fd-in x dom-list: narrows x's domain. If x is a ground number, checks
membership; if x is a logic var, intersects existing domain (or sets
fresh) and stores via fd-set-domain. Fails if domain becomes empty.
fd-label vars: drives search by enumerating each var's domain. Each
var is unified with each value in its domain, in order, via mk-mplus
of singleton streams.
Forward: (fd-in x dom) (fd-label (list x)) iterates x over dom.
Intersection: two fd-in goals on the same var compose via dom-intersect.
Disjoint domains -> empty answer set. Ground value membership check
gates pass/fail. Composes with the rest of the miniKanren machinery —
fresh / conde / membero etc. all work alongside.
9 new tests, 586/586 cumulative.
Foundation for native CLP(FD). The substitution dict carries a reserved
"_fd" key holding a constraint store:
{:domains {var-name -> sorted-int-list}
:constraints (... pending constraints ...)}
This commit ships only the domain machinery + accessors:
fd-dom-from-list / fd-dom-range / fd-dom-empty? / fd-dom-singleton?
fd-dom-min / fd-dom-max / fd-dom-member? / fd-dom-intersect /
fd-dom-without
fd-store-of / fd-domain-of / fd-set-domain / fd-with-store
fd-set-domain returns nil when the domain becomes empty (failure),
which is the wire signal subsequent constraint goals will consume.
The constraints field is reserved for the next iteration.
26 new tests, 577/577 cumulative.
Capture the current state: 17 library files (1229 LOC), 61 test files
(4360 LOC), 551/551 tests passing. Phases 1-5 fully done; Phase 6
covered by minimal FD (ino, all-distincto) plus an intarith escape
hatch; Phase 7 documented via the cyclic-graph divergence test as
motivation for future tabling work.
The lib-guest validation experiment is conclusive: lib/minikanren/
unify.sx adds ~50 lines of local logic over lib/guest/match.sx's
~100-line kit. The kit earns its keep at roughly 3x by line count.
Classic miniKanren tests green: appendo forwards/backwards, Peano
arithmetic enumeration (pluso, *o, lto), 4-queens (both solutions),
Pythagorean triples, family-relation inference, symbolic
differentiation, pet/colour permutation puzzle, Latin square 2x2,
binary tree walker.
(take-while-o pred l result): take elements from l while pred holds,
stopping at the first element that fails. (drop-while-o pred l result):
drop matching elements, return the rest including the first non-match.
Together: (take-while p l) ⊕ (drop-while p l) = l, verified by an
end-to-end roundtrip test.
8 new tests, 546/546 cumulative.
(arith-progo start step len result): result is the list
(start, start+step, ..., start+(len-1)*step). Length 0 yields the
empty list. Negative steps and zero step are supported.
Useful for FD-style domain construction:
(arith-progo 1 1 9 dom) -> (1 2 3 4 5 6 7 8 9)
6 new tests, 538/538 cumulative.
Walks the list with a recursive count. On a head match, recurse and
add 1 via pluso-i; on no match (nafc), recurse forwarding the count.
Empty list yields 0.
6 new tests, 532/532 cumulative.
Walks the list; if the head appears in the tail (membero), drop it and
recurse; otherwise keep it and recurse. Result preserves only the
*last* occurrence of each value.
Caveat: with input like (1 1 1) the membero check succeeds with
multiplicity, so multiple (1) answers may emerge — each is shape-
identical, but the test deliberately checks every-result-is-(1) rather
than asserting answer count.
5 new tests, 526/526 cumulative.
Demonstrates conda for first-match-wins dispatch over a set of rewrite
rules: 0+x = x, x+0 = x, 0*y = 0, x*0 = 0, 1*x = x, x*1 = x, default
unchanged.
Six rules + a fall-through default, all wrapped in a single conda. The
first clause whose head succeeds commits to that rewrite. The fall-
through default ensures the relation always succeeds with at least the
unchanged input.
6 new tests, 521/521 cumulative.
(flat-mapo rel l result): each element x of l is mapped to a list via
rel x list-from-x, and all such lists are concatenated to form result.
(flat-mapo (fn (x r) (== r (list x x))) (list 1 2 3) q)
-> ((1 1 2 2 3 3))
5 new tests, 515/515 cumulative.
