Commit 2ac88879 authored by Ralf Jung's avatar Ralf Jung

start writing a signature for the world-prop solution

parent 209ec3aa
(* For some reason, the order matters. We cannot import Constr last. *)
Require Import ModuRes.Finmap ModuRes.Constr ModuRes.PCM ModuRes.UPred ModuRes.BI ModuRes.PreoMet.
Module Type WorldPropSig (Res : PCM_T).
(** The construction is parametric in the monoid we choose *)
Import Res.
(* The functor is fixed *)
Section Definitions.
(** We'll be working with complete metric spaces, so whenever
something needs an additional preorder, we'll just take a
discrete one. *)
Local Instance pt_disc P `{cmetric P} : preoType P | 2000 := disc_preo P.
Local Instance pcm_disc P `{cmetric P} : pcmType P | 2000 := disc_pcm P.
Definition FProp P `{cmP : cmetric P} :=
(nat -f> P) -m> UPred res.
End Definitions.
Parameter PreProp : Type.
Parameter PrePropS : Setoid PreProp.
Parameter PrePropM : metric PreProp.
Parameter PrePropCM: cmetric PreProp.
Definition Props := FProp PreProp.
Parameter PropS : Setoid Props.
Parameter PropM : metric Props.
Parameter PropCM : cmetric Props.
Definition Wld := (nat -f> PreProp).
Parameter ı : PreProp -> halve (cmfromType Props).
Parameter ı' : halve (cmfromType Props) -> PreProp.
Axiom iso : forall P, ı' (ı P) == P.
Axiom isoR : forall T, ı (ı' T) == T.
(*Parameter PProp_preo : preoType PreProp.
Parameter PProp_pcm : pcmType PreProp.
Parameter PProp_ext : extensible PreProp.*)
End WorldPropSig.
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