Commit 48674eed authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Merge branch 'master' of gitlab.mpi-sws.org:FP/iris-coq

parents 5cc172cf 9a137a0e
......@@ -41,13 +41,13 @@ algebra/cmra_tactics.v
algebra/sts.v
algebra/auth.v
algebra/fin_maps.v
logic/upred.v
algebra/cofe.v
algebra/base.v
algebra/dra.v
algebra/cofe_solver.v
algebra/agree.v
algebra/excl.v
program_logic/upred.v
program_logic/model.v
program_logic/adequacy.v
program_logic/hoare_lifting.v
......
......@@ -17,6 +17,43 @@ Definition LamV (e : {bind expr}) := RecV e.[ren(+1)].
Definition LetCtx (e2 : {bind expr}) := AppRCtx (LamV e2).
Definition SeqCtx (e2 : expr) := LetCtx (e2.[ren(+1)]).
Delimit Scope lang_scope with L.
Bind Scope lang_scope with expr.
Arguments wp {_ _} _ _%L _.
(* TODO: The levels are all random. Also maybe we should not
make 'new' a keyword. What about Arguments for hoare triples?. *)
(* The colons indicate binders. "let" is not consistent here though,
thing are only bound in the "in". *)
Notation "'rec::' e" := (Rec e) (at level 100) : lang_scope.
Notation "'λ:' e" := (Lam e) (at level 100) : lang_scope.
Notation "'let:' e1 'in' e2" := (Let e1 e2) (at level 70) : lang_scope.
Notation "e1 ';' e2" := (Seq e1 e2) (at level 70) : lang_scope.
Notation "'if' e1 'then' e2 'else' e3" := (If e1 e2 e3) : lang_scope.
Notation "#0" := (Var 0) (at level 0) : lang_scope.
Notation "#1" := (Var 1) (at level 0) : lang_scope.
Notation "#2" := (Var 2) (at level 0) : lang_scope.
Notation "#3" := (Var 3) (at level 0) : lang_scope.
Notation "#4" := (Var 4) (at level 0) : lang_scope.
Notation "#5" := (Var 5) (at level 0) : lang_scope.
Notation "#6" := (Var 6) (at level 0) : lang_scope.
Notation "#7" := (Var 7) (at level 0) : lang_scope.
Notation "#8" := (Var 8) (at level 0) : lang_scope.
Notation "#9" := (Var 9) (at level 0) : lang_scope.
Notation "'★' e" := (Load e) (at level 30) : lang_scope.
Notation "e1 '<-' e2" := (Store e1 e2) (at level 60) : lang_scope.
Notation "'new' e" := (Alloc e) (at level 60) : lang_scope.
Notation "e1 '+' e2" := (Plus e1 e2) : lang_scope.
Notation "e1 '≤' e2" := (Le e1 e2) : lang_scope.
Notation "e1 '<' e2" := (Lt e1 e2) : lang_scope.
Coercion LitNat : nat >-> expr.
Coercion LitNatV : nat >-> val.
Coercion Loc : loc >-> expr.
Coercion LocV : loc >-> val.
Coercion App : expr >-> Funclass.
Section suger.
Context {Σ : iFunctor}.
Implicit Types P : iProp heap_lang Σ.
......
(** This file is essentially a bunch of testcases. *)
Require Import logic.upred.
Require Import program_logic.upred.
Require Import heap_lang.lifting heap_lang.sugar.
Import heap_lang.
Import uPred.
Module LangTests.
Definition add := Plus (LitNat 21) (LitNat 21).
Goal σ, prim_step add σ (LitNat 42) σ None.
Definition add := (21 + 21)%L.
Goal σ, prim_step add σ 42 σ None.
Proof. intros; do_step done. Qed.
Definition rec := Rec (App (Var 0) (Var 1)). (* fix f x => f x *)
Definition rec_app := App rec (LitNat 0).
(* FIXME RJ why do I need the %L ? *)
Definition rec : expr := (rec:: #0 #1)%L. (* fix f x => f x *)
Definition rec_app : expr := rec 0.
Goal σ, prim_step rec_app σ rec_app σ None.
Proof. intros; do_step done. Qed.
Definition lam := Lam (Plus (Var 0) (LitNat 21)).
Proof. Set Printing All. intros; do_step done. Qed.
Definition lam : expr := (λ: #0 + 21)%L.
Goal σ, prim_step (App lam (LitNat 21)) σ add σ None.
Proof. intros; do_step done. Qed.
End LangTests.
......@@ -22,11 +23,9 @@ Module LiftingTests.
Implicit Types P : iProp heap_lang Σ.
Implicit Types Q : val iProp heap_lang Σ.
(* TODO RJ: Some syntactic sugar for language expressions would be nice. *)
Definition e3 := Load (Var 0).
