66 lines
1.6 KiB
Coq
66 lines
1.6 KiB
Coq
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(** A library for finite sets with extensional equality.
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Author: Brian Aydemir. *)
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Require Import FSets.
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Require Import ListFacts.
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Require Import AdditionalTactics.
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Require AdditionalTactics.
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(* *********************************************************************** *)
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(** * Interface *)
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(** The following interface wraps the standard library's finite set
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interface with an additional property: extensional equality. *)
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Module Type S.
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Declare Module E : UsualOrderedType.
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Declare Module F : FSetInterface.S with Module E := E.
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Parameter eq_if_Equal :
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forall s s' : F.t, F.Equal s s' -> s = s'.
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End S.
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(* *********************************************************************** *)
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(** * Implementation *)
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(** For documentation purposes, we hide the implementation of a
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functor implementing the above interface. We note only that the
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implementation here assumes (as an axiom) that proof irrelevance
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holds. *)
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Module Make (X : UsualOrderedType) <: S with Module E := X.
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(* begin hide *)
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Module E := X.
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Module F := FSetList.Make E.
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Module OFacts := OrderedType.OrderedTypeFacts E.
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Axiom sort_F_E_lt_proof_irrel : forall xs (p q : sort F.E.lt xs), p = q.
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Lemma eq_if_Equal :
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forall s s' : F.t, F.Equal s s' -> s = s'.
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Proof.
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intros [s1 pf1] [s2 pf2] Eq.
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assert (s1 = s2).
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unfold F.MSet.Raw.t in *.
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(* eapply Sort_InA_eq_ext; eauto.
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intros; eapply E.lt_trans; eauto.
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intros; eapply OFacts.lt_eq; eauto.
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intros; eapply OFacts.eq_lt; eauto.
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subst s1.
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rewrite (sort_F_E_lt_proof_irrel _ pf1 pf2).
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reflexivity.
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Qed.
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*)
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Admitted.
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(* end hide *)
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End Make.
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