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Three coupled fixes plus a new relations module land together because
each is required for the next: appendo can't terminate without all
three.
1. unify.sx — added (:cons h t) tagged cons-cell shape because SX has no
improper pairs. The unifier treats (:cons h t) and the native list
(h . t) as equivalent. mk-walk* re-flattens cons cells back to flat
lists for clean reification.
2. stream.sx — switched mature stream cells from plain SX lists to a
(:s head tail) tagged shape so a mature head can have a thunk tail.
With the old representation, mk-mplus had to (cons head thunk) which
SX rejects (cons requires a list cdr).
3. conde.sx — wraps each clause in Zzz (inverse-eta delay) for laziness.
Zzz uses (gensym "zzz-s-") for the substitution parameter so it does
not capture user goals that follow the (l s ls) convention. Without
gensym, every relation that uses `s` as a list parameter silently
binds it to the substitution dict.
relations.sx is the new module: nullo, pairo, caro, cdro, conso,
firsto, resto, listo, appendo, membero. 25 new tests.
Canary green:
(run* q (appendo (list 1 2) (list 3 4) q))
→ ((1 2 3 4))
(run* q (fresh (l s) (appendo l s (list 1 2 3)) (== q (list l s))))
→ ((() (1 2 3)) ((1) (2 3)) ((1 2) (3)) ((1 2 3) ()))
(run 3 q (listo q))
→ (() (_.0) (_.0 _.1))
152/152 cumulative.
204 lines
12 KiB
Markdown
204 lines
12 KiB
Markdown
# miniKanren-on-SX: relational programming on the CEK/VM
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miniKanren is not a language to parse — it is an **embedded DSL** implemented as a library
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of SX functions. No tokenizer, no transpiler. The entire system is a set of `define` forms
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in `lib/minikanren/`. Programs are SX expressions using the miniKanren API.
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The unique angle: SX's delimited continuation machinery (`perform`/`cek-resume`, call/cc)
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maps almost perfectly to the search monad miniKanren needs. Backtracking is cooperative
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suspension, not a separate trail machine. This is the cleanest possible host for miniKanren.
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End-state goal: **full core miniKanren** (`run`, `fresh`, `==`, `conde`, `condu`, `onceo`,
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`project`, `matche`) + **core.logic-style relations** (`appendo`, `membero`, `listo`,
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`numbero`, etc.) + **arithmetic constraints** (`fd` domain, `CLP(FD)` subset).
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## Ground rules
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- **Scope:** only touch `lib/minikanren/**` and `plans/minikanren-on-sx.md`. Do **not**
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edit `spec/`, `hosts/`, `shared/`, or other `lib/<lang>/`.
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- **Shared-file issues** go under "Blockers" below with a minimal repro; do not fix here.
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- **SX files:** use `sx-tree` MCP tools only.
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- **Architecture:** pure library — no source parser. Programs are written in SX using the API.
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- **Reference:** *The Reasoned Schemer* (Friedman/Byrd/Kiselyov) + Byrd's dissertation.
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- **Commits:** one feature per commit. Keep `## Progress log` updated and tick boxes.
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## Architecture sketch
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```
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SX program using miniKanren API
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│
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├── lib/minikanren/unify.sx — terms, variables, walk, unification, occurs check
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├── lib/minikanren/substitution.sx — substitution as association list / hash table
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├── lib/minikanren/stream.sx — lazy streams of substitutions (via delay/force)
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├── lib/minikanren/goals.sx — == / fresh / conde / condu / onceo / project / matche
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├── lib/minikanren/run.sx — run* / run n — drive the search, extract answers
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├── lib/minikanren/relations.sx — standard relations: appendo, membero, listo, etc.
