Commit 23de2030 authored by Ralf Jung's avatar Ralf Jung

move sugar to separate file, and prove some more rules for it

parent d8ad2335
......@@ -65,4 +65,5 @@ iris/tests.v
......@@ -38,10 +38,9 @@ Instance Rename_expr : Rename expr. derive. Defined.
Instance Subst_expr : Subst expr. derive. Defined.
Instance SubstLemmas_expr : SubstLemmas expr. derive. Qed.
Definition Lam (e : {bind expr}) := Rec e.[ren(+1)].
Definition Let (e1 : expr) (e2: {bind expr}) := App (Lam e2) e1.
Definition Seq (e1 e2 : expr) := Let e1 e2.[ren(+1)].
Definition If (e0 e1 e2 : expr) := Case e0 e1.[ren(+1)] e2.[ren(+1)].
(* This sugar is used by primitive reduction riles (<=, CAS) and hence defined here. *)
Definition LitTrue := InjL LitUnit.
Definition LitFalse := InjR LitUnit.
Inductive value :=
| RecV (e : {bind 2 of expr})
......@@ -53,11 +52,7 @@ Inductive value :=
| LocV (l : loc)
Definition LamV (e : {bind expr}) := RecV e.[ren(+1)].
Definition LitTrue := InjL LitUnit.
Definition LitTrueV := InjLV LitUnitV.
Definition LitFalse := InjR LitUnit.
Definition LitFalseV := InjRV LitUnitV.
Fixpoint v2e (v : value) : expr :=
......@@ -192,9 +187,6 @@ Fixpoint comp_ctx (Ko : ectx) (Ki : ectx) :=
| CasRCtx v0 v1 K2 => CasRCtx v0 v1 (comp_ctx K2 Ki)
Definition LetCtx (K1 : ectx) (e2 : {bind expr}) := AppRCtx (LamV e2) K1.
Definition SeqCtx (K1 : ectx) (e2 : expr) := LetCtx K1 (e2.[ren(+1)]).
Lemma fill_empty e :
fill EmptyCtx e = e.
......@@ -220,16 +220,6 @@ Proof.
apply const_elim_l=>->. done.
Lemma wp_lam E ef e v Q :
e2v e = Some v
wp (Σ:=Σ) E ef.[e/] Q wp (Σ:=Σ) E (App (Lam ef) e) Q.
intros Hv. rewrite -wp_rec; last eassumption.
(* RJ: This pulls in functional extensionality. If that bothers us, we have
to talk to the Autosubst guys. *)
by asimpl.
Lemma wp_plus n1 n2 E Q :
Q (LitNatV (n1 + n2)) wp (Σ:=Σ) E (Plus (LitNat n1) (LitNat n2)) Q.
......@@ -329,13 +319,6 @@ Qed.
(** Some derived stateless axioms *)
Lemma wp_let e1 e2 E Q :
wp (Σ:=Σ) E e1 (λ v, wp (Σ:=Σ) E (e2.[v2e v/]) Q) wp (Σ:=Σ) E (Let e1 e2) Q.
rewrite -(wp_bind (LetCtx EmptyCtx e2)). apply wp_mono=>v.
rewrite -wp_lam //. by rewrite v2v.
Lemma wp_le n1 n2 E P Q :
(n1 n2 P Q LitTrueV)
(n1 > n2 P Q LitFalseV)
(** This file is essentially a bunch of testcases. *)
Require Import modures.logic.
Require Import barrier.lifting.
Require Import barrier.lifting barrier.sugar.
Import uPred.
Module LangTests.
......@@ -62,7 +62,6 @@ Module LiftingTests.
Import Nat.
Definition Lt e1 e2 := Le (Plus e1 $ LitNat 1) e2.
Definition FindPred' n1 Sn1 n2 f := If (Lt Sn1 n2)
(App f Sn1)
......@@ -87,10 +86,12 @@ Module LiftingTests.
rewrite -(wp_let _ (FindPred' (LitNat n1) (Var 0) (LitNat n2) (FindPred $ LitNat n2))).
rewrite -wp_plus. asimpl.
rewrite -(wp_bind (CaseCtx EmptyCtx _ _)).
rewrite -(wp_bind (LeLCtx EmptyCtx _)).
rewrite -wp_plus -!later_intro. simpl.
apply wp_le; intros Hn12.
- rewrite -wp_case_inl //.
rewrite -!later_intro. simpl.
apply wp_lt; intros Hn12.
- (* TODO RJ: It would be better if we could use wp_if_true here
(and below). But we cannot, because the substitutions in there
got already unfolded. *)
rewrite -wp_case_inl //.
rewrite -!later_intro. asimpl.
rewrite (forall_elim (S n1)).
eapply impl_elim; first by eapply and_elim_l. apply and_intro.
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