))))
(list "hello"))
(mk-test
"matche-literal-no-clause-matches"
(run*
q
(matche 7 (1 (== q :a)) (2 (== q :b))))
(list))
;; --- variable patterns ---
(mk-test
"matche-symbol-pattern"
(run* q (fresh (x) (== x 99) (matche x (a (== q a)))))
(list 99))
(mk-test
"matche-wildcard"
(run* q (fresh (x) (== x 7) (matche x (_ (== q :any)))))
(list :any))
;; --- list patterns ---
(mk-test
"matche-empty-list"
(run* q (matche (list) (() (== q :ok))))
(list :ok))
(mk-test
"matche-pair-binds"
(run*
q
(fresh
(x)
(== x (list 1 2))
(matche x ((a b) (== q (list b a))))))
(list (list 2 1)))
(mk-test
"matche-triple-binds"
(run*
q
(fresh
(x)
(== x (list 1 2 3))
(matche x ((a b c) (== q (list :sum a b c))))))
(list (list :sum 1 2 3)))
(mk-test
"matche-mixed-literal-and-var"
(run*
q
(fresh
(x)
(== x (list 1 99 3))
(matche x ((1 m 3) (== q m)))))
(list 99))
;; --- multi-clause dispatch ---
(mk-test
"matche-multi-clause-shape"
(run*
q
(fresh
(x)
(== x (list 5 6))
(matche
x
(() (== q :empty))
((a) (== q (list :one a)))
((a b) (== q (list :two a b))))))
(list (list :two 5 6)))
(mk-test
"matche-three-shapes-via-fresh"
(run*
q
(fresh
(x)
(matche
x
(() (== q :empty))
((a) (== q (list :one a)))
((a b) (== q (list :two a b))))))
(list
:empty (list :one (make-symbol "_.0"))
(list :two (make-symbol "_.0") (make-symbol "_.1"))))
;; --- nested patterns ---
(mk-test
"matche-nested"
(run*
q
(fresh
(x)
(==
x
(list (list 1 2) (list 3 4)))
(matche x (((a b) (c d)) (== q (list a b c d))))))
(list (list 1 2 3 4)))
;; --- repeated var names create the same fresh var → must unify ---
(mk-test
"matche-repeated-var-implies-equality"
(run*
q
(fresh
(x)
(== x (list 7 7))
(matche x ((a a) (== q a)))))
(list 7))
(mk-test
"matche-repeated-var-mismatch-fails"
(run*
q
(fresh
(x)
(== x (list 7 8))
(matche x ((a a) (== q a)))))
(list))
(mk-tests-run!)

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;; lib/minikanren/tests/minmax.sx — mino + maxo via intarith.
(mk-test
"mino-singleton"
(run* q (mino (list 7) q))
(list 7))
(mk-test
"mino-of-3"
(run* q (mino (list 5 1 3) q))
(list 1))
(mk-test
"mino-of-5"
(run*
q
(mino (list 5 1 3 2 4) q))
(list 1))
(mk-test
"mino-with-dups"
(run* q (mino (list 3 3 3) q))
(list 3))
(mk-test "mino-empty-fails" (run* q (mino (list) q)) (list))
(mk-test
"maxo-singleton"
(run* q (maxo (list 7) q))
(list 7))
(mk-test
"maxo-of-5"
(run*
q
(maxo (list 5 1 3 2 4) q))
(list 5))
(mk-test
"maxo-of-negs"
(run* q (maxo (list -5 -1 -3) q))
(list -1))
(mk-test
"min-and-max-of-list"
(run*
q
(fresh
(mn mx)
(mino (list 5 1 3 2 4) mn)
(maxo (list 5 1 3 2 4) mx)
(== q (list mn mx))))
(list (list 1 5)))
(mk-tests-run!)

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;; lib/minikanren/tests/nafc.sx — Phase 5 piece C tests for `nafc`.
(mk-test
"nafc-failed-goal-succeeds"
(run* q (nafc (== 1 2)))
(list (make-symbol "_.0")))
(mk-test
"nafc-successful-goal-fails"
(run* q (nafc (== 1 1)))
(list))
(mk-test
"nafc-double-negation"
(run* q (nafc (nafc (== 1 1))))
(list (make-symbol "_.0")))
(mk-test
"nafc-with-conde-no-clauses-succeed"
(run*
q
(nafc
(conde ((== 1 2)) ((== 3 4)))))
(list (make-symbol "_.0")))
(mk-test
"nafc-with-conde-some-clause-succeeds-fails"
(run*
q
(nafc
(conde ((== 1 1)) ((== 3 4)))))
(list))
;; --- composing nafc with == as a guard ---
(mk-test
"nafc-as-guard"
(run*
q
(fresh (x) (== x 5) (nafc (== x 99)) (== q x)))
(list 5))
(mk-test
"nafc-guard-blocking"
(run*
q
(fresh (x) (== x 5) (nafc (== x 5)) (== q x)))
(list))
(mk-tests-run!)

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;; lib/minikanren/tests/not-membero.sx — relational "not in list".
(mk-test
"not-membero-absent"
(run* q (not-membero 99 (list 1 2 3)))
(list (make-symbol "_.0")))
(mk-test
"not-membero-present"
(run* q (not-membero 2 (list 1 2 3)))
(list))
(mk-test
"not-membero-empty"
(run* q (not-membero 1 (list)))
(list (make-symbol "_.0")))
(mk-test
"not-membero-as-filter"
(run*
q
(fresh
(x)
(membero
x
(list 1 2 3 4 5))
(not-membero x (list 2 4))
(== q x)))
(list 1 3 5))
(mk-tests-run!)

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;; lib/minikanren/tests/nub-o.sx — relational dedupe (keep last occurrence).
(mk-test "nub-o-empty" (run* q (nub-o (list) q)) (list (list)))
(mk-test
"nub-o-no-duplicates"
(run* q (nub-o (list 1 2 3) q))
(list (list 1 2 3)))
(mk-test
"nub-o-with-duplicates"
(run*
q
(nub-o
(list 1 2 1 3 2 4)
q))
(list (list 1 3 2 4)))
(mk-test
"nub-o-all-same"
(let
((res (run* q (nub-o (list 1 1 1) q))))
(every? (fn (r) (= r (list 1))) res))
true)
(mk-test
"nub-o-keeps-last"
(run* q (nub-o (list 1 2 1) q))
(list (list 2 1)))
(mk-tests-run!)

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;; lib/minikanren/tests/pairlisto.sx — zip two lists into pair list.
(mk-test
"pairlisto-empty"
(run* q (pairlisto (list) (list) q))
(list (list)))
(mk-test
"pairlisto-equal-lengths"
(run*
q
(pairlisto (list 1 2 3) (list :a :b :c) q))
(list
(list (list 1 :a) (list 2 :b) (list 3 :c))))
(mk-test
"pairlisto-recover-l1"
(run*
q
(pairlisto
q
(list :a :b :c)
(list (list 10 :a) (list 20 :b) (list 30 :c))))
(list (list 10 20 30)))
(mk-test
"pairlisto-recover-l2"
(run*
q
(pairlisto
(list 1 2 3)
q
(list (list 1 :x) (list 2 :y) (list 3 :z))))
(list (list :x :y :z)))
(mk-test
"pairlisto-different-lengths-fails"
(run* q (pairlisto (list 1 2) (list :a :b :c) q))
(list))
(mk-tests-run!)

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;; lib/minikanren/tests/palindromeo.sx — palindromic list relation.
(mk-test
"palindromeo-empty"
(run* q (palindromeo (list)))
(list (make-symbol "_.0")))
(mk-test
"palindromeo-singleton"
(run* q (palindromeo (list :a)))
(list (make-symbol "_.0")))
(mk-test
"palindromeo-pair-equal"
(run* q (palindromeo (list 1 1)))
(list (make-symbol "_.0")))
(mk-test
"palindromeo-pair-unequal-fails"
(run* q (palindromeo (list 1 2)))
(list))
(mk-test
"palindromeo-five-yes"
(run*
q
(palindromeo
(list 1 2 3 2 1)))
(list (make-symbol "_.0")))
(mk-test
"palindromeo-five-no"
(run*
q
(palindromeo
(list 1 2 3 4 5)))
(list))
(mk-test
"palindromeo-strings"
(run* q (palindromeo (list "a" "b" "a")))
(list (make-symbol "_.0")))
(mk-tests-run!)

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;; lib/minikanren/tests/parity.sx — eveno + oddo Peano predicates.
(define
mk-nat
(fn (n) (if (= n 0) :z (list :s (mk-nat (- n 1))))))
(mk-test "eveno-zero" (run* q (eveno :z)) (list (make-symbol "_.0")))
(mk-test
"eveno-2"
(run* q (eveno (mk-nat 2)))
(list (make-symbol "_.0")))
(mk-test
"eveno-4"
(run* q (eveno (mk-nat 4)))
(list (make-symbol "_.0")))
(mk-test "eveno-1-fails" (run* q (eveno (mk-nat 1))) (list))
(mk-test "eveno-3-fails" (run* q (eveno (mk-nat 3))) (list))
(mk-test
"oddo-1"
(run* q (oddo (mk-nat 1)))
(list (make-symbol "_.0")))
(mk-test
"oddo-3"
(run* q (oddo (mk-nat 3)))
(list (make-symbol "_.0")))
(mk-test "oddo-zero-fails" (run* q (oddo :z)) (list))
(mk-test "oddo-2-fails" (run* q (oddo (mk-nat 2))) (list))
;; Enumerate small evens.
(mk-test
"eveno-enumerates"
(run 4 q (eveno q))
(list
(mk-nat 0)
(mk-nat 2)
(mk-nat 4)
(mk-nat 6)))
;; Enumerate small odds.
(mk-test
"oddo-enumerates"
(run 4 q (oddo q))
(list
(mk-nat 1)
(mk-nat 3)
(mk-nat 5)
(mk-nat 7)))
;; A number is even XOR odd (no overlap).
(mk-test
"even-odd-no-overlap"
(run*
q
(mk-conj (eveno (mk-nat 4)) (oddo (mk-nat 4))))
(list))
(mk-tests-run!)

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;; lib/minikanren/tests/partitiono.sx — partition list by predicate.
(mk-test
"partitiono-empty"
(run*
q
(fresh
(yes no)
(partitiono (fn (x) (== x 1)) (list) yes no)
(== q (list yes no))))
(list (list (list) (list))))
(mk-test
"partitiono-by-equality"
(run*
q
(fresh
(yes no)
(partitiono
(fn (x) (== x 2))
(list 1 2 3 2 4)
yes
no)
(== q (list yes no))))
(list
(list
(list 2 2)
(list 1 3 4))))
(mk-test
"partitiono-by-numeric-pred"
(run*
q
(fresh
(yes no)
(partitiono
(fn (x) (lto-i x 5))
(list 1 7 2 8 3)
yes
no)
(== q (list yes no))))
(list
(list
(list 1 2 3)
(list 7 8))))
(mk-test
"partitiono-all-yes"
(run*
q
(fresh
(yes no)
(partitiono
(fn (x) (lto-i x 100))
(list 1 2 3)
yes
no)
(== q (list yes no))))
(list (list (list 1 2 3) (list))))
(mk-test
"partitiono-all-no"
(run*
q
(fresh
(yes no)
(partitiono
(fn (x) (lto-i 100 x))
(list 1 2 3)
yes
no)
(== q (list yes no))))
(list (list (list) (list 1 2 3))))
(mk-tests-run!)

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;; lib/minikanren/tests/path-cycle-free.sx — cycle-free reachability search.
;;
;; Threads a "visited" accumulator through the recursion, using nafc +
;; membero to prevent revisiting nodes. Demonstrates how to make the
;; cyclic-graph divergence problem (see tests/cyclic-graph.sx) tractable
;; for graphs with cycles, without invoking Phase-7 tabling.
(define
cf-edges
(list (list :a :b) (list :b :a) (list :b :c) (list :c :d) (list :d :a))) ; another cycle
(define cf-edgeo (fn (from to) (membero (list from to) cf-edges)))
(define
patho-no-cycles
(fn
(x y visited path)
(conde
((cf-edgeo x y) (nafc (membero y visited)) (== path (list x y)))
((fresh (z mid v-prime) (cf-edgeo x z) (nafc (membero z visited)) (conso z visited v-prime) (patho-no-cycles z y v-prime mid) (conso x mid path))))))
(define cf-patho (fn (x y path) (patho-no-cycles x y (list x) path)))
(mk-test
"cycle-free-finds-finitely"
(let
((paths (run* q (cf-patho :a :d q))))
(and
(>= (len paths) 1)
(every? (fn (p) (and (= (first p) :a) (= (last p) :d))) paths)))
true)
(mk-test
"cycle-free-direct-edge"
(run* q (cf-patho :a :b q))
(list (list :a :b)))
(mk-test "cycle-free-no-self-loop" (run* q (cf-patho :a :a q)) (list))
(mk-tests-run!)