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└── lib/minikanren/clpfd.sx — arithmetic constraints (CLP(FD) subset)
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```
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Key semantic mappings:
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- **Logic variable** → SX vector of length 1 (mutable box); `make-var` creates fresh one;
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`walk` follows the substitution chain
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- **Substitution** → SX association list (or hash table for performance) mapping var → term
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- **Stream of substitutions** → lazy list using `delay`/`force` (Phase 9 of primitives)
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- **Goal** → SX function `substitution → stream-of-substitutions`
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- **`==`** → unifies two terms, extending substitution or failing (empty stream)
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- **`fresh`** → introduces new logic variables; `(fresh (x y) goal)` → goal with x, y bound
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- **`conde`** → interleave streams from multiple goal clauses (depth-first with interleaving)
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- **`run n`** → drive the stream, collect first n substitutions, reify answers
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## Roadmap
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### Phase 1 — variables + unification
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- [x] `make-var` → fresh logic variable (unique mutable box)
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- [x] `var?` `v` → bool — is this a logic variable?
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- [x] `walk` `term` `subst` → follow substitution chain to ground term or unbound var
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- [x] `walk*` `term` `subst` → deep walk (recurse into lists/dicts)
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- [x] `unify` `u` `v` `subst` → extended substitution or `#f` (failure)
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Handles: var/var, var/term, term/var, list unification, number/string/symbol equality.
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No occurs check by default; `unify-check` with occurs check as opt-in.
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- [x] Empty substitution `empty-s` (dict-based via kit's `empty-subst` — assoc list was a sketch; kit ships dict, kept it)
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- [x] Tests in `lib/minikanren/tests/unify.sx`: ground terms, vars, lists, failure, occurs
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### Phase 2 — streams + goals
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- [x] Stream type: `mzero` (empty), `unit s` (singleton), `mk-mplus` (interleave),
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`mk-bind` (apply goal to stream). Names mk-prefixed because SX has a host
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`bind` primitive that silently shadows user defines.
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- [x] Lazy streams via thunks: a paused stream is a zero-arg fn; mk-mplus suspends
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and swaps when its left operand is paused, giving fair interleaving.
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- [x] `==` goal: `(fn (s) (let ((s2 (mk-unify u v s))) (if s2 (unit s2) mzero)))`
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- [x] `==-check` — opt-in occurs-checked equality goal
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- [x] `succeed` / `fail` — trivial goals
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- [x] `conj2` / `mk-conj` (variadic) — sequential conjunction
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- [x] `disj2` / `mk-disj` (variadic) — interleaved disjunction (raw — `conde`
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adds the implicit-conj-per-clause sugar later)
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- [x] `fresh` — introduces logic variables inside a goal body. Implemented as a
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defmacro: `(fresh (x y) g1 g2 ...)` ⇒ `(let ((x (make-var)) (y (make-var)))
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(mk-conj g1 g2 ...))`. Also `call-fresh` for programmatic goal building.
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- [x] `conde` — sugar over disj+conj, one row per clause; defmacro that
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wraps each clause body in `mk-conj` and folds via `mk-disj`. Notes:
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with eager streams ordering is left-clause-first DFS; true interleaving
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requires paused thunks (Phase 4 recursive relations).
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- [x] `condu` — committed choice. defmacro folding clauses into a runtime
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`condu-try` walker; first clause whose head goal yields a non-empty
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stream commits its first answer, rest-goals run on that single subst.
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- [x] `onceo` — `(stream-take 1 (g s))`; trims a goal's stream to ≤1 answer.
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- [x] Tests: basic goal composition, backtracking, interleaving (110 cumulative)
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### Phase 3 — run + reification
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- [x] `run*` `goal` → list of all answers (reified). defmacro: bind q-name as
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fresh var, conj goals, take all from stream, reify each.
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- [x] `run n` `goal` → list of first n answers (defmacro; n = -1 means all)
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- [x] `reify` `term` `subst` → walk* + build reification subst + walk* again
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- [x] `reify-s` → maps each unbound var (in left-to-right walk order) to a
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`_.N` symbol via `(make-symbol (str "_." n))`
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- [x] `fresh` with multiple variables — already shipped Phase 2B.
