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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.
84 lines
2.0 KiB
Plaintext
84 lines
2.0 KiB
Plaintext
;; lib/minikanren/relations.sx — Phase 4 standard relations.
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;;
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;; Programs use native SX lists as data. Relations decompose lists via the
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;; tagged cons-cell shape `(:cons h t)` because SX has no improper pairs;
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;; the unifier treats `(:cons h t)` and the native list `(h . t)` as
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;; equivalent, and `mk-walk*` flattens cons cells back to flat lists for
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;; reification.
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;; --- pair / list shape relations ---
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(define nullo (fn (l) (== l (list))))
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(define pairo (fn (p) (fresh (a d) (== p (mk-cons a d)))))
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(define caro (fn (p a) (fresh (d) (== p (mk-cons a d)))))
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(define cdro (fn (p d) (fresh (a) (== p (mk-cons a d)))))
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(define conso (fn (a d p) (== p (mk-cons a d))))
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(define firsto caro)
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(define resto cdro)
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(define
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listo
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(fn (l) (conde ((nullo l)) ((fresh (a d) (conso a d l) (listo d))))))
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;; --- appendo: the canary ---
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;;
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;; (appendo l s ls) — `ls` is the concatenation of `l` and `s`.
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;; Runs forwards (l, s known → ls), backwards (ls known → all (l, s) pairs),
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;; and bidirectionally (mix of bound + unbound).
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(define
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appendo
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(fn
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(l s ls)
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(conde
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((nullo l) (== s ls))
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((fresh (a d res) (conso a d l) (conso a res ls) (appendo d s res))))))
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;; --- membero ---
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;; (membero x l) — x appears (at least once) in l.
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(define
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membero
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(fn
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(x l)
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(conde
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((fresh (d) (conso x d l)))
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((fresh (a d) (conso a d l) (membero x d))))))
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(define
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reverseo
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(fn
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(l r)
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(conde
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((nullo l) (nullo r))
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((fresh (a d res-rev) (conso a d l) (reverseo d res-rev) (appendo res-rev (list a) r))))))
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(define
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lengtho
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(fn
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(l n)
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(conde
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((nullo l) (== n :z))
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((fresh (a d n-1) (conso a d l) (== n (list :s n-1)) (lengtho d n-1))))))
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(define
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inserto
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(fn
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(a l p)
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(conde
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((conso a l p))
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((fresh (h t pt) (conso h t l) (conso h pt p) (inserto a t pt))))))
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(define
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permuteo
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(fn
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(l p)
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(conde
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((nullo l) (nullo p))
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((fresh (a d perm-d) (conso a d l) (permuteo d perm-d) (inserto a perm-d p))))))
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