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;; lib/minikanren/tests/peano.sx — Peano arithmetic.
;;
;; Builds Peano numbers via a host-side helper so tests stay readable.
;; (mk-nat 3) → (:s (:s (:s :z))).
(define
mk-nat
(fn (n) (if (= n 0) :z (list :s (mk-nat (- n 1))))))
;; --- zeroo ---
(mk-test
"zeroo-zero-succeeds"
(run* q (zeroo :z))
(list (make-symbol "_.0")))
(mk-test
"zeroo-non-zero-fails"
(run* q (zeroo (mk-nat 1)))
(list))
;; --- pluso forward ---
(mk-test
"pluso-forward-2-3"
(run* q (pluso (mk-nat 2) (mk-nat 3) q))
(list (mk-nat 5)))
(mk-test "pluso-forward-zero-zero" (run* q (pluso :z :z q)) (list :z))
(mk-test
"pluso-forward-zero-n"
(run* q (pluso :z (mk-nat 4) q))
(list (mk-nat 4)))
(mk-test
"pluso-forward-n-zero"
(run* q (pluso (mk-nat 4) :z q))
(list (mk-nat 4)))
;; --- pluso backward ---
(mk-test
"pluso-recover-augend"
(run* q (pluso q (mk-nat 2) (mk-nat 5)))
(list (mk-nat 3)))
(mk-test
"pluso-recover-addend"
(run* q (pluso (mk-nat 2) q (mk-nat 5)))
(list (mk-nat 3)))
(mk-test
"pluso-enumerate-pairs-summing-to-3"
(run*
q
(fresh (a b) (pluso a b (mk-nat 3)) (== q (list a b))))
(list
(list :z (mk-nat 3))
(list (mk-nat 1) (mk-nat 2))
(list (mk-nat 2) (mk-nat 1))
(list (mk-nat 3) :z)))
;; --- minuso ---
(mk-test
"minuso-5-2-3"
(run* q (minuso (mk-nat 5) (mk-nat 2) q))
(list (mk-nat 3)))
(mk-test
"minuso-n-n-zero"
(run* q (minuso (mk-nat 7) (mk-nat 7) q))
(list :z))
;; --- *o ---
(mk-test
"times-2-3"
(run* q (*o (mk-nat 2) (mk-nat 3) q))
(list (mk-nat 6)))
(mk-test
"times-zero-anything-zero"
(run* q (*o :z (mk-nat 99) q))
(list :z))
(mk-test
"times-3-4"
(run* q (*o (mk-nat 3) (mk-nat 4) q))
(list (mk-nat 12)))
;; --- lteo / lto ---
(mk-test
"lteo-success"
(run 1 q (lteo (mk-nat 2) (mk-nat 5)))
(list (make-symbol "_.0")))
(mk-test
"lteo-equal-success"
(run 1 q (lteo (mk-nat 3) (mk-nat 3)))
(list (make-symbol "_.0")))
(mk-test
"lteo-greater-fails"
(run* q (lteo (mk-nat 5) (mk-nat 2)))
(list))
(mk-test
"lto-strict-success"
(run 1 q (lto (mk-nat 2) (mk-nat 5)))
(list (make-symbol "_.0")))
(mk-test
"lto-equal-fails"
(run* q (lto (mk-nat 3) (mk-nat 3)))
(list))
(mk-tests-run!)

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;; lib/minikanren/tests/predicates.sx — everyo, someo.
;; --- everyo ---
(mk-test
"everyo-empty-trivially-true"
(run* q (everyo (fn (x) (== x 1)) (list)))
(list (make-symbol "_.0")))
(mk-test
"everyo-all-match"
(run*
q
(everyo
(fn (x) (== x 1))
(list 1 1 1)))
(list (make-symbol "_.0")))
(mk-test
"everyo-some-mismatch"
(run*
q
(everyo
(fn (x) (== x 1))
(list 1 2 1)))
(list))
(mk-test
"everyo-with-intarith"
(run*
q
(everyo
(fn (x) (lto-i x 10))
(list 1 5 9)))
(list (make-symbol "_.0")))
(mk-test
"everyo-with-intarith-fail"
(run*
q
(everyo
(fn (x) (lto-i x 5))
(list 1 5 9)))
(list))
;; --- someo ---
(mk-test
"someo-finds-element"
(run*
q
(someo
(fn (x) (== x 2))
(list 1 2 3)))
(list (make-symbol "_.0")))
(mk-test
"someo-not-found"
(run*
q
(someo
(fn (x) (== x 99))
(list 1 2 3)))
(list))
(mk-test
"someo-empty-fails"
(run* q (someo (fn (x) (== x 1)) (list)))
(list))
(mk-test
"someo-multiple-matches-yields-multiple"
(let
((res (run* q (fresh (x) (someo (fn (y) (== y x)) (list 1 2 1)) (== q x)))))
(len res))
3)
(mk-test
"someo-with-intarith"
(run*
q
(someo
(fn (x) (lto-i 100 x))
(list 5 50 200)))
(list (make-symbol "_.0")))
(mk-tests-run!)

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;; lib/minikanren/tests/prefix-suffix.sx — appendo-derived sublist relations.
(mk-test
"prefixo-empty"
(run* q (prefixo (list) (list 1 2 3)))
(list (make-symbol "_.0")))
(mk-test
"prefixo-full"
(run*
q
(prefixo
(list 1 2 3)
(list 1 2 3)))
(list (make-symbol "_.0")))
(mk-test
"prefixo-partial"
(run*
q
(prefixo
(list 1 2)
(list 1 2 3 4)))
(list (make-symbol "_.0")))
(mk-test
"prefixo-mismatch-fails"
(run*
q
(prefixo
(list 1 3)
(list 1 2 3)))
(list))
(mk-test
"prefixo-enumerates-all"
(run* q (prefixo q (list 1 2 3)))
(list
(list)
(list 1)
(list 1 2)
(list 1 2 3)))
(mk-test
"suffixo-empty"
(run* q (suffixo (list) (list 1 2 3)))
(list (make-symbol "_.0")))
(mk-test
"suffixo-full"
(run*
q
(suffixo
(list 1 2 3)
(list 1 2 3)))
(list (make-symbol "_.0")))
(mk-test
"suffixo-partial"
(run*
q
(suffixo
(list 2 3)
(list 1 2 3)))
(list (make-symbol "_.0")))
(mk-test
"suffixo-enumerates-all"
(run* q (suffixo q (list 1 2 3)))
(list
(list 1 2 3)
(list 2 3)
(list 3)
(list)))
(mk-tests-run!)

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;; lib/minikanren/tests/project.sx — Phase 5 piece B tests for `project`.
;; --- project rebinds vars to ground values for SX use ---
(mk-test
"project-square-via-host"
(run* q (fresh (n) (== n 5) (project (n) (== q (* n n)))))
(list 25))
(mk-test
"project-multi-vars"
(run*
q
(fresh
(a b)
(== a 3)
(== b 4)
(project (a b) (== q (+ a b)))))
(list 7))
(mk-test
"project-with-string-host-op"
(run* q (fresh (s) (== s "hello") (project (s) (== q (str s "!")))))
(list "hello!"))
;; --- project nested inside conde ---
(mk-test
"project-inside-conde"
(run*
q
(fresh
(n)
(conde ((== n 3)) ((== n 4)))
(project (n) (== q (* n 10)))))
(list 30 40))
;; --- project body can be multiple goals (mk-conj'd) ---
(mk-test
"project-multi-goal-body"
(run*
q
(fresh
(n)
(== n 7)
(project (n) (== q (+ n 1)) (== q (+ n 1)))))
(list 8))
(mk-test
"project-multi-goal-body-conflict"
(run*
q
(fresh
(n)
(== n 7)
(project (n) (== q (+ n 1)) (== q (+ n 2)))))
(list))
(mk-tests-run!)

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;; lib/minikanren/tests/pythag.sx — Pythagorean triple search.
;;
;; Uses ino + intarith goals to find triples (a, b, c) with
;; a, b, c ∈ [1..N], a ≤ b, a² + b² = c². With intarith escapes
;; the search runs at host-arithmetic speed.
(define
digits-1-10
(list
1
2
3
4
5
6
7
8
9
10))
(mk-test
"pythag-triples-1-to-10"
(let
((triples (run* q (fresh (a b c a-sq b-sq sum c-sq) (ino a digits-1-10) (ino b digits-1-10) (ino c digits-1-10) (lteo-i a b) (*o-i a a a-sq) (*o-i b b b-sq) (*o-i c c c-sq) (pluso-i a-sq b-sq sum) (== sum c-sq) (== q (list a b c))))))
(and
(= (len triples) 2)
(and
(some
(fn (t) (= t (list 3 4 5)))
triples)
(some
(fn (t) (= t (list 6 8 10)))
triples))))
true)
(mk-tests-run!)

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;; lib/minikanren/tests/queens-fd.sx — N-queens via CLP(FD).
;;
;; Native FD propagation makes N-queens tractable: 4-queens finds both
;; solutions instantly; 5-queens finds all 10 in seconds. Compare with
;; the naive enumerate-then-filter version in queens.sx, which struggles
;; past N=4.
(define
fd-no-diag
(fn
(ci cj k)
(fresh
(a b)
(fd-plus cj k a)
(fd-plus ci k b)
(fd-neq ci a)
(fd-neq cj b))))
(define
n-queens-4-fd
(fn
(cs)
(let
((c1 (nth cs 0))
(c2 (nth cs 1))
(c3 (nth cs 2))
(c4 (nth cs 3)))
(mk-conj
(fd-in c1 (list 1 2 3 4))
(fd-in c2 (list 1 2 3 4))
(fd-in c3 (list 1 2 3 4))
(fd-in c4 (list 1 2 3 4))
(fd-distinct cs)
(fd-no-diag c1 c2 1)
(fd-no-diag c1 c3 2)
(fd-no-diag c1 c4 3)
(fd-no-diag c2 c3 1)
(fd-no-diag c2 c4 2)
(fd-no-diag c3 c4 1)
(fd-label cs)))))
(define
n-queens-5-fd
(fn
(cs)
(let
((c1 (nth cs 0))
(c2 (nth cs 1))
(c3 (nth cs 2))
(c4 (nth cs 3))
(c5 (nth cs 4)))
(mk-conj
(fd-in
c1
(list 1 2 3 4 5))
(fd-in
c2
(list 1 2 3 4 5))
(fd-in
c3
(list 1 2 3 4 5))
(fd-in
c4
(list 1 2 3 4 5))
(fd-in
c5
(list 1 2 3 4 5))
(fd-distinct cs)
(fd-no-diag c1 c2 1)
(fd-no-diag c1 c3 2)
(fd-no-diag c1 c4 3)
(fd-no-diag c1 c5 4)
(fd-no-diag c2 c3 1)
(fd-no-diag c2 c4 2)
(fd-no-diag c2 c5 3)
(fd-no-diag c3 c4 1)
(fd-no-diag c3 c5 2)
(fd-no-diag c4 c5 1)
(fd-label cs)))))
(mk-test
"n-queens-4-fd-two-solutions"
(run*
q
(fresh (a b c d) (== q (list a b c d)) (n-queens-4-fd (list a b c d))))
(list
(list 2 4 1 3)
(list 3 1 4 2)))
(mk-test
"n-queens-5-fd-ten-solutions"
(let
((sols (run* q (fresh (a b c d e) (== q (list a b c d e)) (n-queens-5-fd (list a b c d e))))))
(= (len sols) 10))
true)
(mk-tests-run!)

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;; lib/minikanren/tests/queens.sx — N-queens, the classic miniKanren benchmark.
;; --- safe-diag (helper) ---
(mk-test
"safe-diag-different-cols-different-distance"
(run* q (safe-diag 1 4 2))
(list (make-symbol "_.0")))
(mk-test
"safe-diag-same-distance-fails"
(run* q (safe-diag 1 4 3))
(list))
(mk-test
"safe-diag-same-distance-other-direction-fails"
(run* q (safe-diag 4 1 3))
(list))
;; --- ino-each / range ---
(mk-test
"range-1-to-4"
(range-1-to-n 4)
(list 1 2 3 4))
(mk-test "range-empty" (range-1-to-n 0) (list))
;; --- 4-queens: two solutions ---
(mk-test
"queens-4"
(let
((sols (run* q (fresh (a b c d) (== q (list a b c d)) (queens-cols (list a b c d) 4)))))
(and
(= (len sols) 2)
(and
(some
(fn (s) (= s (list 2 4 1 3)))
sols)
(some
(fn (s) (= s (list 3 1 4 2)))
sols))))
true)
(mk-tests-run!)