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- [x] Query variable conventions: `q` as canonical query variable (matches TRS)
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- [x] Tests: classic miniKanren programs — `(run* q (== q 1))` → `(1)`,
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`(run* q (conde ((== q 1)) ((== q 2))))` → `(1 2)`,
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`(run* q (fresh (x y) (== q (list x y))))` → `((_.0 _.1))`. Peano +
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`appendo` deferred to Phase 4.
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### Phase 4 — standard relations
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- [x] `appendo` `l` `s` `ls` — list append, runs forwards AND backwards.
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Canary green: `(run* q (appendo (1 2) (3 4) q))` → `((1 2 3 4))`;
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`(run* q (fresh (l s) (appendo l s (1 2 3)) (== q (list l s))))` →
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all four splits.
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- [x] `membero` `x` `l` — enumerates: `(run* q (membero q (a b c)))` → `(a b c)`
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- [x] `listo` `l` — l is a proper list; enumerates list shapes with laziness
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- [x] `nullo` `l` — l is empty
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- [x] `pairo` `p` — p is a (non-empty) cons-cell / list
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- [x] `caro` / `cdro` / `conso` / `firsto` / `resto`
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- [ ] `reverseo` `l` `r` — reverse of list
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- [ ] `flatteno` `l` `f` — flatten nested lists
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- [ ] `permuteo` `l` `p` — permutation of list
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- [ ] `lengtho` `l` `n` — length as a relation (Peano or integer)
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- [x] Tests: run each relation forwards and backwards (so far 25 in
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`tests/relations.sx`; reverseo/flatteno/permuteo/lengtho deferred)
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### Phase 5 — `project` + `matche` + negation
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- [ ] `project` `(x ...) body` — access reified values of logic vars inside a goal;
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escapes to ground values for arithmetic or string ops
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- [ ] `matche` — pattern matching over logic terms (extension from core.logic)
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`(matche l ((head . tail) goal) (() goal))`
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- [ ] `conda` — soft-cut disjunction (like Prolog `->`)
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- [ ] `condu` — committed choice (already in phase 2; refine semantics here)
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- [ ] `nafc` — negation as finite failure with constraint
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- [ ] Tests: Zebra puzzle, N-queens, Sudoku via `project`, family relations via `matche`
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### Phase 6 — arithmetic constraints CLP(FD)
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- [ ] Finite domain variables: `fd-var` with domain `[lo..hi]`
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- [ ] `in` `x` `domain` — constrain x to domain
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- [ ] `fd-eq` `x` `y` — x = y (constraint propagation)
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- [ ] `fd-neq` `x` `y` — x ≠ y
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- [ ] `fd-lt` `fd-lte` `fd-gt` `fd-gte` — ordering constraints
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- [ ] `fd-plus` `x` `y` `z` — x + y = z (constraint)
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- [ ] `fd-times` `x` `y` `z` — x * y = z
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- [ ] Arc consistency propagation — when domain narrows, propagate to constrained vars
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- [ ] Labelling: `fd-run` drives search by splitting domains when propagation stalls
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- [ ] Tests: send-more-money, N-queens with CLP(FD), map coloring, cryptarithmetic
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### Phase 7 — tabling (memoization of relations)
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- [ ] `tabled` annotation: memoize calls to a relation using a hash table
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- [ ] Prevents infinite loops in recursive relations like `patho` on cyclic graphs
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- [ ] Producer/consumer scheduling for tabled relations (variant of SLG resolution)
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- [ ] Tests: cyclic graph reachability, mutual recursion, Fibonacci via tabling
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## Blockers
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_(none yet)_
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## Progress log
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_Newest first._
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- **2026-05-07** — **Phase 4 piece A — appendo canary green**: cons-cell support
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in `unify.sx` + `(:s head tail)` lazy stream refactor in `stream.sx` + hygienic
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`Zzz` (gensym'd subst-name) wrapping each `conde` clause + `lib/minikanren/
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relations.sx` with `nullo` / `pairo` / `caro` / `cdro` / `conso` / `firsto` /
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`resto` / `listo` / `appendo` / `membero`. 25 new tests in `tests/relations.sx`,
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152/152 cumulative.
