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Migrate MSet to use quotients to eliminate axioms #1061

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strub merged 1 commit into from
Jun 25, 2026
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Migrate MSet to use quotients to eliminate axioms #1061

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28 changes: 21 additions & 7 deletions theories/datatypes/MSet.ec
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Original file line number Diff line number Diff line change
@@ -1,20 +1,34 @@
require import Core Int List StdRing StdOrder FMap FSet StdBigop.
require import Core Int List StdRing StdOrder FMap FSet StdBigop Quotient.
(*---*) import IntOrder.


(* -------------------------------------------------------------------- *)
(* Finite multisets are represented as lists up to permutation *)

type 'a mset.
section.
declare type a.

op elems : 'a mset -> 'a list.
op oflist : 'a list -> 'a mset.
clone include Quotient.EquivQuotient with
type T <- a list,
op eqv <- perm_eq
rename "pi" as "oflist"
rename "repr" as "elems"
rename "qT" as "mset"
rename "quot" as "mset"
rename "oflistK" as "oflistK'"
proof *.

axiom elemsK: cancel elems<:'a> oflist.
axiom oflistK (s : 'a list): perm_eq s (elems (oflist s)).
realize EqvEquiv.eqv_refl by apply perm_eq_refl.
realize EqvEquiv.eqv_sym by rewrite /symmetric => x y; rewrite perm_eq_sym.
realize EqvEquiv.eqv_trans by apply perm_eq_trans.
end section.

axiom mset_eq (s1 s2 : 'a mset):
lemma oflistK (s : 'a list): perm_eq s (elems (oflist s)).
proof. by apply eqv_oflist; rewrite elemsK. qed.

lemma mset_eq (s1 s2 : 'a mset):
(perm_eq (elems s1) (elems s2)) => (s1 = s2).
proof. by rewrite eqv_oflist !elemsK. qed.

(* -------------------------------------------------------------------- *)

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