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.
(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.
(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.
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.
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.
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.
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.
(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.
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.
inserto a l p: p is l with a inserted at some position. Recursive: head
of l first, then push past head and recurse.
permuteo l p: classical recursive permutation. Empty -> empty; otherwise
take a head off l, recursively permute the tail, insert head at any
position in the recursive result.
7 new tests including all-6-perms-of-3 as a set check (independent of
generation order). 208/208 cumulative.
reverseo: standard recursive definition via appendo. Forward works in
run*; backward (input fresh, output ground) works in run 1 but run*
diverges trying to enumerate the unique answer (canonical TRS issue
with naive reverseo).
lengtho: Peano encoding (:z / (:s :z) / (:s (:s :z)) ...) so it works
relationally in both directions without arithmetic-as-relation. Forward
returns the Peano length; backward enumerates lists of a given length.
162/162 cumulative.
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.