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- **Three deep fixes shipped together**, all required to make `appendo`
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terminate in both directions:
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1. SX has no improper pairs, so a stream cell of mature subst + thunk
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tail can't use `cons` — moved to a `(:s head tail)` tagged shape.
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2. `(Zzz g)` wrapped its inner fn in a parameter named `s`, capturing
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the user goal's own `s` binding (the `(appendo l s ls)` convention).
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Replaced with `(gensym "zzz-s-")` for hygiene.
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3. SX cons cells `(:cons h t)` for relational decomposition (so
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`(conso a d l)` can split a list by head/tail without proper
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improper pairs); `mk-walk*` re-flattens cons cells back to native
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lists for clean reification output.
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- **2026-05-07** — **Phase 3 done** (run + reification): `lib/minikanren/run.sx` (~28 lines).
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`reify`/`reify-s`/`reify-name` for canonical `_.N` rendering of unbound vars in
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left-to-right occurrence order; `run*` / `run` / `run-n` defmacros. 18 new tests
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in `tests/run.sx`, including the **first classic miniKanren tests green**:
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`(run* q (== q 1))` → `(1)`; `(run* q (fresh (x y) (== q (list x y))))` →
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`((_.0 _.1))`. 128/128 cumulative.
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- **2026-05-07** — **Phase 2 piece D + done** (`condu` / `onceo`): `lib/minikanren/condu.sx`.
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Both are commitment forms: `onceo` is `(stream-take 1 ...)`; `condu` walks clauses
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and commits the first one whose head produces an answer. 10 tests in `tests/condu.sx`,
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110/110 cumulative. Phase 2 complete — ready for Phase 3 (run + reification).
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- **2026-05-07** — **Phase 2 piece C** (`conde`): `lib/minikanren/conde.sx` — single
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defmacro folding clauses through `mk-disj` with internal `mk-conj`. 9 tests in
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`tests/conde.sx`, 100/100 cumulative. Confirmed eager DFS ordering for ==-only
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streams; true interleaving is a Phase 4 concern (paused thunks under recursion).
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- **2026-05-07** — **Phase 2 piece B** (`fresh`): `lib/minikanren/fresh.sx` (~10 lines).
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defmacro form for nice user-facing syntax + `call-fresh` for programmatic use.
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9 new tests in `tests/fresh.sx`, 91/91 cumulative.
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- **2026-05-07** — **Phase 2 piece A** (streams + ==/conj/disj): `lib/minikanren/stream.sx`
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(mzero/unit/mk-mplus/mk-bind/stream-take, ~25 lines of code) + `lib/minikanren/goals.sx`
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(succeed/fail/==/==-check/conj2/disj2/mk-conj/mk-disj, ~30 lines). Found and noted
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a host-primitive name clash: `bind` is built in and silently shadows user defines —
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must use `mk-bind`/`mk-mplus` etc. throughout. 34 tests in `tests/goals.sx`,
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82/82 cumulative all green. fresh/conde/condu/onceo still pending.
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- **2026-05-07** — **Phase 1 done**: `lib/minikanren/unify.sx` (53 lines, ~22 lines of actual code) +
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`lib/minikanren/tests/unify.sx` (48 tests, all green). Kit consumption: `walk-with`,
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`unify-with`, `occurs-with`, `extend`, `empty-subst`, `mk-var`, `is-var?`, `var-name`
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all supplied by `lib/guest/match.sx`. Local additions: a miniKanren-flavoured cfg
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(treats native SX lists as cons-pairs via `:ctor-head = :pair`, occurs-check off),
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`make-var` fresh-counter, deep `mk-walk*` (kit's `walk*` only recurses into `:ctor`
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form, not native lists), and `mk-unify` / `mk-unify-check` thin wrappers. The kit
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earns its keep ~3× over by line count — confirms lib-guest match kit is reusable
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for logic-language hosts as designed.
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