Library model_validity_cbv

Additional structure for call-by-value models


Require Import model_structure.


Module sforces_cbv (ks : Kripke_structure).
  Export ks.
  Module ks_monad := (Kripke_structure_monad ks).
  Export ks_monad.

sforces is the strong forcing relation for call-by-value models
  Fixpoint sforces (w:K)(annot:bool)(A:formula) {struct A} : Type :=
    match A with
      | Func A1 A2 =>
        forall w', w <= w' ->
                   forall annot', leb annot annot' ->
                                  sforces w' annot' A1 -> Kont sforces w' annot' A2
                                                             
      | Sum A1 A2 => sum (sforces w annot A1) (sforces w annot A2)

      | Nat => X w annot Nat
    end.

Monotonicity properties of sforces

  Lemma sforces_mon : forall A w annot, sforces w annot A ->
                      forall w', w <= w' -> sforces w' annot A.

  Lemma sforces_mon2 : forall A w, sforces w false A -> sforces w true A.

The "run" of the continuations monad
  Definition run {w annot} :
    Kont sforces w annot Nat -> X w annot Nat.
End sforces_cbv.

A module type specifying an interpretation of the ground type Nat
Module Type Nat_instance_cbv (ks : Kripke_structure).
  Export ks.
  Module ks_monad := Kripke_structure_monad ks.
  Export ks_monad.
  Module cbv_validity := sforces_cbv ks.
  Export cbv_validity.

  Parameter Zero_interpretation : forall w annot, Kont sforces w annot Nat.
  Parameter Succ_interpretation : forall w annot, Kont sforces w annot Nat -> Kont sforces w annot Nat.
  Parameter Rec_interpretation : forall A w annot, Kont sforces w annot Nat -> Kont sforces w annot A -> Kont sforces w annot (Func Nat (Func A A)) -> Kont sforces w annot A.
  Parameter Reset_interpretation : forall w, Kont sforces w true Nat -> Kont sforces w false Nat.
End Nat_instance_cbv.

This page has been generated by coqdoc