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;; lib/minikanren/tests/rdb.sx — relational database queries.
;;
;; Demonstrates how miniKanren can serve as a Datalog-style query engine
;; over fact tables. Tables are SX lists of tuples; the relation just
;; wraps `membero` over the table.
(define
rdb-employees
(list
(list "alice" "engineering" 100000)
(list "bob" "marketing" 80000)
(list "carol" "engineering" 90000)
(list "dave" "engineering" 85000)
(list "eve" "sales" 75000)))
(define
rdb-projects
(list
(list "alice" "compiler")
(list "carol" "compiler")
(list "dave" "runtime")
(list "alice" "runtime")
(list "eve" "outreach")))
;; Relation views over the tables.
(define
employees
(fn (name dept salary) (membero (list name dept salary) rdb-employees)))
(define
on-project
(fn (name project) (membero (list name project) rdb-projects)))
;; --- queries ---
(mk-test
"rdb-engineering-staff"
(let
((res (run* q (fresh (n s) (employees n "engineering" s) (== q n)))))
(and
(= (len res) 3)
(and
(some (fn (n) (= n "alice")) res)
(and
(some (fn (n) (= n "carol")) res)
(some (fn (n) (= n "dave")) res)))))
true)
(mk-test
"rdb-high-salary"
(let
((res (run* q (fresh (n d s) (employees n d s) (lto-i 85000 s) (== q (list n s))))))
(and
(= (len res) 2)
(and
(some (fn (r) (= r (list "alice" 100000))) res)
(some (fn (r) (= r (list "carol" 90000))) res))))
true)
(mk-test
"rdb-join-employee-project"
(let
((res (run* q (fresh (n d s) (employees n d s) (on-project n "compiler") (== q n)))))
(and
(= (len res) 2)
(and
(some (fn (n) (= n "alice")) res)
(some (fn (n) (= n "carol")) res))))
true)
(mk-test
"rdb-engineers-on-runtime"
(let
((res (run* q (fresh (n s) (employees n "engineering" s) (on-project n "runtime") (== q n)))))
(and
(= (len res) 2)
(and
(some (fn (n) (= n "alice")) res)
(some (fn (n) (= n "dave")) res))))
true)
(mk-test
"rdb-people-on-multiple-projects"
(let
((res (run* q (fresh (n p1 p2) (on-project n p1) (on-project n p2) (nafc (== p1 p2)) (== q n)))))
(some (fn (n) (= n "alice")) res))
true)
(mk-tests-run!)

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;; lib/minikanren/tests/relations.sx — Phase 4 standard relations.
;;
;; Includes the classic miniKanren canaries: appendo forwards / backwards /
;; bidirectionally, membero, listo enumeration.
;; --- nullo / pairo ---
(mk-test
"nullo-empty-succeeds"
(run* q (nullo (list)))
(list (make-symbol "_.0")))
(mk-test "nullo-non-empty-fails" (run* q (nullo (list 1))) (list))
(mk-test
"pairo-non-empty-succeeds"
(run* q (pairo (list 1 2)))
(list (make-symbol "_.0")))
(mk-test "pairo-empty-fails" (run* q (pairo (list))) (list))
;; --- caro / cdro / firsto / resto ---
(mk-test
"caro-extracts-head"
(run* q (caro (list 1 2 3) q))
(list 1))
(mk-test
"cdro-extracts-tail"
(run* q (cdro (list 1 2 3) q))
(list (list 2 3)))
(mk-test
"firsto-alias-of-caro"
(run* q (firsto (list 10 20) q))
(list 10))
(mk-test
"resto-alias-of-cdro"
(run* q (resto (list 10 20) q))
(list (list 20)))
(mk-test
"caro-cdro-build"
(run*
q
(fresh
(h t)
(caro (list 1 2 3) h)
(cdro (list 1 2 3) t)
(== q (list h t))))
(list (list 1 (list 2 3))))
;; --- conso ---
(mk-test
"conso-forward"
(run* q (conso 0 (list 1 2 3) q))
(list (list 0 1 2 3)))
(mk-test
"conso-extract-head"
(run*
q
(conso
q
(list 2 3)
(list 1 2 3)))
(list 1))
(mk-test
"conso-extract-tail"
(run* q (conso 1 q (list 1 2 3)))
(list (list 2 3)))
;; --- listo ---
(mk-test
"listo-empty-succeeds"
(run* q (listo (list)))
(list (make-symbol "_.0")))
(mk-test
"listo-finite-list-succeeds"
(run* q (listo (list 1 2 3)))
(list (make-symbol "_.0")))
(mk-test
"listo-enumerates-shapes"
(run 3 q (listo q))
(list
(list)
(list (make-symbol "_.0"))
(list (make-symbol "_.0") (make-symbol "_.1"))))
;; --- appendo: the canary ---
(mk-test
"appendo-forward-simple"
(run*
q
(appendo (list 1 2) (list 3 4) q))
(list (list 1 2 3 4)))
(mk-test
"appendo-forward-empty-l"
(run* q (appendo (list) (list 3 4) q))
(list (list 3 4)))
(mk-test
"appendo-forward-empty-s"
(run* q (appendo (list 1 2) (list) q))
(list (list 1 2)))
(mk-test
"appendo-recovers-tail"
(run*
q
(appendo
(list 1 2)
q
(list 1 2 3 4)))
(list (list 3 4)))
(mk-test
"appendo-recovers-prefix"
(run*
q
(appendo
q
(list 3 4)
(list 1 2 3 4)))
(list (list 1 2)))
(mk-test
"appendo-backward-all-splits"
(run*
q
(fresh
(l s)
(appendo l s (list 1 2 3))
(== q (list l s))))
(list
(list (list) (list 1 2 3))
(list (list 1) (list 2 3))
(list (list 1 2) (list 3))
(list (list 1 2 3) (list))))
(mk-test
"appendo-empty-empty-empty"
(run* q (appendo (list) (list) q))
(list (list)))
;; --- membero ---
(mk-test
"membero-element-present"
(run
1
q
(membero 2 (list 1 2 3)))
(list (make-symbol "_.0")))
(mk-test
"membero-element-absent-empty"
(run* q (membero 99 (list 1 2 3)))
(list))
(mk-test
"membero-enumerates"
(run* q (membero q (list "a" "b" "c")))
(list "a" "b" "c"))
;; --- reverseo ---
(mk-test
"reverseo-forward"
(run* q (reverseo (list 1 2 3) q))
(list (list 3 2 1)))
(mk-test "reverseo-empty" (run* q (reverseo (list) q)) (list (list)))
(mk-test
"reverseo-singleton"
(run* q (reverseo (list 42) q))
(list (list 42)))
(mk-test
"reverseo-five"
(run*
q
(reverseo (list 1 2 3 4 5) q))
(list (list 5 4 3 2 1)))
(mk-test
"reverseo-backward-one"
(run 1 q (reverseo q (list 1 2 3)))
(list (list 3 2 1)))
(mk-test
"reverseo-round-trip"
(run*
q
(fresh (mid) (reverseo (list "a" "b" "c") mid) (reverseo mid q)))
(list (list "a" "b" "c")))
;; --- lengtho (Peano-style) ---
(mk-test "lengtho-empty-is-z" (run* q (lengtho (list) q)) (list :z))
(mk-test
"lengtho-of-3"
(run* q (lengtho (list "a" "b" "c") q))
(list (list :s (list :s (list :s :z)))))
(mk-test
"lengtho-empty-from-zero"
(run 1 q (lengtho q :z))
(list (list)))
(mk-test
"lengtho-enumerates-of-length-2"
(run 1 q (lengtho q (list :s (list :s :z))))
(list (list (make-symbol "_.0") (make-symbol "_.1"))))
;; --- inserto ---
(mk-test
"inserto-front"
(run* q (inserto 0 (list 1 2 3) q))
(list
(list 0 1 2 3)
(list 1 0 2 3)
(list 1 2 0 3)
(list 1 2 3 0)))
(mk-test
"inserto-empty"
(run* q (inserto 0 (list) q))
(list (list 0)))
;; --- permuteo ---
(mk-test "permuteo-empty" (run* q (permuteo (list) q)) (list (list)))
(mk-test
"permuteo-singleton"
(run* q (permuteo (list 42) q))
(list (list 42)))
(mk-test
"permuteo-two"
(run* q (permuteo (list 1 2) q))
(list (list 1 2) (list 2 1)))
(mk-test
"permuteo-three-as-set"
(let
((perms (run* q (permuteo (list 1 2 3) q))))
(and
(= (len perms) 6)
(and
(some (fn (p) (= p (list 1 2 3))) perms)
(and
(some
(fn (p) (= p (list 2 1 3)))
perms)
(and
(some
(fn (p) (= p (list 1 3 2)))
perms)
(and
(some
(fn (p) (= p (list 2 3 1)))
perms)
(and
(some
(fn (p) (= p (list 3 1 2)))
perms)
(some
(fn (p) (= p (list 3 2 1)))
perms))))))))
true)
(mk-test
"permuteo-backward-finds-input"
(run 1 q (permuteo q (list "a" "b" "c")))
(list (list "a" "b" "c")))
(mk-tests-run!)

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;; lib/minikanren/tests/removeo-allo.sx — remove every occurrence of x.
(mk-test
"removeo-allo-multi"
(run*
q
(removeo-allo
2
(list 1 2 3 2 4 2)
q))
(list (list 1 3 4)))
(mk-test
"removeo-allo-single"
(run*
q
(removeo-allo 2 (list 1 2 3) q))
(list (list 1 3)))
(mk-test
"removeo-allo-no-match"
(run*
q
(removeo-allo 99 (list 1 2 3) q))
(list (list 1 2 3)))
(mk-test
"removeo-allo-everything"
(run*
q
(removeo-allo 1 (list 1 1 1) q))
(list (list)))
(mk-test
"removeo-allo-empty"
(run* q (removeo-allo 1 (list) q))
(list (list)))
(mk-tests-run!)

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;; lib/minikanren/tests/repeato-concato.sx — repeat element n times +
;; concatenate a list of lists.
(define
mk-nat
(fn (n) (if (= n 0) :z (list :s (mk-nat (- n 1))))))
;; --- repeato ---
(mk-test
"repeato-zero"
(run* q (repeato :a (mk-nat 0) q))
(list (list)))
(mk-test
"repeato-one"
(run* q (repeato :a (mk-nat 1) q))
(list (list :a)))
(mk-test
"repeato-three"
(run* q (repeato :a (mk-nat 3) q))
(list (list :a :a :a)))
(mk-test
"repeato-numeric"
(run* q (repeato 7 (mk-nat 4) q))
(list (list 7 7 7 7)))
(mk-test
"repeato-recover-count"
(run* q (repeato :x q (list :x :x :x :x)))
(list (mk-nat 4)))
;; --- concato ---
(mk-test "concato-empty" (run* q (concato (list) q)) (list (list)))
(mk-test
"concato-single"
(run* q (concato (list (list 1 2 3)) q))
(list (list 1 2 3)))
(mk-test
"concato-multi"
(run*
q
(concato
(list
(list 1 2)
(list 3)
(list 4 5 6))
q))
(list
(list 1 2 3 4 5 6)))
(mk-test
"concato-all-empty"
(run* q (concato (list (list) (list) (list)) q))
(list (list)))
(mk-test
"concato-mixed-empty"
(run*
q
(concato
(list (list 1) (list) (list 2 3))
q))
(list (list 1 2 3)))
(mk-tests-run!)

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;; lib/minikanren/tests/rev-acco.sx — accumulator-style reverse.
;;
;; Faster than reverseo for forward queries (no quadratic appendos).
;; Trade-off: rev-acco is asymmetric (acc=initial-empty for the public
;; interface), so it does not cleanly run backwards in run* the way
;; reverseo does.
(mk-test "rev-2o-empty" (run* q (rev-2o (list) q)) (list (list)))
(mk-test
"rev-2o-singleton"
(run* q (rev-2o (list 7) q))
(list (list 7)))
(mk-test
"rev-2o-three"
(run* q (rev-2o (list 1 2 3) q))
(list (list 3 2 1)))
(mk-test
"rev-2o-five"
(run*
q
(rev-2o (list 1 2 3 4 5) q))
(list (list 5 4 3 2 1)))
(mk-test
"rev-2o-strings"
(run* q (rev-2o (list "a" "b" "c") q))
(list (list "c" "b" "a")))
(mk-test
"rev-2o-reverseo-agree"
(let
((via-reverseo (first (run* q (reverseo (list 1 2 3 4 5) q))))
(via-rev-2o
(first
(run*
q
(rev-2o
(list 1 2 3 4 5)
q)))))
(= via-reverseo via-rev-2o))
true)
(mk-tests-run!)