(enumerate-i l result): result is l with each element paired with its
0-based index. (enumerate-from-i n l result): same but starts at n.
(enumerate-i (list :a :b :c) q) -> (((0 :a) (1 :b) (2 :c)))
5 new tests, 501/501 cumulative.
(partitiono pred l yes no) — yes is the elements of l where pred
succeeds; no is the rest. Conde dispatches on each element via the
predicate goal vs nafc-of-the-predicate, threading the head through
the matching output list.
Composes with intarith / membero / etc. for any predicate-shaped goal:
(partitiono (fn (x) (lto-i x 5)) (list 1 7 2 8 3) yes no)
yes -> (1 2 3); no -> (7 8)
5 new tests, 496/496 cumulative.
Composes two appendos: (appendo a b mid) ∧ (appendo mid c r). Runs
forward (concatenate three known lists) and backward (recover any of
the three from the other two and the result).
5 new tests, 491/491 cumulative.
Drop-in fast replacement for Peano lengtho when the count fits in a
host integer. Two conde clauses: empty list -> 0; recurse, n = 1 +
length(tail). Uses pluso-i so the length walks to a native int.
5 new tests, 486/486 cumulative.
Sum and product over a list of ground integers via fold + intarith.
Empty list yields the identity (0 for sum, 1 for product). Recurse
combines the head with the recursively-computed tail value via
pluso-i / *o-i.
9 new tests, 481/481 cumulative.
Two conde clauses each: singleton -> the element; multi -> compare head
against the recursive min/max of the tail and pick. Uses lteo-i / lto-i
for the comparisons, so the input must be ground integers.
mino + maxo can run together: (fresh (mn mx) (mino l mn) (maxo l mx)
(== q (list mn mx))) recovers both.
9 new tests, 472/472 cumulative.
Three conde clauses: empty list / singleton list / two-or-more (where
the first two satisfy lteo-i and the rest is recursively sorted). Uses
ground-only integer comparison (intarith), so the input list must
walk to ground integers.
7 new tests, 463/463 cumulative.
Recursive: empty l1 trivially holds; otherwise the head is in l2 (via
membero) and the tail is a subset. Duplicates in l1 are allowed since
each is independently checked.
7 new tests, 456/456 cumulative.
Mitigation for the cyclic-graph divergence (see tests/cyclic-graph.sx).
Threads a `visited` accumulator through the recursion; each candidate
next-step is gated by `nafc (membero z visited)`. Terminates on graphs
with cycles, no Phase-7 tabling required for the simple acyclic-path
query.
Demonstrates a viable alternative to tabling for the common case where
the user wants finite path enumeration over a graph with cycles.
3 new tests, 449/449 cumulative.
Three conde clauses: empty list -> empty result; head matches x ->
skip and recurse; head differs (nafc-gated) -> keep and recurse.
Distinct from rembero, which removes only the first occurrence.
5 new tests, 446/446 cumulative.
Demo of matche dispatch + conde + recursion for tree traversal:
(matche tree
((:leaf x) (== v x))
((:node l r) (conde ((btree-walko l v)) ((btree-walko r v)))))
Test tree ((1 2) (3 (4 5))) yields all 5 leaves under run*. Also tests
membership (run 1) and absence.
4 new tests, 441/441 cumulative.
Four conso calls express the (a b . rest) -> (b a . rest) rewrite as a
purely relational constraint. Self-inverse on length-2+ lists; runs
forward (swap given input) and backward (recover original from the
swapped form). Fails on lists shorter than 2.
6 new tests, 437/437 cumulative.
(pairlisto l1 l2 pairs): pairs is the zipped list of pairs (l1[i] l2[i]).
Recurses on both l1 and l2 in lockstep, building pairs in parallel.
Runs forward, can recover l1 given l2 and pairs, can recover l2 given
l1 and pairs. Different-length lists fail.
5 new tests, 431/431 cumulative.
(iterate-no rel n x result) holds when applying the 2-arg relation rel
n times (Peano n) starting from x produces result. Base case: zero
iterations means result equals x. Recursive case: rel x mid, then
iterate-no n-1 from mid.
Generalises common chains:
succ iteration: (iterate-no succ-rel n :z q) -> n in Peano
list growth: (iterate-no cons-rel n () q) -> n-element list
4 new tests, 426/426 cumulative.
rev-acco is the standard tail-recursive reverse with an accumulator;
rev-2o starts the accumulator at the empty list. Faster than the
appendo-driven reverseo for forward queries because there is no nested
appendo per element.
