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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.
298 lines
6.6 KiB
Plaintext
298 lines
6.6 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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appendo3
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(fn
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(l1 l2 l3 result)
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(fresh (l12) (appendo l1 l2 l12) (appendo l12 l3 result))))
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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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not-membero
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(fn
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(x l)
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(conde
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((nullo l))
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((fresh (a d) (conso a d l) (nafc (== a x)) (not-membero x d))))))
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(define
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subseto
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(fn
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(l1 l2)
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(conde
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((nullo l1))
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((fresh (a d) (conso a d l1) (membero a l2) (subseto d l2))))))
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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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rev-acco
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(fn
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(l acc result)
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(conde
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((nullo l) (== result acc))
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((fresh (a d acc-prime) (conso a d l) (conso a acc acc-prime) (rev-acco d acc-prime result))))))
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(define rev-2o (fn (l result) (rev-acco l (list) result)))
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(define palindromeo (fn (l) (fresh (rev) (reverseo l rev) (== l rev))))
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(define prefixo (fn (p l) (fresh (rest) (appendo p rest l))))
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(define suffixo (fn (s l) (fresh (front) (appendo front s l))))
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(define
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subo
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(fn
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(s l)
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(fresh
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(front-and-s back front)
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(appendo front-and-s back l)
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(appendo front s front-and-s))))
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(define
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selecto
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(fn
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(x rest l)
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(conde
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((conso x rest l))
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((fresh (a d r) (conso a d l) (conso a r rest) (selecto x r d))))))
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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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(define
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flatteno
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(fn
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(tree flat)
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(conde
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((nullo tree) (nullo flat))
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((pairo tree)
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(fresh
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(h t hf tf)
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(conso h t tree)
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(flatteno h hf)
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(flatteno t tf)
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(appendo hf tf flat)))
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((nafc (nullo tree)) (nafc (pairo tree)) (== flat (list tree))))))
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(define
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rembero
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(fn
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(x l out)
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(conde
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((nullo l) (nullo out))
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((fresh (a d) (conso a d l) (== a x) (== out d)))
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((fresh (a d res) (conso a d l) (nafc (== a x)) (conso a res out) (rembero x d res))))))
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(define
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removeo-allo
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(fn
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(x l result)
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(conde
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((nullo l) (nullo result))
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((fresh (a d) (conso a d l) (== a x) (removeo-allo x d result)))
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((fresh (a d r-rest) (conso a d l) (nafc (== a x)) (conso a r-rest result) (removeo-allo x d r-rest))))))
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(define
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assoco
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(fn
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(key pairs val)
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(fresh
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(rest)
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(conde
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((conso (list key val) rest pairs))
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((fresh (other) (conso other rest pairs) (assoco key rest val)))))))
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(define
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nth-o
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(fn
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(n l elem)
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(conde
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((== n :z) (fresh (d) (conso elem d l)))
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((fresh (n-1 a d) (== n (list :s n-1)) (conso a d l) (nth-o n-1 d elem))))))
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(define
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samelengtho
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(fn
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(l1 l2)
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(conde
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((nullo l1) (nullo l2))
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((fresh (a d a-prime d-prime) (conso a d l1) (conso a-prime d-prime l2) (samelengtho d d-prime))))))
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(define
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mapo
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(fn
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(rel l1 l2)
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(conde
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((nullo l1) (nullo l2))
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((fresh (a d a-prime d-prime) (conso a d l1) (conso a-prime d-prime l2) (rel a a-prime) (mapo rel d d-prime))))))
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(define
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iterate-no
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(fn
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(rel n x result)
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(conde
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((== n :z) (== result x))
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((fresh (n-1 mid) (== n (list :s n-1)) (rel x mid) (iterate-no rel n-1 mid result))))))
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(define
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pairlisto
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(fn
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(l1 l2 pairs)
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(conde
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((nullo l1) (nullo l2) (nullo pairs))
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((fresh (a1 d1 a2 d2 d-pairs) (conso a1 d1 l1) (conso a2 d2 l2) (conso (list a1 a2) d-pairs pairs) (pairlisto d1 d2 d-pairs))))))
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(define
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swap-firsto
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(fn
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(l result)
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(fresh
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(a b rest mid-l mid-r)
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(conso a mid-l l)
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(conso b rest mid-l)
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(conso b mid-r result)
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(conso a rest mid-r))))
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(define
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everyo
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(fn
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(rel l)
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(conde
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((nullo l))
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((fresh (a d) (conso a d l) (rel a) (everyo rel d))))))
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(define
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someo
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(fn
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(rel l)
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(conde
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((fresh (a d) (conso a d l) (rel a)))
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((fresh (a d) (conso a d l) (someo rel d))))))
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(define
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lasto
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(fn
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(l x)
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(conde
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((conso x (list) l))
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((fresh (a d) (conso a d l) (lasto d x))))))
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(define
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init-o
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(fn
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(l init)
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(conde
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((fresh (x) (conso x (list) l) (== init (list))))
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((fresh (a d d-init) (conso a d l) (conso a d-init init) (init-o d d-init))))))
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(define
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tako
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(fn
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(n l prefix)
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(conde
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((== n :z) (== prefix (list)))
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((fresh (n-1 a d p-rest) (== n (list :s n-1)) (conso a d l) (conso a p-rest prefix) (tako n-1 d p-rest))))))
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(define
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dropo
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(fn
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(n l suffix)
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(conde
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((== n :z) (== suffix l))
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((fresh (n-1 a d) (== n (list :s n-1)) (conso a d l) (dropo n-1 d suffix))))))
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(define
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repeato
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(fn
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(x n result)
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(conde
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((== n :z) (== result (list)))
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((fresh (n-1 r-rest) (== n (list :s n-1)) (conso x r-rest result) (repeato x n-1 r-rest))))))
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(define
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concato
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(fn
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(lists result)
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(conde
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((nullo lists) (nullo result))
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((fresh (h t r-rest) (conso h t lists) (appendo h r-rest result) (concato t r-rest))))))
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