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.
Two hardcoded paths returned the native marker regardless of user
override: js-invoke-function-method and the lambda branch of
js-to-string. Both now look up Function.prototype.toString via
js-dict-get-walk and invoke it on the function, falling back to
the native marker only if no override exists.
built-ins/String: 84/99 → 85/99. conformance.sh: 148/148.
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.
Per ES, Boolean.prototype is a Boolean wrapper around false,
Number.prototype wraps 0, String.prototype wraps "". So
Boolean.prototype == false (loose-eq unwraps), and
Object.prototype.toString.call(Number.prototype) ===
"[object Number]". Set __js_*_value__ on each in post-init.
built-ins/Boolean: 23/27 → 24/27, String: 80/99 → 84/99.
conformance.sh: 148/148.
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.
Mirrors the earlier js-to-string fix. Number(obj) must throw
if ToPrimitive cannot extract a primitive (both valueOf and
toString return objects). Was returning NaN silently. Replaced
the inner (js-nan-value) fallback with (raise (js-new-call
TypeError ...)).
built-ins/Number: 45/50 → 46/50. conformance.sh: 148/148.
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.
Three conde clauses: nullo tree -> nullo flat; pairo tree -> recurse on
car & cdr, appendo their flattenings; otherwise tree must be a ground
non-list atom (nafc nullo + nafc pairo) and flat = (list tree).
Works on ground inputs of arbitrary nesting:
(run* q (flatteno (list 1 (list 2 3) (list (list 4) 5)) q))
-> ((1 2 3 4 5))
7 tests, 253/253 cumulative. Phase 4 list relations now complete.
Verifies that the Zzz-wraps-each-conde-clause + mk-mplus-suspend-on-
paused-left machinery produces fair interleaving and gives finite
prefixes from infinitely-recursive relations:
- listo-aux has no base case under run* but run 4 q ... produces
exactly the four shortest list shapes, in order.
- mk-disj of two infinite generators (ones-gen, twos-gen) with
run 4 q ... must include both 1-prefixed and 2-prefixed answers
(no starvation).
- run* terminates on a goal that has a finite answer set.
3 tests, 246/246 cumulative.
Bug: dl-magic-query was skipping EDB facts for relations that had
rules ("rule-headed"). When a single relation has both EDB facts
and rules deriving more (mixed EDB+IDB), the rewritten run would
miss the EDB portion entirely, producing too few or zero results.
Fix: copy ALL existing facts to the internal mdb regardless of
whether the relation has rules. EDB-only relations bring their
tuples; mixed relations bring both EDB and any pre-saturated IDB
(which the rewritten rules would re-derive anyway).
1 new test: link relation seeded with 3 EDB tuples plus a
recursive rule via via/2. dl-magic-query rooted at `a` returns
2 results (a→b direct, a→c via via(a,e), link(e,c)).
queens.sx encodes a queen in row i at column ci. ino-each constrains
each ci to {1..n}; all-distincto handles the row/column distinct
property; safe-diag uses project to escape into host arithmetic for the
|c_i - c_j| != |i - j| diagonal guard. all-cells-safe iterates pairs at
goal-construction time so the constraint set is materialised once,
then driven by the search.
(run* q (fresh (a b c d) (== q (list a b c d))
(queens-cols (list a b c d) 4)))
-> ((2 4 1 3) (3 1 4 2))
Both valid 4-queens placements found. 6 new tests including the
two-solution invariant; 243/243 cumulative.
Bug: dl-magic-query was always trying to seed a magic_<rel>^<adn>
fact for the query goal. For aggregate goals like (count N X (p X))
this produced a non-ground "fact" (magic_count^... N X (p X)) and
dl-add-fact! correctly rejected it, surfacing as an error.
Fix: dl-magic-query now detects built-in / aggregate / negation
goals up front and dispatches to plain dl-query for those cases —
magic-sets only applies to positive non-builtin literals against
rule-defined relations. Other shapes don't benefit from the
rewrite anyway.
1 new test confirms (count N X (p X)) returns the expected
{:N 3} via dl-magic-query.
Adds dl-demo-org-rules: (subordinate Mgr Emp) over a (manager
EMP MGR) graph, and (headcount Mgr N) using count aggregation
grouped by manager. Demonstrates real-world hierarchy queries
(e.g. "everyone reporting up to the CEO") + per-manager rollup.
3 new demo tests: transitive subordinates of CEO (5 entries),
CEO headcount, and direct manager headcount.
Per ES, every native prototype's [[Prototype]] is Object.prototype
(and Function.prototype.[[Prototype]] is too). Was missing those
links, so Object.prototype.isPrototypeOf(Boolean.prototype)
returned false (the explicit isPrototypeOf walks __proto__, not
the recent fallback). Added 5 dict-set! lines to the post-init.
built-ins/Boolean: 22/27 → 23/27, built-ins/Number: 44/50 → 45/50.
conformance.sh: 148/148.
(dl-rules-of db rel-name) → list of rules with head matching
the given relation name. Useful for tooling and debugging
("show me how this relation is derived") without exposing the
internal :rules list directly.
2 new api tests cover hit and miss cases.
Returns true iff one more saturation step would derive no new
tuples. Walks every rule under the current bindings and short-
circuits as soon as one derivation would add a fresh tuple.
Useful in tests that want to assert "no work left" after a call,
or for tooling that wants to know whether `dl-saturate!` would
do anything.
3 new eval tests cover the after-saturation, before-saturation,
and after-assert states.