Trade-off: rev-acco is asymmetric. The accumulator's initial-empty
cannot be enumerated backwards the way reverseo does, so reverseo is
still the right choice when both directions matter.
A test verifies rev-2o and reverseo agree on forward queries.
6 new tests, 422/422 cumulative.
Classic miniKanren relation. (selecto x rest l) holds when l contains
x at any position with `rest` being everything else. Direct base case
(l = (x . rest)) plus the skip-head recursion that threads the head
through to the result rest.
Run modes: enumerate every (x, rest) split; recover rest given an
element; recover an element given the rest; (and ground/all combinations).
6 new tests, 411/411 cumulative.
Composes two appendos: l = front ++ s ++ back, equivalently
(appendo front-and-s back l) and (appendo front s front-and-s).
Goal order matters: doing the (appendo ground:l) split first makes the
search finitary; the second appendo is then deterministic given
front-and-s and ground s. Reversing the order causes divergence on
failing inputs (the front search becomes unbounded).
7 new tests, 405/405 cumulative.
Two-line definitions over appendo:
(prefixo p l) ≡ ∃rest. (appendo p rest l)
(suffixo s l) ≡ ∃front. (appendo front s l)
Both enumerate all prefixes/suffixes when called with a fresh first
arg, and serve as decision relations when called with both grounded.
9 new tests, 398/398 cumulative.
Two-line definition: a list is a palindrome iff it equals its reverse.
Direct composition of reverseo + ==.
7 new tests: empty / singleton / equal pair / unequal pair /
5-element-yes / 5-element-no / strings.
389/389 cumulative.
Mirrors the structure all-distincto already uses internally: walk the
list, ensure each element is not equal to x via nafc, recurse on tail.
Useful as a constraint-style filter:
(membero x (list 1 2 3 4 5))
(not-membero x (list 2 4))
-> x in {1, 3, 5}
4 new tests, 382/382 cumulative.
repeato: produces (or recognizes) a list of n copies of a value, with n
Peano-encoded. Runs forward, backward (recover the count from a uniform
list), and bidirectionally.
concato: fold-appendo over a list-of-lists. (concato (list (list 1 2)
(list) (list 3 4 5)) q) -> ((1 2 3 4 5)).
10 new tests, 378/378 cumulative.
(tako n l prefix) — prefix is the first n elements of l.
(dropo n l suffix) — suffix is l after dropping the first n.
Both use a Peano natural for the count. Round-trip holds:
(tako n l) ⊕ (dropo n l) = l (verified by an end-to-end test)
9 new tests, 368/368 cumulative.
eveno: zero, or (s (s m)) when m is even.
oddo: one, or (s (s m)) when m is odd.
Both run forward (predicate test on a Peano number) and backward
(enumerate even / odd numbers). The two are mutually exclusive — no
number satisfies both.
12 new tests, 359/359 cumulative.
(defrel (NAME ARGS...) (CLAUSE1 ...) (CLAUSE2 ...) ...) expands to
(define NAME (fn (ARGS...) (conde (CLAUSE1 ...) (CLAUSE2 ...) ...))).
Mirrors Prolog's `name(Args) :- goals.` shape. Inherits the Zzz-on-each-
clause laziness from conde, so user relations defined via defrel
terminate on partial answers without needing manual delay. Tests
redefine membero / listo / pluso through defrel and verify equivalence.
3 new tests, 347/347 cumulative.
lasto: x is the final element of l. Direct base case (l = (x)) plus
recurse-on-cdr.
init-o: init is l without its last element. Base case for singleton:
(== init ()). Otherwise recurse, threading the head through to the
init result via conso.
Together with appendo, the round-trip init append (list last) = l
holds, which is exercised by an end-to-end test.
8 new tests, 344/344 cumulative.
tests/rdb.sx shows the library as a small Datalog engine over fact
tables. Each table is an SX list of tuples, wrapped by a relation that
does (membero (list ...) table). Queries compose selection, projection,
and joins entirely in run* / fresh / conde / membero / intarith / nafc.
Five queries: dept filter, salary > threshold, employee-project join,
intersection (engineers on a specific project), anyone on multiple
distinct projects.