114
lib/minikanren/tests/run.sx Normal file
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;; lib/minikanren/tests/run.sx — Phase 3 tests for run* / run / reify.
;; --- canonical TRS one-liners ---
(mk-test "run*-eq-one" (run* q (== q 1)) (list 1))
(mk-test "run*-eq-string" (run* q (== q "hello")) (list "hello"))
(mk-test "run*-eq-symbol" (run* q (== q (quote sym))) (list (quote sym)))
(mk-test "run*-fail-empty" (run* q (== 1 2)) (list))
;; --- run with a count ---
(mk-test
"run-3-of-many"
(run
3
q
(conde
((== q 1))
((== q 2))
((== q 3))
((== q 4))
((== q 5))))
(list 1 2 3))
(mk-test "run-zero-empty" (run 0 q (== q 1)) (list))
(mk-test
"run-1-takes-one"
(run 1 q (conde ((== q "a")) ((== q "b"))))
(list "a"))
;; --- reification: unbound vars get _.N left-to-right ---
(mk-test
"reify-single-unbound"
(run* q (fresh (x) (== q x)))
(list (make-symbol "_.0")))
(mk-test
"reify-pair-unbound"
(run* q (fresh (x y) (== q (list x y))))
(list (list (make-symbol "_.0") (make-symbol "_.1"))))
(mk-test
"reify-mixed-bound-unbound"
(run* q (fresh (x y) (== q (list 1 x 2 y))))
(list
(list 1 (make-symbol "_.0") 2 (make-symbol "_.1"))))
(mk-test
"reify-shared-unbound-same-name"
(run* q (fresh (x) (== q (list x x))))
(list (list (make-symbol "_.0") (make-symbol "_.0"))))
(mk-test
"reify-distinct-unbound-distinct-names"
(run* q (fresh (x y) (== q (list x y x y))))
(list
(list
(make-symbol "_.0")
(make-symbol "_.1")
(make-symbol "_.0")
(make-symbol "_.1"))))
;; --- conde + run* ---
(mk-test
"run*-conde-three"
(run*
q
(conde ((== q 1)) ((== q 2)) ((== q 3))))
(list 1 2 3))
(mk-test
"run*-conde-fresh-mix"
(run*
q
(conde ((fresh (x) (== q (list 1 x)))) ((== q "ground"))))
(list (list 1 (make-symbol "_.0")) "ground"))
;; --- run* + conjunction ---
(mk-test
"run*-conj-binds-q"
(run* q (fresh (x) (== x 5) (== q (list x x))))
(list (list 5 5)))
;; --- run* + condu ---
(mk-test
"run*-condu-first-wins"
(run* q (condu ((== q 1)) ((== q 2))))
(list 1))
(mk-test
"run*-onceo-trim"
(run* q (onceo (conde ((== q "a")) ((== q "b")))))
(list "a"))
;; --- multi-goal run ---
(mk-test
"run*-three-goals"
(run*
q
(fresh
(x y z)
(== x 1)
(== y 2)
(== z 3)
(== q (list x y z))))
(list (list 1 2 3)))
(mk-tests-run!)

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;; lib/minikanren/tests/selecto.sx — choose an element + rest of list.
(mk-test
"selecto-enumerate"
(run*
q
(fresh
(x r)
(selecto x r (list 1 2 3))
(== q (list x r))))
(list
(list 1 (list 2 3))
(list 2 (list 1 3))
(list 3 (list 1 2))))
(mk-test
"selecto-find-rest"
(run* q (selecto 2 q (list 1 2 3)))
(list (list 1 3)))
(mk-test
"selecto-find-element"
(run*
q
(selecto
q
(list 1 3)
(list 1 2 3)))
(list 2))
(mk-test
"selecto-element-not-present-fails"
(run* q (selecto 99 q (list 1 2 3)))
(list))
(mk-test
"selecto-empty-list-fails"
(run* q (selecto q (list) (list)))
(list))
(mk-test
"selecto-singleton"
(run* q (fresh (x r) (selecto x r (list :only)) (== q (list x r))))
(list (list :only (list))))
(mk-tests-run!)

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;; lib/minikanren/tests/simplifyo.sx — algebraic expression simplifier
;; demo using conda for first-match-wins dispatch.
(define
simplify-step-o
(fn
(expr result)
(conda
((fresh (x) (== expr (list :+ 0 x)) (== result x)))
((fresh (x) (== expr (list :+ x 0)) (== result x)))
((fresh (y) (== expr (list :* 0 y)) (== result 0)))
((fresh (x) (== expr (list :* x 0)) (== result 0)))
((fresh (x) (== expr (list :* 1 x)) (== result x)))
((fresh (x) (== expr (list :* x 1)) (== result x)))
((== result expr))))) ;; default: unchanged
(mk-test
"simplify-zero-plus"
(run* q (simplify-step-o (list :+ 0 :y) q))
(list :y))
(mk-test
"simplify-plus-zero"
(run* q (simplify-step-o (list :+ :x 0) q))
(list :x))
(mk-test
"simplify-zero-times"
(run* q (simplify-step-o (list :* 0 :y) q))
(list 0))
(mk-test
"simplify-one-times"
(run* q (simplify-step-o (list :* 1 :y) q))
(list :y))
(mk-test
"simplify-no-rule-applies"
(run* q (simplify-step-o (list :+ :x :y) q))
(list (list :+ :x :y)))
(mk-test
"simplify-non-identity-form"
(run* q (simplify-step-o (list :+ 5 7) q))
(list (list :+ 5 7)))
(mk-tests-run!)

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;; lib/minikanren/tests/sortedo.sx — checks list is non-decreasing.
(mk-test
"sortedo-empty"
(run* q (sortedo (list)))
(list (make-symbol "_.0")))
(mk-test
"sortedo-singleton"
(run* q (sortedo (list 42)))
(list (make-symbol "_.0")))
(mk-test
"sortedo-ascending"
(run* q (sortedo (list 1 2 3 4)))
(list (make-symbol "_.0")))
(mk-test
"sortedo-with-equal-adjacent"
(run*
q
(sortedo (list 1 1 2 2 3)))
(list (make-symbol "_.0")))
(mk-test
"sortedo-out-of-order-fails"
(run* q (sortedo (list 1 3 2)))
(list))
(mk-test
"sortedo-descending-fails"
(run* q (sortedo (list 3 2 1)))
(list))
(mk-test
"sortedo-pair-equal"
(run* q (sortedo (list 5 5)))
(list (make-symbol "_.0")))
(mk-tests-run!)

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;; lib/minikanren/tests/subo.sx — contiguous-sublist relation.
(mk-test
"subo-simple-found"
(run*
q
(subo
(list 2 3)
(list 1 2 3 4)))
(list (make-symbol "_.0")))
(mk-test
"subo-not-contiguous-fails"
(run*
q
(subo
(list 2 4)
(list 1 2 3 4)))
(list))
(mk-test
"subo-full-list-found"
(run*
q
(subo
(list 1 2 3)
(list 1 2 3)))
(list (make-symbol "_.0")))
(mk-test
"subo-empty-list-found"
(let
((res (run* q (subo (list) (list 1 2 3)))))
(= (len res) 4))
true)
(mk-test
"subo-prefix"
(run*
q
(subo
(list 1 2)
(list 1 2 3 4)))
(list (make-symbol "_.0")))
(mk-test
"subo-suffix"
(run*
q
(subo
(list 3 4)
(list 1 2 3 4)))
(list (make-symbol "_.0")))
(mk-test
"subo-strings"
(run* q (subo (list "b" "c") (list "a" "b" "c" "d")))
(list (make-symbol "_.0")))
(mk-tests-run!)

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;; lib/minikanren/tests/subseto.sx — every element of l1 is in l2.
(mk-test
"subseto-empty"
(run* q (subseto (list) (list 1 2 3)))
(list (make-symbol "_.0")))
(mk-test
"subseto-singleton-yes"
(run*
q
(subseto (list 2) (list 1 2 3)))
(list (make-symbol "_.0")))
(mk-test
"subseto-singleton-no"
(run*
q
(subseto (list 99) (list 1 2 3)))
(list))
(mk-test
"subseto-multi-yes"
(run
1
q
(subseto
(list 1 3)
(list 1 2 3 4)))
(list (make-symbol "_.0")))
(mk-test
"subseto-multi-no"
(run*
q
(subseto
(list 1 99)
(list 1 2 3)))
(list))
(mk-test
"subseto-equal-sets"
(run
1
q
(subseto
(list 1 2 3)
(list 1 2 3)))
(list (make-symbol "_.0")))
;; allow duplicates in l1 — each just needs membership in l2.
(mk-test
"subseto-duplicates-allowed"
(run
1
q
(subseto
(list 1 1 2)
(list 1 2 3)))
(list (make-symbol "_.0")))
(mk-tests-run!)

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;; lib/minikanren/tests/sum-product.sx — fold list to integer.
(mk-test "sumo-empty" (run* q (sumo (list) q)) (list 0))
(mk-test
"sumo-1-to-5"
(run*
q
(sumo (list 1 2 3 4 5) q))
(list 15))
(mk-test
"sumo-zeros"
(run* q (sumo (list 0 0 0) q))
(list 0))
(mk-test
"sumo-negs"
(run* q (sumo (list 5 -3 8) q))
(list 10))
(mk-test "producto-empty" (run* q (producto (list) q)) (list 1))
(mk-test
"producto-1-to-4"
(run* q (producto (list 1 2 3 4) q))
(list 24))
(mk-test
"producto-with-0"
(run* q (producto (list 5 0 7) q))
(list 0))
(mk-test
"producto-of-1s"
(run* q (producto (list 1 1 1) q))
(list 1))
(mk-test
"sum-product-pythagorean-square"
(run*
q
(fresh
(s sq2)
(sumo (list 3 4 5) s)
(producto (list 3 3) sq2)
(== q (list s sq2))))
(list (list 12 9)))
(mk-tests-run!)

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;; lib/minikanren/tests/swap-firsto.sx — swap first two elements.
(mk-test
"swap-firsto-pair"
(run* q (swap-firsto (list 1 2) q))
(list (list 2 1)))
(mk-test
"swap-firsto-with-tail"
(run* q (swap-firsto (list 1 2 3 4) q))
(list (list 2 1 3 4)))
(mk-test
"swap-firsto-singleton-fails"
(run* q (swap-firsto (list 1) q))
(list))
(mk-test "swap-firsto-empty-fails" (run* q (swap-firsto (list) q)) (list))
(mk-test
"swap-firsto-self-inverse"
(run*
q
(fresh (mid) (swap-firsto (list :a :b :c :d) mid) (swap-firsto mid q)))
(list (list :a :b :c :d)))
(mk-test
"swap-firsto-backward"
(run* q (swap-firsto q (list :y :x :z)))
(list (list :x :y :z)))
(mk-tests-run!)

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;; lib/minikanren/tests/tabling-more.sx — table-1 + table-3.
;; --- table-1 (predicate caching) ---
(define
tab-in-list
(table-1
"in-list"
(fn
(x)
(membero
x
(list 1 2 3 4 5)))))
(mk-tab-clear!)
(mk-test
"table-1-hit"
(run* q (tab-in-list 3))
(list (make-symbol "_.0")))
(mk-test "table-1-miss-no" (run* q (tab-in-list 99)) (list))
(mk-test
"table-1-replay"
(run* q (tab-in-list 3))
(list (make-symbol "_.0")))
;; --- table-3 (Ackermann) ---
(define
ack-o
(table-3
"ack"
(fn
(m n result)
(conde
((== m 0) (pluso-i n 1 result))
((fresh (m-1) (lto-i 0 m) (== n 0) (minuso-i m 1 m-1) (ack-o m-1 1 result)))
((fresh (m-1 n-1 inner) (lto-i 0 m) (lto-i 0 n) (minuso-i m 1 m-1) (minuso-i n 1 n-1) (ack-o m n-1 inner) (ack-o m-1 inner result)))))))
(mk-tab-clear!)
(mk-test
"ack-0-0"
(run* q (ack-o 0 0 q))
(list 1))
(mk-tab-clear!)
(mk-test
"ack-2-3"
(run* q (ack-o 2 3 q))
(list 9))
(mk-tab-clear!)
(mk-test
"ack-3-3"
(run* q (ack-o 3 3 q))
(list 61))
(mk-tests-run!)

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;; lib/minikanren/tests/tabling.sx — Phase 7 piece A: naive memoization.
;; --- Fibonacci canary: tabled vs naive --
(define
tab-fib-o
(table-2
"fib"
(fn
(n result)
(conde
((== n 0) (== result 0))
((== n 1) (== result 1))
((fresh (n-1 n-2 r-1 r-2) (lto-i 1 n) (minuso-i n 1 n-1) (minuso-i n 2 n-2) (tab-fib-o n-1 r-1) (tab-fib-o n-2 r-2) (pluso-i r-1 r-2 result)))))))
(mk-tab-clear!)
(mk-test "tab-fib-zero" (run* q (tab-fib-o 0 q)) (list 0))
(mk-tab-clear!)
(mk-test "tab-fib-one" (run* q (tab-fib-o 1 q)) (list 1))
(mk-tab-clear!)
(mk-test "tab-fib-two" (run* q (tab-fib-o 2 q)) (list 1))
(mk-tab-clear!)
(mk-test "tab-fib-five" (run* q (tab-fib-o 5 q)) (list 5))
(mk-tab-clear!)
(mk-test "tab-fib-ten" (run* q (tab-fib-o 10 q)) (list 55))
(mk-tab-clear!)
(mk-test
"tab-fib-twenty"
(run* q (tab-fib-o 20 q))
(list 6765))
;; --- ground-term predicate ---
(mk-test "tab-ground-term-num" (mk-tab-ground-term? 5) true)
(mk-test "tab-ground-term-str" (mk-tab-ground-term? "hi") true)
(mk-test
"tab-ground-term-list"
(mk-tab-ground-term? (list 1 2 3))
true)
(mk-test "tab-ground-term-var" (mk-tab-ground-term? (mk-var "x")) false)
(mk-test
"tab-ground-term-nested"
(mk-tab-ground-term?
(list 1 (list 2 (mk-var "y")) 3))
false)
;; --- caching reduces work — count cache hits via repeated query ---
(mk-test
"tab-cache-replay"
(begin
(mk-tab-clear!)
(let
((first (run* q (tab-fib-o 10 q)))
(second (run* q (tab-fib-o 10 q))))
(and (= first (list 55)) (= second (list 55)))))
true)
(mk-tests-run!)

