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Work around #334 in definition of allperms #975

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330e4b0
work around #334 in definition of `allperms`
oskgo Apr 10, 2026
f4d702c
add back definitional lemmas and rewrite hints
oskgo Apr 10, 2026
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14 changes: 11 additions & 3 deletions theories/algebra/Perms.ec
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Original file line number Diff line number Diff line change
Expand Up @@ -3,13 +3,21 @@ require import AllCore List IntDiv Binomial Ring StdOrder.
(*---*) import IntID IntOrder.

(* -------------------------------------------------------------------- *)
op allperms_r (n : unit list) (s : 'a list) : 'a list list =
op [opaque smt_opaque] allperms_r (n : unit list) (s : 'a list) : 'a list list =
with n = [] => [[]]
with n = x::n => flatten (
map (fun x => map ((::) x) (allperms_r n (rem x s))) (undup s)).
with n = x::n => (fun rec => flatten (
map (fun x => map ((::) x) (rec (rem x s))) (undup s))) (allperms_r n).

lemma allperms_r0 (s : 'a list) :
allperms_r [] s = [[]] by done.

lemma allperms_rS (x : unit) (n : unit list) (s : 'a list) :
allperms_r (x :: n) s = flatten (
map (fun x => map ((::) x) (allperms_r n (rem x s))) (undup s)) by done.

op allperms (s : 'a list) = allperms_r (nseq (size s) tt) s.

hint rewrite ap_r : allperms_r0 allperms_rS.
(* -------------------------------------------------------------------- *)
lemma allperms_rP n (s t : 'a list) : size s = size n =>
(mem (allperms_r n s) t) <=> (perm_eq s t).
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