5 new tests, 336/336 cumulative.
Demonstrates the naive-patho behaviour on a 2-cycle (a <-> b, plus
b -> c). Without Phase-7 tabling, the search produces ever-longer
paths: (a b), (a b a b), (a b a b a b), ... `run 5` truncates to a
finite prefix; `run*` diverges. Documenting this as a regression-style
test gives Phase 7 a concrete starting point.
3 new tests, 331/331 cumulative.
Ground-only type tests via project. Each succeeds iff its argument
walks to the corresponding host value type. Composes with membero for
type-filtered enumeration:
(fresh (x) (membero x (list 1 "a" 2 "b" 3)) (numbero x) (== q x))
-> (1 2 3)
12 new tests, 328/328 cumulative. Caveat: SX keywords are strings, so
(stringo :k) succeeds.
Defines a small graph as a fact list, edgeo for fact lookup, and patho
that recursively constructs paths. Direct-edge clause yields (x y);
otherwise traverse one edge to z, recurse for z->y, prepend x.
Enumerates all paths between two nodes, including alternates through
shortcut edges:
(run* q (patho :a :d q))
-> ((:a :b :c :d) (:a :c :d)) ; both routes
6 new tests, 316/316 cumulative.
(everyo rel l): every element of l satisfies the unary relation rel.
(someo rel l): some element does. Both compose with intarith and other
predicate-shaped goals:
(everyo (fn (x) (lto-i x 10)) (list 1 5 9)) -> succeeds
(someo (fn (x) (lto-i 100 x)) (list 5 50 200)) -> succeeds
10 new tests, 310/310 cumulative.
(mapo rel l1 l2) takes a 2-argument relation rel and asserts l2 is l1
with each element rel-related to its counterpart. Recursive on both
lists in lockstep. Works forward (fixed l1, find l2), backward (fixed
l2, find l1), or constraining mid-pipeline.
Composes with intarith for arithmetic transforms:
(mapo (fn (a b) (*o-i a a b)) (list 1 2 3 4) q) -> ((1 4 9 16))
7 new tests, 300/300 cumulative.
Recurses positionally, dropping a head from each list each step. Both
arguments can be unbound, giving the natural enumeration:
(run 3 q (fresh (l1 l2) (samelengtho l1 l2) (== q (list l1 l2))))
-> (((), ()) empty/empty
((_.0), (_.1)) pair of 1-element lists
((_.0 _.1), (_.2 _.3))) pair of 2-element lists
5 new tests, 293/293 cumulative.
Finds all (a, b, c) with a, b, c in [1..10], a <= b, a^2 + b^2 = c^2.
Result: ((3 4 5) (6 8 10)) — the two smallest Pythagorean triples
within the domain.
Demonstrates the enumerate-then-filter pattern:
(ino a dom) (ino b dom) (ino c dom) — generate
(lteo-i a b) — symmetry break
(*o-i a a a-sq) (*o-i b b b-sq) (*o-i c c c-sq) — squares
(pluso-i a-sq b-sq sum) (== sum c-sq) — Pythagorean equation
288/288 cumulative.
pluso-i / minuso-i / *o-i / lto-i / lteo-i / neqo-i wrap host arithmetic
in project. They run at native speed but require their inputs to walk
to ground numbers — they are NOT relational the way Peano pluso is.
Use them when puzzle size makes Peano impractical (which is most cases
beyond toy examples).
Composes with relational goals — for instance,
(fresh (x) (membero x (1 2 3 4 5)) (lto-i x 3) (== q x))
filters the domain by < 3 and returns (1 2).
18 new tests, 287/287 cumulative.
Defines latin-2x2 over 4 cells and 4 all-distincto constraints. Enumerates
exactly 2 squares ((1 2)(2 1)) and ((2 1)(1 2)); a corner clue narrows to
one. 3 new tests, 269/269 cumulative.
3x3 (12 squares, the natural showcase) is too slow under naive enumerate-
then-filter — that is the motivating test for Phase 6 arc-consistency.
rembero (remove-first) uses nafc to gate the skip-element clause so
the result is well-defined on ground lists. assoco is alist lookup —
runs forward (key -> value) and backward (find keys with a given
value). nth-o uses Peano-encoded indices into a list, mirroring lengtho.
13 new tests, 266/266 cumulative.