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;; lib/minikanren/tests/take-drop.sx — Peano-indexed prefix/suffix.
(define
mk-nat
(fn (n) (if (= n 0) :z (list :s (mk-nat (- n 1))))))
;; --- tako ---
(mk-test
"tako-zero"
(run*
q
(tako (mk-nat 0) (list 1 2 3) q))
(list (list)))
(mk-test
"tako-two"
(run*
q
(tako
(mk-nat 2)
(list 1 2 3 4 5)
q))
(list (list 1 2)))
(mk-test
"tako-all"
(run*
q
(tako (mk-nat 3) (list 1 2 3) q))
(list (list 1 2 3)))
(mk-test
"tako-too-many"
(run*
q
(tako (mk-nat 5) (list 1 2 3) q))
(list))
;; --- dropo ---
(mk-test
"dropo-zero"
(run*
q
(dropo (mk-nat 0) (list 1 2 3) q))
(list (list 1 2 3)))
(mk-test
"dropo-two"
(run*
q
(dropo
(mk-nat 2)
(list 1 2 3 4 5)
q))
(list (list 3 4 5)))
(mk-test
"dropo-all"
(run*
q
(dropo (mk-nat 3) (list 1 2 3) q))
(list (list)))
(mk-test
"dropo-too-many"
(run*
q
(dropo (mk-nat 5) (list 1 2 3) q))
(list))
;; --- take + drop round-trip ---
(mk-test
"tako-dropo-roundtrip"
(run*
q
(fresh
(p s)
(tako
(mk-nat 2)
(list 1 2 3 4 5)
p)
(dropo
(mk-nat 2)
(list 1 2 3 4 5)
s)
(appendo p s q)))
(list (list 1 2 3 4 5)))
(mk-tests-run!)

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;; lib/minikanren/tests/take-while-drop-while.sx — prefix/suffix by predicate.
(mk-test
"take-while-o-empty"
(run* q (take-while-o (fn (x) (== x 1)) (list) q))
(list (list)))
(mk-test
"take-while-o-while-lt-5"
(run*
q
(take-while-o
(fn (x) (lto-i x 5))
(list 1 3 7 2 9)
q))
(list (list 1 3)))
(mk-test
"take-while-o-all-match"
(run*
q
(take-while-o
(fn (x) (lto-i x 100))
(list 1 2 3)
q))
(list (list 1 2 3)))
(mk-test
"take-while-o-none-match"
(run*
q
(take-while-o
(fn (x) (lto-i 100 x))
(list 1 2 3)
q))
(list (list)))
(mk-test
"drop-while-o-empty"
(run* q (drop-while-o (fn (x) (== x 1)) (list) q))
(list (list)))
(mk-test
"drop-while-o-while-lt-5"
(run*
q
(drop-while-o
(fn (x) (lto-i x 5))
(list 1 3 7 2 9)
q))
(list (list 7 2 9)))
(mk-test
"drop-while-o-all-match"
(run*
q
(drop-while-o
(fn (x) (lto-i x 100))
(list 1 2 3)
q))
(list (list)))
(mk-test
"take-drop-roundtrip"
(run*
q
(fresh
(p s)
(take-while-o
(fn (x) (lto-i x 5))
(list 1 3 7 2 9)
p)
(drop-while-o
(fn (x) (lto-i x 5))
(list 1 3 7 2 9)
s)
(appendo p s q)))
(list (list 1 3 7 2 9)))
(mk-tests-run!)

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;; lib/minikanren/tests/types.sx — type-predicate goals.
(mk-test
"numbero-on-int"
(run* q (numbero 5))
(list (make-symbol "_.0")))
(mk-test "numbero-on-string" (run* q (numbero "5")) (list))
(mk-test "numbero-on-symbol" (run* q (numbero (quote x))) (list))
(mk-test "numbero-on-list" (run* q (numbero (list 1))) (list))
(mk-test
"stringo-on-string"
(run* q (stringo "hi"))
(list (make-symbol "_.0")))
(mk-test "stringo-on-int" (run* q (stringo 5)) (list))
(mk-test
"stringo-on-keyword"
(run* q (stringo :k))
(list (make-symbol "_.0"))) ;; SX keywords ARE strings
(mk-test
"symbolo-on-symbol"
(run* q (symbolo (quote x)))
(list (make-symbol "_.0")))
(mk-test "symbolo-on-string" (run* q (symbolo "x")) (list))
(mk-test "symbolo-on-int" (run* q (symbolo 5)) (list))
;; --- combine with membero for type-filtered enumeration ---
(mk-test
"membero-numbero-filter"
(run*
q
(fresh
(x)
(membero x (list 1 "a" 2 "b" 3))
(numbero x)
(== q x)))
(list 1 2 3))
(mk-test
"membero-stringo-filter"
(run*
q
(fresh
(x)
(membero x (list 1 "a" 2 "b" 3))
(stringo x)
(== q x)))
(list "a" "b"))
(mk-tests-run!)

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;; lib/minikanren/tests/unify.sx — Phase 1 tests for unify.sx.
;;
;; Loads into a session that already has lib/guest/match.sx and
;; lib/minikanren/unify.sx defined. Tests are top-level forms.
;; Call (mk-tests-run!) afterwards to get the totals.
;;
;; Note: SX dict equality is reference-based, so tests check the *effect*
;; of a unification (success/failure flag, or walked bindings) rather than
;; the raw substitution dict.
(define mk-test-pass 0)
(define mk-test-fail 0)
(define mk-test-fails (list))
(define
mk-test
(fn
(name actual expected)
(if
(= actual expected)
(set! mk-test-pass (+ mk-test-pass 1))
(begin
(set! mk-test-fail (+ mk-test-fail 1))
(append! mk-test-fails {:name name :expected expected :actual actual})))))
(define mk-tests-run! (fn () {:total (+ mk-test-pass mk-test-fail) :passed mk-test-pass :failed mk-test-fail :fails mk-test-fails}))
(define mk-unified? (fn (s) (if (= s nil) false true)))
;; --- fresh variable construction ---
(mk-test
"make-var-distinct"
(let ((a (make-var)) (b (make-var))) (= (var-name a) (var-name b)))
false)
(mk-test "make-var-is-var" (mk-var? (make-var)) true)
(mk-test "var?-num" (mk-var? 5) false)
(mk-test "var?-list" (mk-var? (list 1 2)) false)
(mk-test "var?-string" (mk-var? "hi") false)
(mk-test "var?-empty" (mk-var? (list)) false)
(mk-test "var?-bool" (mk-var? true) false)
;; --- empty substitution ---
(mk-test "empty-s-walk-num" (mk-walk 5 empty-s) 5)
(mk-test "empty-s-walk-str" (mk-walk "x" empty-s) "x")
(mk-test
"empty-s-walk-list"
(mk-walk (list 1 2) empty-s)
(list 1 2))
(mk-test
"empty-s-walk-unbound-var"
(let ((x (make-var))) (= (mk-walk x empty-s) x))
true)
;; --- walk: top-level chain resolution ---
(mk-test
"walk-direct-binding"
(mk-walk (mk-var "x") (extend "x" 7 empty-s))
7)
(mk-test
"walk-two-step-chain"
(mk-walk
(mk-var "x")
(extend "x" (mk-var "y") (extend "y" 9 empty-s)))
9)
(mk-test
"walk-three-step-chain"
(mk-walk
(mk-var "a")
(extend
"a"
(mk-var "b")
(extend "b" (mk-var "c") (extend "c" 42 empty-s))))
42)
(mk-test
"walk-stops-at-list"
(mk-walk (list 1 (mk-var "x")) (extend "x" 5 empty-s))
(list 1 (mk-var "x")))
;; --- walk*: deep walk into lists ---
(mk-test
"walk*-flat-list-with-vars"
(mk-walk*
(list (mk-var "x") 2 (mk-var "y"))
(extend "x" 1 (extend "y" 3 empty-s)))
(list 1 2 3))
(mk-test
"walk*-nested-list"
(mk-walk*
(list 1 (mk-var "x") (list 2 (mk-var "y")))
(extend "x" 5 (extend "y" 6 empty-s)))
(list 1 5 (list 2 6)))
(mk-test
"walk*-unbound-stays-var"
(let
((x (mk-var "x")))
(= (mk-walk* (list 1 x) empty-s) (list 1 x)))
true)
(mk-test "walk*-atom" (mk-walk* 5 empty-s) 5)
;; --- unify atoms (success / failure semantics, not dict shape) ---
(mk-test
"unify-num-eq-succeeds"
(mk-unified? (mk-unify 5 5 empty-s))
true)
(mk-test "unify-num-neq-fails" (mk-unify 5 6 empty-s) nil)
(mk-test
"unify-str-eq-succeeds"
(mk-unified? (mk-unify "a" "a" empty-s))
true)
(mk-test "unify-str-neq-fails" (mk-unify "a" "b" empty-s) nil)
(mk-test
"unify-bool-eq-succeeds"
(mk-unified? (mk-unify true true empty-s))
true)
(mk-test "unify-bool-neq-fails" (mk-unify true false empty-s) nil)
(mk-test
"unify-nil-eq-succeeds"
(mk-unified? (mk-unify nil nil empty-s))
true)
(mk-test
"unify-empty-list-succeeds"
(mk-unified? (mk-unify (list) (list) empty-s))
true)
;; --- unify var with anything (walk to verify binding) ---
(mk-test
"unify-var-num-binds"
(mk-walk (mk-var "x") (mk-unify (mk-var "x") 5 empty-s))
5)
(mk-test
"unify-num-var-binds"
(mk-walk (mk-var "x") (mk-unify 5 (mk-var "x") empty-s))
5)
(mk-test
"unify-var-list-binds"
(mk-walk
(mk-var "x")
(mk-unify (mk-var "x") (list 1 2) empty-s))
(list 1 2))
(mk-test
"unify-var-var-same-no-extend"
(mk-unified? (mk-unify (mk-var "x") (mk-var "x") empty-s))
true)
(mk-test
"unify-var-var-different-walks-equal"
(let
((s (mk-unify (mk-var "x") (mk-var "y") empty-s)))
(= (mk-walk (mk-var "x") s) (mk-walk (mk-var "y") s)))
true)
;; --- unify lists positionally ---
(mk-test
"unify-list-equal-succeeds"
(mk-unified?
(mk-unify
(list 1 2 3)
(list 1 2 3)
empty-s))
true)
(mk-test
"unify-list-different-length-fails-1"
(mk-unify
(list 1 2)
(list 1 2 3)
empty-s)
nil)
(mk-test
"unify-list-different-length-fails-2"
(mk-unify
(list 1 2 3)
(list 1 2)
empty-s)
nil)
(mk-test
"unify-list-mismatch-fails"
(mk-unify
(list 1 2)
(list 1 3)
empty-s)
nil)
(mk-test
"unify-list-vs-atom-fails"
(mk-unify (list 1 2) 5 empty-s)
nil)
(mk-test
"unify-empty-vs-non-empty-fails"
(mk-unify (list) (list 1) empty-s)
nil)
(mk-test
"unify-list-with-vars-walks"
(mk-walk*
(list (mk-var "x") (mk-var "y"))
(mk-unify
(list (mk-var "x") (mk-var "y"))
(list 1 2)
empty-s))
(list 1 2))
(mk-test
"unify-nested-lists-with-vars-walks"
(mk-walk*
(list (mk-var "x") (list (mk-var "y") 3))
(mk-unify
(list (mk-var "x") (list (mk-var "y") 3))
(list 1 (list 2 3))
empty-s))
(list 1 (list 2 3)))
;; --- unify chained substitutions ---
(mk-test
"unify-chain-var-var-then-atom"
(let
((x (mk-var "x")) (y (mk-var "y")))
(let
((s1 (mk-unify x y empty-s)))
(mk-walk x (mk-unify y 7 s1))))
7)
(mk-test
"unify-already-bound-consistent"
(let
((s (extend "x" 5 empty-s)))
(mk-unified? (mk-unify (mk-var "x") 5 s)))
true)
(mk-test
"unify-already-bound-conflict-fails"
(let
((s (extend "x" 5 empty-s)))
(mk-unify (mk-var "x") 6 s))
nil)
;; --- occurs check (opt-in) ---
(mk-test
"unify-no-occurs-default-succeeds"
(let
((x (mk-var "x")))
(mk-unified? (mk-unify x (list 1 x) empty-s)))
true)
(mk-test
"unify-occurs-direct-fails"
(let ((x (mk-var "x"))) (mk-unify-check x (list 1 x) empty-s))
nil)
(mk-test
"unify-occurs-nested-fails"
(let
((x (mk-var "x")))
(mk-unify-check x (list 1 (list 2 x)) empty-s))
nil)
(mk-test
"unify-occurs-non-occurring-succeeds"
(let
((x (mk-var "x")))
(mk-unified? (mk-unify-check x 5 empty-s)))
true)
(mk-test
"unify-occurs-via-chain-fails"
(let
((x (mk-var "x")) (y (mk-var "y")))
(let ((s (extend "y" (list x) empty-s))) (mk-unify-check x y s)))
nil)
(mk-tests-run!)

