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.
Demonstrates the practical effect of goal-directed evaluation:
chain of 12 nodes, semi-naive derives the full ancestor closure
(78 = 12·13/2 tuples), while a magic-rooted query at node 0
returns only its 12 descendants. Concrete check that magic
limits derivation to the query's transitive cone.
Wipes every rule-headed relation (the IDB) — leaves EDB facts and
rule definitions intact. Useful for inspecting the EDB-only
baseline or for forcing a clean re-saturation.
(dl-saturate! db)
(dl-clear-idb! db) ; ancestor relation now empty
(dl-saturate! db) ; re-derives ancestor from parents
2 new api tests verify IDB-wipe and EDB-preservation.
Symmetric to dl-eval but routes single-positive-literal queries
through dl-magic-query for goal-directed evaluation. Multi-literal
query bodies fall back to standard dl-query (magic-sets is wired
for single goals only).
(dl-eval-magic source-string "?- ancestor(a, X).")
1 new api test.
Two disjoint chains, query rooted in cluster 1. Semi-naive
derives the full closure over both clusters (6 ancestor tuples).
Magic-sets only seeds magic_ancestor^bf for cluster 1, so only
2 query-relevant tuples are returned (a→b, a→c). The test
asserts both numbers, demonstrating the actual perf-shape
benefit of goal-directed evaluation.
End-to-end magic-sets entry point. Given (db, query-goal):
- copies the caller's EDB facts (relations not headed by any
rule) into a fresh internal db
- adds the magic seed fact
- adds the rewritten rules
- saturates and runs the query
- returns the substitution list
Caller's db is untouched. Equivalent to dl-query for any
fully-stratifiable program; intended as a perf alternative on
goal-shaped queries against large recursive relations.
2 new tests: equivalence to dl-query on chain-3 ancestor, and
non-mutation of the caller's db (rules count unchanged).
dl-magic-rewrite rules query-rel adn args returns:
{:rules <rewritten-rules> :seed <magic-seed-fact>}
Worklist over (rel, adn) pairs starts from the query and stops
when no new pairs appear. For each rule with head matching a
worklist pair:
- Adorned rule: head :- magic_<rel>^<adn>(bound), body...
- Propagation rules: for each positive non-builtin body lit
at position i:
magic_<lit-rel>^<lit-adn>(bound-of-lit) :-
magic_<rel>^<adn>(bound-of-head),
body[0..i-1]
- Add (lit-rel, lit-adn) to the worklist.
Built-ins, negation, and aggregates pass through without
generating propagation rules. EDB facts are unchanged.
3 new tests cover seed structure, equivalence on chain-3 (full
closure, 6 ancestor tuples — magic helps only when the EDB has
nodes outside the seed's transitive cone), and same-query-answers
under the rewritten program. Total 202/202.
Wiring up a `dl-saturate-magic!` driver and large-graph perf
benchmarks is left for a future iteration.
Adds the primitives a future magic-sets rewriter will compose:
dl-magic-rel-name rel adornment → "magic_<rel>^<adornment>"
dl-magic-lit rel adn bound-args → magic literal as SX list
dl-bound-args lit adornment → bound-position arg values
Rewriter algorithm (worklist over (rel, adornment) pairs,
generating seed, propagation, and adorned-rule outputs) is still
TODO — these helpers are inspection-only for now.
4 new magic tests cover naming, lit construction, and bound-args
extraction (mixed/free).
New lib/datalog/magic.sx — first piece of magic-sets:
dl-adorn-arg arg bound → "b" or "f"
dl-adorn-args args bound → adornment string
dl-adorn-goal goal → adornment under empty bound set
dl-adorn-lit lit bound → adornment of any literal
dl-vars-bound-by-lit lit bound → free vars this lit will bind
dl-init-head-bound head adn → bound set seeded from head adornment
dl-rule-sips rule head-adn → ({:lit :adornment} ...) per body lit
SIPS walks left-to-right tracking the bound set; recognises `is` and
aggregate result-vars as new binders, lets comparisons and negation
pass through with computed adornments.
Inspection-only — saturator doesn't yet consume these. Lays
groundwork for a future magic-sets transformation.
10 new tests cover pure adornment, SIPS over a chain rule,
head-fully-bound rules, comparisons, and `is`. Total 194/194.
js-delete-prop was setting value to js-undefined instead of
removing the key, so 'key' in obj remained true and proto-chain
lookup didn't fall through. Switched to dict-delete!.
Now delete Boolean.prototype.toString; Boolean.prototype.toString()
walks up to Object.prototype.toString and returns "[object Boolean]".
built-ins/Boolean: 21/27 → 22/27. conformance.sh: 148/148.