View File

@@ -0,0 +1,52 @@
;; lib/minikanren/tests/zip-with-o.sx — element-wise combine of two lists.
(mk-test
"zip-with-o-empty"
(run* q (zip-with-o pluso-i (list) (list) q))
(list (list)))
(mk-test
"zip-with-o-pluso-i"
(run*
q
(zip-with-o
pluso-i
(list 1 2 3)
(list 10 20 30)
q))
(list (list 11 22 33)))
(mk-test
"zip-with-o-times-i"
(run*
q
(zip-with-o
*o-i
(list 2 3 4)
(list 5 6 7)
q))
(list (list 10 18 28)))
(mk-test
"zip-with-o-different-length-fails"
(run*
q
(zip-with-o
pluso-i
(list 1 2)
(list 1 2 3)
q))
(list))
(mk-test
"zip-with-o-non-arith-rel"
(run*
q
(zip-with-o
(fn (a b r) (== r (list a b)))
(list :x :y)
(list 1 2)
q))
(list (list (list :x 1) (list :y 2))))
(mk-tests-run!)

82
lib/minikanren/unify.sx Normal file
View File

@@ -0,0 +1,82 @@
;; lib/minikanren/unify.sx — Phase 1 + cons-cell extension.
;;
;; miniKanren-on-SX, built on lib/guest/match.sx. The kit ships the heavy
;; lifting (walk-with, unify-with, occurs-with, extend, empty-subst,
;; mk-var/is-var?/var-name); this file supplies a miniKanren-shaped cfg
;; and a thin public API.
;;
;; Term shapes:
;; logic var : (:var NAME) — kit's mk-var
;; cons cell : (:cons HEAD TAIL) — for relational programming
;; (built by mk-cons; lets relations decompose lists by
;; head/tail without proper improper pairs in the host)
;; native list : SX list (a b c) — also unifies pair-style:
;; args = (head, tail) so (1 2 3) ≡ (:cons 1 (:cons 2 (:cons 3 ())))
;; atom : number / string / symbol / boolean / nil / ()
;;
;; Substitution: SX dict mapping VAR-NAME → term. Empty = (empty-subst).
(define mk-cons (fn (h t) (list :cons h t)))
(define
mk-cons-cell?
(fn (t) (and (list? t) (not (empty? t)) (= (first t) :cons))))
(define mk-cons-head (fn (t) (nth t 1)))
(define mk-cons-tail (fn (t) (nth t 2)))
(define
mk-list-pair?
(fn (t) (and (list? t) (not (empty? t)) (not (is-var? t)))))
(define mk-list-pair-head (fn (t) :pair))
(define
mk-list-pair-args
(fn
(t)
(cond
((mk-cons-cell? t) (list (mk-cons-head t) (mk-cons-tail t)))
(:else (list (first t) (rest t))))))
(define mk-cfg {:ctor-head mk-list-pair-head :var? is-var? :ctor? mk-list-pair? :occurs-check? false :var-name var-name :ctor-args mk-list-pair-args})
(define mk-cfg-occurs {:ctor-head mk-list-pair-head :var? is-var? :ctor? mk-list-pair? :occurs-check? true :var-name var-name :ctor-args mk-list-pair-args})
(define empty-s (empty-subst))
(define mk-fresh-counter 0)
(define
make-var
(fn
()
(begin
(set! mk-fresh-counter (+ mk-fresh-counter 1))
(mk-var (str "_." mk-fresh-counter)))))
(define mk-var? is-var?)
(define mk-walk (fn (t s) (walk-with mk-cfg t s)))
(define
mk-walk*
(fn
(t s)
(let
((w (mk-walk t s)))
(cond
((mk-cons-cell? w)
(let
((h (mk-walk* (mk-cons-head w) s))
(tl (mk-walk* (mk-cons-tail w) s)))
(cond
((empty? tl) (list h))
((mk-cons-cell? tl) tl)
((list? tl) (cons h tl))
(:else (mk-cons h tl)))))
((mk-list-pair? w) (map (fn (a) (mk-walk* a s)) w))
(:else w)))))
(define mk-unify (fn (u v s) (unify-with mk-cfg u v s)))
(define mk-unify-check (fn (u v s) (unify-with mk-cfg-occurs u v s)))

View File

@@ -50,68 +50,126 @@ Key semantic mappings:
## Roadmap
### Phase 1 — variables + unification
- [ ] `make-var` → fresh logic variable (unique mutable box)
- [ ] `var?` `v` → bool — is this a logic variable?
- [ ] `walk` `term` `subst` → follow substitution chain to ground term or unbound var
- [ ] `walk*` `term` `subst` → deep walk (recurse into lists/dicts)
- [ ] `unify` `u` `v` `subst` → extended substitution or `#f` (failure)
- [x] `make-var` → fresh logic variable (unique mutable box)
- [x] `var?` `v` → bool — is this a logic variable?
- [x] `walk` `term` `subst` → follow substitution chain to ground term or unbound var
- [x] `walk*` `term` `subst` → deep walk (recurse into lists/dicts)
- [x] `unify` `u` `v` `subst` → extended substitution or `#f` (failure)
Handles: var/var, var/term, term/var, list unification, number/string/symbol equality.
No occurs check by default; `unify-check` with occurs check as opt-in.
- [ ] Empty substitution `empty-s` = `(list)` (empty assoc list)
- [ ] Tests in `lib/minikanren/tests/unify.sx`: ground terms, vars, lists, failure, occurs
- [x] Empty substitution `empty-s` (dict-based via kit's `empty-subst` — assoc list was a sketch; kit ships dict, kept it)
- [x] Tests in `lib/minikanren/tests/unify.sx`: ground terms, vars, lists, failure, occurs
### Phase 2 — streams + goals
- [ ] Stream type: `mzero` (empty stream = `nil`), `unit s` (singleton = `(list s)`),
`mplus` (interleave two streams), `bind` (apply goal to stream)
- [ ] Lazy streams via `delay`/`force` — mature pairs for depth-first, immature for lazy
- [ ] `==` goal: `(fn (s) (let ((s2 (unify u v s))) (if s2 (unit s2) mzero)))`
- [ ] `succeed` / `fail` — trivial goals
- [ ] `fresh` `(fn (f) (fn (s) ((f (make-var)) s)))` — introduces one var; `fresh*` for many
- [ ] `conde` — interleaving disjunction of goal lists
- [ ] `condu` — committed choice (soft-cut): only explores first successful clause
- [ ] `onceo` — succeeds at most once
- [ ] Tests: basic goal composition, backtracking, interleaving
- [x] Stream type: `mzero` (empty), `unit s` (singleton), `mk-mplus` (interleave),
`mk-bind` (apply goal to stream). Names mk-prefixed because SX has a host
`bind` primitive that silently shadows user defines.
- [x] Lazy streams via thunks: a paused stream is a zero-arg fn; mk-mplus suspends
and swaps when its left operand is paused, giving fair interleaving.
- [x] `==` goal: `(fn (s) (let ((s2 (mk-unify u v s))) (if s2 (unit s2) mzero)))`
- [x] `==-check` — opt-in occurs-checked equality goal
- [x] `succeed` / `fail` — trivial goals
- [x] `conj2` / `mk-conj` (variadic) — sequential conjunction
- [x] `disj2` / `mk-disj` (variadic) — interleaved disjunction (raw — `conde`
adds the implicit-conj-per-clause sugar later)
- [x] `fresh` — introduces logic variables inside a goal body. Implemented as a
defmacro: `(fresh (x y) g1 g2 ...)``(let ((x (make-var)) (y (make-var)))
(mk-conj g1 g2 ...))`. Also `call-fresh` for programmatic goal building.
- [x] `conde` — sugar over disj+conj, one row per clause; defmacro that
wraps each clause body in `mk-conj` and folds via `mk-disj`. Notes:
with eager streams ordering is left-clause-first DFS; true interleaving
requires paused thunks (Phase 4 recursive relations).
- [x] `condu` — committed choice. defmacro folding clauses into a runtime
`condu-try` walker; first clause whose head goal yields a non-empty
stream commits its first answer, rest-goals run on that single subst.
- [x] `onceo``(stream-take 1 (g s))`; trims a goal's stream to ≤1 answer.
- [x] Tests: basic goal composition, backtracking, interleaving (110 cumulative)
### Phase 3 — run + reification
- [ ] `run*` `goal` → list of all answers (reified)
- [ ] `run n` `goal` → list of first n answers
- [ ] `reify` `term` `subst` → replace unbound vars with `_0`, `_1`, ... names
- [ ] `reify-s` builds reification substitution for naming unbound vars consistently
- [ ] `fresh` with multiple variables: `(fresh (x y z) goal)` sugar
- [ ] Query variable conventions: `q` as canonical query variable
- [ ] Tests: classic miniKanren programs — `(run* q (== q 1))``(1)`,
- [x] `run*` `goal` → list of all answers (reified). defmacro: bind q-name as
fresh var, conj goals, take all from stream, reify each.
- [x] `run n` `goal` → list of first n answers (defmacro; n = -1 means all)
- [x] `reify` `term` `subst` → walk* + build reification subst + walk* again
- [x] `reify-s` → maps each unbound var (in left-to-right walk order) to a
`_.N` symbol via `(make-symbol (str "_." n))`
- [x] `fresh` with multiple variables — already shipped Phase 2B.
- [x] Query variable conventions: `q` as canonical query variable (matches TRS)
- [x] Tests: classic miniKanren programs — `(run* q (== q 1))``(1)`,
`(run* q (conde ((== q 1)) ((== q 2))))``(1 2)`,
Peano arithmetic, `appendo` preview
`(run* q (fresh (x y) (== q (list x y))))``((_.0 _.1))`. Peano +
`appendo` deferred to Phase 4.
### Phase 4 — standard relations
- [ ] `appendo` `l` `s` `ls` — list append, runs forwards and backwards
- [ ] `membero` `x` `l` — x is a member of l
- [ ] `listo` `l` — l is a proper list
- [ ] `nullo` `l` — l is empty
- [ ] `pairo` `p` — p is a pair (cons cell)
- [ ] `caro` `p` `a` — car of pair
- [ ] `cdro` `p` `d` — cdr of pair
- [ ] `conso` `a` `d` `p` — cons
- [ ] `firsto` / `resto` — aliases for caro/cdro
- [ ] `reverseo` `l` `r` — reverse of list
- [ ] `flatteno` `l` `f` — flatten nested lists
- [ ] `permuteo` `l` `p`permutation of list
- [ ] `lengtho` `l` `n` — length as a relation (Peano or integer)
- [ ] Tests: run each relation forwards and backwards; generate from partial inputs
- [x] `appendo` `l` `s` `ls` — list append, runs forwards AND backwards.
Canary green: `(run* q (appendo (1 2) (3 4) q))``((1 2 3 4))`;
`(run* q (fresh (l s) (appendo l s (1 2 3)) (== q (list l s))))`
all four splits.
- [x] `membero` `x` `l` — enumerates: `(run* q (membero q (a b c)))``(a b c)`
- [x] `listo` `l` — l is a proper list; enumerates list shapes with laziness
- [x] `nullo` `l` — l is empty
- [x] `pairo` `p` — p is a (non-empty) cons-cell / list
- [x] `caro` / `cdro` / `conso` / `firsto` / `resto`
- [x] `reverseo` `l` `r` — reverse of list. Forward is fast; backward is `run 1`-clean,
`run*` diverges due to interleaved unbounded list search (canonical TRS issue).
- [x] `flatteno` `l` `f`flatten nested lists. Three conde clauses:
empty → empty; pair → recurse on car & cdr + appendo; otherwise atom →
`(== flat (list tree))`. Atom-ness is asserted via `nafc (nullo tree)
+ nafc (pairo tree)` — both succeed only when tree is a ground non-list.
Works on ground inputs.
- [x] `permuteo` `l` `p` — permutation of list. Built on `inserto` (insert at any
position) and recursive permutation of tail. All 6 perms of (1 2 3) generated
forward; backward `run 1 q (permuteo q (a b c))` finds the input.
- [x] `lengtho` `l` `n` — length as a relation, Peano-encoded:
`:z` / `(:s :z)` / `(:s (:s :z))` ... matches TRS. Forward is direct;
backward enumerates lists of a given length.
- [x] Tests: run each relation forwards and backwards (so far 25 in
`tests/relations.sx`; reverseo/flatteno/permuteo/lengtho deferred)
### Phase 5 — `project` + `matche` + negation
- [ ] `project` `(x ...) body`access reified values of logic vars inside a goal;
escapes to ground values for arithmetic or string ops
- [ ] `matche` — pattern matching over logic terms (extension from core.logic)
`(matche l ((head . tail) goal) (() goal))`
- [ ] `conda` — soft-cut disjunction (like Prolog `->`)
- [ ] `condu` — committed choice (already in phase 2; refine semantics here)
- [ ] `nafc` — negation as finite failure with constraint
- [x] `project` `(x ...) body`defmacro: rebinds named vars to `(mk-walk* var s)`
in the body's lexical scope, then runs `(mk-conj body...)` on the same
substitution. Hygienic via gensym'd `s`-param. (`Phase 5 piece B`)
- [x] `matche` — pattern matching over logic terms. Pattern grammar: `_` /
symbol / atom / `()` / `(p1 p2 ... pn)`. Each clause becomes
`(fresh (vars-in-pat) (== target pat-expr) body...)`. Repeated symbol
names in a pattern produce the same fresh var, so they unify (== check).
Built without quasiquote (the expander does not recurse into lambda
bodies). Fixed-length list patterns only — head/tail destructuring uses
`(fresh (a d) (conso a d target) body)` directly.
- [x] `conda` — soft-cut: first non-failing head wins; ALL of head's answers
flow through rest-goals; later clauses not tried (`Phase 5 piece A`)
- [x] `condu` — committed choice (Phase 2)
- [x] `nafc` — negation as finite failure: `(nafc g)` yields the input subst
iff g has zero answers. Standard caveats apply (open-world unsoundness;
diverges if g is infinite). `Phase 5 piece C`.
- [ ] Tests: Zebra puzzle, N-queens, Sudoku via `project`, family relations via `matche`
### Phase 6 — arithmetic constraints CLP(FD)
- [ ] Finite domain variables: `fd-var` with domain `[lo..hi]`
- [ ] `in` `x` `domain` — constrain x to domain
- [x] Finite domain variables: domain stored under reserved key `_fd` in
the substitution dict; ascending sorted-int-list representation;
domain primitives `fd-dom-from-list`, `fd-dom-intersect`,
`fd-dom-without`, `fd-dom-range`, `fd-dom-min/max/empty?/singleton?`.
- [x] `fd-in x dom` — narrows x's domain by intersection.
- [x] `fd-eq x y`, `fd-neq x y`, `fd-lt`, `fd-lte` — propagator-store
goals. Each adds a closure to the constraints field and runs it
on post; closures re-fire after every label step via fd-fire-store.
- [x] `fd-plus x y z`, `fd-times x y z` — ground-cases propagators
(when 2 of 3 walk to numbers, the third is derived).
- [x] `fd-distinct vars` — pairwise alldifferent via fd-neq folds.
- [x] Constraint reactivation: `fd-fire-store` iterates to fixed point
using a domain+bindings signature comparison; ensures multi-step
propagation chains (e.g. fd-plus binds a fresh var, which then
lets a downstream fd-neq fire).
- [x] Labelling: `fd-label vars` enumerates each var's domain via
mk-mplus over singleton bindings; constraint store re-fires after
each binding.
- [x] Tests: N-queens via FD — 4-queens finds both solutions, 5-queens
finds all 10 in seconds (vs the naive enumerate-then-filter
version which times out past N=4).
- [x] `ino` `x` `domain` — alias for `(membero x domain)` (kept for
the simple enumerate-then-filter pattern alongside fd-in).
- [x] `all-distincto` `l` — original membero-based version (kept alongside
the newer fd-distinct).
- [ ] `fd-eq` `x` `y` — x = y (constraint propagation)
- [ ] `fd-neq` `x` `y` — x ≠ y
- [ ] `fd-lt` `fd-lte` `fd-gt` `fd-gte` — ordering constraints
@@ -122,10 +180,22 @@ Key semantic mappings:
- [ ] Tests: send-more-money, N-queens with CLP(FD), map coloring, cryptarithmetic
### Phase 7 — tabling (memoization of relations)
- [ ] `tabled` annotation: memoize calls to a relation using a hash table
- [ ] Prevents infinite loops in recursive relations like `patho` on cyclic graphs
- [ ] Producer/consumer scheduling for tabled relations (variant of SLG resolution)
- [ ] Tests: cyclic graph reachability, mutual recursion, Fibonacci via tabling
- [x] `table-1`, `table-2`, `table-3` wrappers: ground-arg memoization
for 1-, 2-, and 3-argument relations.
- [x] `table-2` wrapper: ground-arg memoization for 2-arg relations.
Cache keyed by walked input; on miss runs underlying relation,
collects all output values from the answer stream, stores, and
replays. Subsequent calls with the same ground input replay the
cached values (no recomputation).
- [x] Fibonacci canary green: tabled `fib(25) = 75025` in seconds;
naive `fib(25)` times out at 60s. Memoization turns exponential
recursion into linear.
- [x] Ackermann canary green via `table-3`: `A(3, 3) = 61`.
- [ ] Producer/consumer SLG scheduling — required to handle recursive
tabled calls with the SAME ground key (e.g. cyclic `patho` with a
shared key); naive memoization deferred to a future iteration.
- [ ] Tests: cyclic graph reachability via tabled patho (deferred —
requires SLG); mutual recursion (deferred).
## Blockers
@@ -135,4 +205,242 @@ _(none yet)_
_Newest first._
_(awaiting phase 1)_
- **2026-05-08** — **Session snapshot**: 17 lib files, 61 test files, 1229
library LOC + 4360 test LOC, **551/551 tests cumulative**. Library covers
Phases 15 fully, Phase 6 partial (FD helpers + intarith escape), Phase 7
documented via cyclic-graph divergence test. lib-guest validation
completed: `lib/minikanren/unify.sx` ≈ 50 LOC of local logic over
`lib/guest/match.sx`'s ≈100 LOC kit (kit earns ~3× by line count). Major
classic miniKanren tests green: appendo forwards/backwards, Peano
arithmetic, 4-queens, Pythagorean triples, family-relations / pet
puzzle / symbolic differentiation, 2x2 Latin square. Ready for Phase 6
(native FD with arc-consistency) and Phase 7 (tabling) as future work.
- **2026-05-08** — **zip-with-o**: element-wise relational combine over two
lists with a 3-arg combiner. Ground-only by composition. 5 new tests.
- **2026-05-08** — **take-while-o + drop-while-o**: predicate-driven
prefix/suffix split. Roundtrip property verified. 8 new tests.
- **2026-05-08** — **arith-progo**: arithmetic-progression list generator
via project. 6 new tests.
- **2026-05-08** — **counto**: count occurrences of x in l (intarith).
6 new tests.
- **2026-05-08** — **nub-o**: dedupe via membero-on-tail. Multiplicity
caveat documented in tests. 5 new tests.
- **2026-05-08** — **simplify-step-o**: algebraic identity simplifier
(conda demo). 6 new tests.
- **2026-05-08** — **flat-mapo**: concatMap-style relation. 5 new tests.
- **2026-05-08** — **foldl-o (relational left fold)**: complement to foldr-o. Combiner has args (acc, head) -> new-acc. (foldl-o pluso-i (1 2 3 4 5) 0 q) -> 15; (foldl-o flipped-conso l () q) reverses l. 5 new tests, 510/510 cumulative.
- **2026-05-08** — **foldr-o (relational right fold)**: takes a 3-arg combiner relation rel, a list, an initial accumulator, produces the result. (foldr-o appendo lists () q) is a flatten; (foldr-o conso l () q) rebuilds l. 4 new tests, 505/505 cumulative.
- **2026-05-08** — **enumerate-i / enumerate-from-i — 500-test milestone**: index-each-element relations. (enumerate-i l result) -> result is l with each element paired with its 0-based index. (enumerate-from-i n l result) starts at n. 5 new tests, **501/501** cumulative.
- **2026-05-08** — **partitiono**: relational partition. (partitiono pred l yes no) splits l so yes contains elements where pred succeeds and no contains the rest. Composes with intarith for numeric predicates. 5 new tests, 496/496 cumulative.
- **2026-05-08** — **appendo3**: 3-list append via two appendos. (appendo3 a b c r) is (appendo a b mid) ∧ (appendo mid c r). Recovers any of the three lists given the other two and the result. 5 new tests, 491/491 cumulative.
- **2026-05-08** — **lengtho-i**: integer-indexed length (intarith). Empty list -> 0; recurse with pluso-i. Drop-in fast replacement for Peano lengtho when the count fits in a host integer. 5 new tests, 486/486 cumulative.
- **2026-05-08** — **sumo + producto (intarith)**: fold a list of ground integers to its sum or product. Empty list -> identity (0 / 1). Recurse via pluso-i / *o-i. 9 new tests, 481/481 cumulative.
- **2026-05-08** — **mino + maxo (intarith)**: find the minimum/maximum of a non-empty list of ground integers. Two conde clauses each: singleton (return the element) / multi (compare head against recursive min/max of tail). 9 new tests, 472/472 cumulative.
- **2026-05-08** — **sortedo (intarith)**: list is non-decreasing under integer ordering. Three conde clauses: empty / singleton / pair-and-recurse. Uses lteo-i for the adjacent-pair check (ground integers). 7 new tests, 463/463 cumulative.
- **2026-05-08** — **subseto**: every element of l1 is a member of l2. Recurses on l1, checking each element via membero. Allows duplicates in l1 (each independently in l2). 7 new tests, 456/456 cumulative.
- **2026-05-08** — **cycle-free path search**: mitigation for the cyclic-graph divergence — thread a accumulator through the recursion, gate each step with nafc + membero on visited. Terminates on graphs with cycles; no Phase-7 tabling required for the simple case. 3 new tests, 449/449 cumulative.
- **2026-05-08** — **removeo-allo**: removes every occurrence of x (vs rembero, which removes only the first). Three conde clauses: empty -> empty; head matches -> skip and recurse; head differs (nafc) -> keep and recurse. 5 new tests, 446/446 cumulative.
- **2026-05-08** — **btree-walko (matche showcase)**: walks a binary tree (:leaf v) | (:node l r) and emits each leaf value via conde. Demonstrates matche dispatch on tagged-list patterns, recursion through both branches via conde, and run* enumerating all 5 leaves of a small tree. 4 new tests, 441/441 cumulative.
- **2026-05-08** — **swap-firsto**: swap the first two elements of a list. Built via four conso constraints. Self-inverse on length-2+ lists; runs forward and backward. 6 new tests, 437/437 cumulative.
- **2026-05-08** — **pairlisto**: relational zip — pairs is the zipped list of (l1[i] l2[i]). Runs forward, recovers l1 given l2 and pairs, recovers l2 given l1 and pairs. 5 new tests, 431/431 cumulative.
- **2026-05-08** — **iterate-no**: relational iterated application. Applies a 2-arg relation n times (Peano n) starting from x to produce result. Generalises succ-iteration / list-cons-iteration / etc. 4 new tests, 426/426 cumulative.
- **2026-05-08** — **rev-acco / rev-2o**: accumulator-style reversal — faster than appendo-driven reverseo for forward queries because no quadratic appendos. Trade-off: rev-acco is asymmetric (cannot run cleanly backward in run*). 6 new tests, 422/422 cumulative.
- **2026-05-08** — **even-i / odd-i (intarith)**: ground-only parity goals via project. Composes with membero for filtered enumeration: -> . 5 new tests, 416/416 cumulative.
- **2026-05-08** — **selecto**: classic miniKanren "choose an element + rest". Direct base (l = (x . rest)) plus skip-head recurse. Enumerates all (element, rest) splits in run*; runs forward, backward, mid-pipeline. 6 new tests, 411/411 cumulative.
- **2026-05-08** — **subo (contiguous sublist)**: Two appendos chained — l = front ++ s ++ back. Goal order matters: appendo on the ground l first, so the search is finitary; then constrain front. 7 new tests, 405/405 cumulative.
- **2026-05-08** — **prefixo + suffixo**: classic appendo-derived sublist relations. (prefixo p l) ≡ p ⊕ ? = l; (suffixo s l) ≡ ? ⊕ s = l. Both enumerate all prefixes/suffixes when given a fresh first arg. 9 new tests, 398/398 cumulative.
- **2026-05-08** — **palindromeo**: 2-line definition (reverseo + ==). Succeeds when a list reads the same forwards and backwards. 7 new tests, 389/389 cumulative.
- **2026-05-08** — **not-membero**: relational "x is not a member of l".
Uses `nafc + ==` per element (the same skeleton all-distincto uses).
Useful as a constraint-style filter: `(membero x dom) (not-membero x
excluded)`. 4 new tests, 382/382 cumulative.
- **2026-05-08** — **repeato + concato**: repeato builds a list of n copies
(Peano n); concato is fold-appendo over a list of lists. Both run forward
and backward — repeato can recover the count from a uniform list. 10 new
tests, 378/378 cumulative.
- **2026-05-08** — **tako + dropo (Peano-indexed prefix/suffix)**: takes / drops
the first n elements via a Peano-encoded count. Round-trip
`(tako n l) ⊕ (dropo n l) = l` holds. 9 new tests, 368/368 cumulative.
- **2026-05-08** — **eveno / oddo Peano predicates**: classic miniKanren parity
relations. eveno: 0 or successor-of-successor of even; oddo: 1 or
successor-of-successor of odd. Both run forward (test) and backward
(enumerate). 12 new tests, 359/359 cumulative.
- **2026-05-08** — **defrel — Prolog-style relation definition macro**:
`(defrel (NAME ARGS...) (CLAUSE1 ...) (CLAUSE2 ...) ...)` expands to
`(define NAME (fn (ARGS...) (conde (CLAUSE1 ...) (CLAUSE2 ...) ...)))`.
Mirrors Prolog's clause syntax and inherits Zzz-via-conde so recursive
relations terminate. 3 new tests, 347/347 cumulative.
- **2026-05-08** — **lasto / init-o**: classic head/tail-style list relations.
lasto extracts the final element; init-o extracts everything-but-the-last.
Together with appendo, the round-trip `init ⊕ (last) = l` holds. 8 new
tests, 344/344 cumulative.
- **2026-05-08** — **Datalog-style relational database queries**: tests/rdb.sx
shows miniKanren as a query engine over fact tables. Defines two tables
(employees + project assignments), wraps each with a relation that does
membero over the table, then expresses queries: dept filter, salary >
threshold (intarith), join engineers ↔ runtime project, find anyone on
multiple distinct projects (nafc + ==). 5 new tests, 336/336 cumulative.
- **2026-05-08** — **Cyclic graph behaviour test (motivates Phase 7 tabling)**:
Demonstrates that naive patho on a 2-cycle generates ever-longer paths.
`run 5` truncates to a finite prefix; `run*` would diverge. This is
exactly the test case Phase 7 (tabled / SLG resolution) is designed
to fix. 3 new tests, 331/331 cumulative.
- **2026-05-08** — **numbero / stringo / symbolo (type predicates)**: ground-only
type tests via project. Compose with `membero` for type-filtered enumeration:
`(fresh (x) (membero x (1 "a" 2 "b" 3)) (numbero x) (== q x))``(1 2 3)`.
Note: SX keywords are strings, so `(stringo :k)` succeeds. 12 new tests,
328/328 cumulative.
- **2026-05-08** — **Graph reachability via patho**: classic miniKanren
graph search. `edgeo` looks up edges in a fact list via `membero`; `patho`
recursively builds paths via direct-edge OR (one edge + recurse + cons).
Enumerates all paths between two nodes, including alternates through
shortcuts. 6 new tests, 316/316 cumulative.
- **2026-05-08** — **everyo / someo (predicate-style relations)**:
`(everyo rel l)` — every element of l satisfies rel; `(someo rel l)`
some element does. Both compose with intarith for numeric tests:
`(everyo (fn (x) (lto-i x 10)) (list 1 5 9))` succeeds. 10 new tests,
310/310 cumulative.
- **2026-05-08** — **mapo (relational map) — 300 test milestone**: `(mapo
rel l1 l2)` succeeds when l2 is l1 with each element rel-related. Works
forward and backward; composes with intarith — `(mapo (fn (a b) (*o-i
a a b)) (1 2 3 4) q)` → `((1 4 9 16))`. 7 new tests, **300/300** cumulative.
- **2026-05-08** — **samelengtho**: classic miniKanren relation that
succeeds when two lists have equal length. Symmetric — works to enumerate
both lists fresh: `(run 3 q (fresh (l1 l2) (samelengtho l1 l2) (== q
(list l1 l2))))` produces empty/empty, then 1-elem pairs, then 2-elem.
5 new tests, 293/293 cumulative.
- **2026-05-08** — **Pythagorean triples (intarith showcase)**: search for
(a, b, c) ∈ [1..10]³, a ≤ b, a² + b² = c² via `ino + lteo-i + *o-i +
pluso-i + ==`. Finds exactly `(3 4 5)` and `(6 8 10)`. Demonstrates the
enumerate-then-filter pattern with intarith escape into host arithmetic.
1 new test, 288/288 cumulative.
- **2026-05-08** — **intarith.sx — fast ground-only integer arithmetic**:
pluso-i / minuso-i / *o-i / lto-i / lteo-i / neqo-i wrap host arithmetic
via `project`. They are not relational like Peano `pluso` (require args
to walk to numbers), but run at native host speed — a viable escape
hatch when puzzle size makes Peano impractical. Composes with relational
goals: `(membero x dom) (lto-i x 3)` filters dom by `< 3`. 18 new tests,
287/287 cumulative.
- **2026-05-08** — **2x2 Latin square**: small classic constraint demo using
`ino` + 4 `all-distincto` constraints. Enumerates exactly 2 squares
(`((1 2)(2 1))` and `((2 1)(1 2))`); a clue (top-left = 1) narrows to one.
3 new tests, 269/269 cumulative. Note: 3x3 (12 squares) is the natural
showcase but too slow under naive enumerate-then-filter — needs Phase 6
arc-consistency.
- **2026-05-08** — **rembero / assoco / nth-o**: more standard list relations.
rembero removes the first occurrence (uses `nafc (== a x)` to gate the
skip clause, so it's well-defined on ground lists). assoco is alist
lookup — works forward (key → value) and backward (value → key). nth-o
uses Peano indices into a list. 13 new tests, 266/266 cumulative.
- **2026-05-08** — **flatteno**: nested-list flattener via conde + appendo.
Atom-ness is detected via `nafc (nullo ...) + nafc (pairo ...)` so the
third clause only fires when the input is a ground non-list. Works for
`()` / atoms / flat lists / arbitrarily-nested lists. 7 new tests,
253/253 cumulative. Phase 4 list relations all complete.
- **2026-05-08** — **Laziness tests**: explicitly verifies the
Zzz-on-conde-clauses + mk-mplus-swap-on-paused machinery: an
infinitely-recursive relation truncated via `run 4 q (listo-aux q)`
produces exactly `(() (_.0) (_.0 _.1) (_.0 _.1 _.2))`; mixing two
infinite generators via `mk-disj` keeps both alive (no starvation);
`run*` terminates on a bounded query. 3 new tests, 246/246 cumulative.
- **2026-05-08** — **N-queens (classic miniKanren benchmark green)**:
`lib/minikanren/queens.sx`. Encoding cols(i) = column of queen in row i;
`ino-each` + `all-distincto` cover row/column constraints; `safe-diag`
uses `project` to escape into host arithmetic for the `|c_i - c_j| ≠
|i - j|` diagonal check; `all-cells-safe` walks pairs at construction
time. `(run* q (fresh (a b c d) (== q (list a b c d)) (queens-cols
(list a b c d) 4)))` returns the two valid 4-queens placements
`(2 4 1 3)` and `(3 1 4 2)`. 6 new tests, 243/243 cumulative.
- **2026-05-08** — **Phase 6 piece A — minimal FD (ino + all-distincto)**:
`lib/minikanren/fd.sx`. `ino` is `membero` with the FD-style argument
order; `all-distincto` is `nafc + membero` walking the list. Together
they cover the enumerate-then-filter style of finite-domain solving —
`(fresh (a b c) (ino a D) (ino b D) (ino c D) (all-distincto (list a b c)))`
enumerates all distinct triples from D. Full FD with arc-consistency,
fd-plus etc. is still pending. 9 new tests, 237/237 cumulative.
- **2026-05-08** — **Classic puzzles + matche keyword fix**: matche now emits
keywords bare in the pattern->expr conversion so they self-evaluate to their
string name and unify with the same-keyword target value (instead of becoming
a quoted-keyword type). New `tests/classics.sx`: pet permutation puzzle,
parent/grandparent inference over a fact list, symbolic differentiation
driven by matche dispatch on `:x` / `(:+ a b)` / `(:* a b)` patterns.
6 new tests, 228/228 cumulative.
- **2026-05-08** — **Phase 5 piece D — matche, Phase 5 done**: pattern matching
macro (`lib/minikanren/matche.sx`) — symbols become fresh vars, atoms become
literals, lists recurse positionally, repeated names unify. 14 new tests
(literals, vars, wildcards, list patterns, multi-clause dispatch, nested
patterns, repeated-var-implies-eq). Built via `cons`/`list` rather than
quasiquote because SX's quasiquote does not recurse into lambda bodies — a
worth-knowing gotcha. 222/222 cumulative.
- **2026-05-08** — **Phase 4 piece C — permuteo + inserto**: standard recursive
insert-at-any-position + permute-tail. 7 new tests, including all-6-perms-of-3
as a set check. 208/208 cumulative.
- **2026-05-07** — **Phase 5 piece C — nafc**: `lib/minikanren/nafc.sx`. Three-line
primitive: stream-take 1; if empty, `(unit s)`, else `mzero`. 7 tests including
double-negation and use as a guard. 201/201 cumulative.
- **2026-05-07** — **Phase 5 piece B — project**: `lib/minikanren/project.sx` —
defmacro that walks each named var, rebinds them, and runs the body's mk-conj.
Demonstrated escape into host arithmetic / string ops (`(* n n)`, `(str s "!")`).
Hygienic gensym'd s-param. 6 new tests, 194/194 cumulative.
- **2026-05-07** — **Peano arithmetic** (`lib/minikanren/peano.sx`): zeroo, pluso,
minuso, lteo, lto, *o on Peano-encoded naturals (`:z` / `(:s n)`). pluso runs
forward, backward, and enumerates: `(run* q (fresh (a b) (pluso a b 3)
(== q (list a b))))` → all 4 pairs summing to 3. *o uses repeated pluso —
works for small inputs, slower for larger. 19 new tests, 188/188 cumulative.
- **2026-05-07** — **Phase 5 piece A — conda**: soft-cut. Mirrors `condu` minus
the `onceo` on the head: all head answers are conjuncted through the rest of
the chosen clause. 7 new tests including the conda-vs-condu divergence test.
169/169 cumulative.
- **2026-05-07** — **Phase 4 piece B — reverseo + lengtho**: reverseo runs forward
cleanly and `run 1`-cleanly backward; lengtho uses Peano-encoded lengths so it
works as a true relation in both directions (tests use the encoding directly).
10 new tests, 162/162 cumulative.
- **2026-05-07** — **Phase 4 piece A — appendo canary green**: cons-cell support
in `unify.sx` + `(:s head tail)` lazy stream refactor in `stream.sx` + hygienic
`Zzz` (gensym'd subst-name) wrapping each `conde` clause + `lib/minikanren/
relations.sx` with `nullo` / `pairo` / `caro` / `cdro` / `conso` / `firsto` /
`resto` / `listo` / `appendo` / `membero`. 25 new tests in `tests/relations.sx`,
152/152 cumulative.
- **Three deep fixes shipped together**, all required to make `appendo`
terminate in both directions:
1. SX has no improper pairs, so a stream cell of mature subst + thunk
tail can't use `cons` — moved to a `(:s head tail)` tagged shape.
2. `(Zzz g)` wrapped its inner fn in a parameter named `s`, capturing
the user goal's own `s` binding (the `(appendo l s ls)` convention).
Replaced with `(gensym "zzz-s-")` for hygiene.
3. SX cons cells `(:cons h t)` for relational decomposition (so
`(conso a d l)` can split a list by head/tail without proper
improper pairs); `mk-walk*` re-flattens cons cells back to native
lists for clean reification output.
- **2026-05-07** — **Phase 3 done** (run + reification): `lib/minikanren/run.sx` (~28 lines).
`reify`/`reify-s`/`reify-name` for canonical `_.N` rendering of unbound vars in
left-to-right occurrence order; `run*` / `run` / `run-n` defmacros. 18 new tests
in `tests/run.sx`, including the **first classic miniKanren tests green**:
`(run* q (== q 1))` → `(1)`; `(run* q (fresh (x y) (== q (list x y))))` →
`((_.0 _.1))`. 128/128 cumulative.
- **2026-05-07** — **Phase 2 piece D + done** (`condu` / `onceo`): `lib/minikanren/condu.sx`.
Both are commitment forms: `onceo` is `(stream-take 1 ...)`; `condu` walks clauses
and commits the first one whose head produces an answer. 10 tests in `tests/condu.sx`,
110/110 cumulative. Phase 2 complete — ready for Phase 3 (run + reification).
- **2026-05-07** — **Phase 2 piece C** (`conde`): `lib/minikanren/conde.sx` — single
defmacro folding clauses through `mk-disj` with internal `mk-conj`. 9 tests in
`tests/conde.sx`, 100/100 cumulative. Confirmed eager DFS ordering for ==-only
streams; true interleaving is a Phase 4 concern (paused thunks under recursion).
- **2026-05-07** — **Phase 2 piece B** (`fresh`): `lib/minikanren/fresh.sx` (~10 lines).
defmacro form for nice user-facing syntax + `call-fresh` for programmatic use.
9 new tests in `tests/fresh.sx`, 91/91 cumulative.
- **2026-05-07** — **Phase 2 piece A** (streams + ==/conj/disj): `lib/minikanren/stream.sx`
(mzero/unit/mk-mplus/mk-bind/stream-take, ~25 lines of code) + `lib/minikanren/goals.sx`
(succeed/fail/==/==-check/conj2/disj2/mk-conj/mk-disj, ~30 lines). Found and noted
a host-primitive name clash: `bind` is built in and silently shadows user defines —
must use `mk-bind`/`mk-mplus` etc. throughout. 34 tests in `tests/goals.sx`,
82/82 cumulative all green. fresh/conde/condu/onceo still pending.
- **2026-05-07** — **Phase 1 done**: `lib/minikanren/unify.sx` (53 lines, ~22 lines of actual code) +
`lib/minikanren/tests/unify.sx` (48 tests, all green). Kit consumption: `walk-with`,
`unify-with`, `occurs-with`, `extend`, `empty-subst`, `mk-var`, `is-var?`, `var-name`
all supplied by `lib/guest/match.sx`. Local additions: a miniKanren-flavoured cfg
(treats native SX lists as cons-pairs via `:ctor-head = :pair`, occurs-check off),
`make-var` fresh-counter, deep `mk-walk*` (kit's `walk*` only recurses into `:ctor`
form, not native lists), and `mk-unify` / `mk-unify-check` thin wrappers. The kit
earns its keep ~3× over by line count — confirms lib-guest match kit is reusable
for logic-language hosts as designed.