Definition e2 := Seq (Store (Var 0) (Plus (Load $ Var 0) (LitNat 1))) e3.
Definition e := Let (Alloc (LitNat 1)) e2.
Goal σ E, (ownP σ : iProp heap_lang Σ) (wp E e (λ v, (v = LitNatV 2))).
(* FIXME: Fix levels so that we do not need the parenthesis here. *)
Definition e : expr := let: new 1 in (#0 <- #0 + 1 ; #0)%L.
Goal σ E, (ownP σ : iProp heap_lang Σ) (wp E e (λ v, (v = 2))).
Proof.
move=> σ E. rewrite /e.
rewrite -wp_let. rewrite -wp_alloc_pst; last done.
......@@ -34,11 +33,13 @@ Module LiftingTests.
rewrite -later_intro. apply forall_intro=>l.
apply wand_intro_l. rewrite right_id. apply const_elim_l; move=>_.
rewrite -later_intro. asimpl.
(* TODO RJ: If you go here, you can see how the sugar does not print
all so nicely. *)
rewrite -(wp_bindi (SeqCtx (Load (Loc _)))).
rewrite -(wp_bindi (StoreRCtx (LocV _))).
rewrite -(wp_bindi (PlusLCtx _)).
rewrite -wp_load_pst; first (apply sep_intro_True_r; first done); last first.
{ by rewrite lookup_insert. } (* RJ TODO: figure out why apply and eapply fail. *)
{ by rewrite lookup_insert. } (* RJ FIXME: figure out why apply and eapply fail. *)
rewrite -later_intro. apply wand_intro_l. rewrite right_id.
rewrite -wp_plus -later_intro.
rewrite -wp_store_pst; first (apply sep_intro_True_r; first done); last first.
......@@ -52,19 +53,22 @@ Module LiftingTests.
by apply const_intro.
Qed.
Definition FindPred' n1 Sn1 n2 f := If (Lt Sn1 n2)
(App f Sn1)
n1.
Definition FindPred n2 := Rec (Let (Plus (Var 1) (LitNat 1))
(FindPred' (Var 2) (Var 0) n2.[ren(+3)] (Var 1))).
Definition Pred := Lam (If (Le (Var 0) (LitNat 0))
(LitNat 0)
(App (FindPred (Var 0)) (LitNat 0))
).
(* TODO: once asimpl preserves notation, we don't need
FindPred' anymore. *)
(* FIXME: fix notation so that we do not need parenthesis or %L *)
Definition FindPred' n1 Sn1 n2 f : expr := if Sn1 < n2
then f Sn1
else n1.
Definition FindPred n2 : expr := rec:: (let: (#1 + 1) in
FindPred' #2 #0 n2.[ren(+3)] #1)%L.
Definition Pred : expr := λ: (if #0 0
then 0
else FindPred (#0) 0
)%L.
Lemma FindPred_spec n1 n2 E Q :
((n1 < n2) Q (LitNatV $ pred n2))
wp E (App (FindPred (LitNat n2)) (LitNat n1)) Q.
((n1 < n2) Q (pred n2))
wp E (FindPred n2 n1) Q.
Proof.
revert n1. apply löb_all_1=>n1.
rewrite -wp_rec //. asimpl.
......@@ -73,7 +77,7 @@ Module LiftingTests.
{ apply and_mono; first done. by rewrite -later_intro. }
apply later_mono.
(* Go on. *)
rewrite -(wp_let _ _ (FindPred' (LitNat n1) (Var 0) (LitNat n2) (FindPred $ LitNat n2))).
rewrite -(wp_let _ _ (FindPred' n1 #0 n2 (FindPred n2))).
rewrite -wp_plus. asimpl.
rewrite -(wp_bindi (CaseCtx _ _)).
rewrite -!later_intro /=.
......@@ -94,7 +98,7 @@ Module LiftingTests.
Qed.
Lemma Pred_spec n E Q :
Q (LitNatV $ pred n) wp E (App Pred (LitNat n)) Q.
Q (pred n) wp E (Pred n) Q.
Proof.
rewrite -wp_lam //. asimpl.
rewrite -(wp_bindi (CaseCtx _ _)).
......@@ -109,7 +113,8 @@ Module LiftingTests.
Goal E,
True wp (Σ:=Σ) E
(Let (App Pred (LitNat 42)) (App Pred (Var 0))) (λ v, (v = LitNatV 40)).
(* FIXME why do we need %L here? *)
(let: Pred 42 in Pred #0)%L (λ v, (v = 40)).
Proof.
intros E. rewrite -wp_let. rewrite -Pred_spec -!later_intro.
asimpl. (* TODO RJ: Can we somehow make it so that Pred gets folded again? *)
......
Require Export logic.upred program_logic.resources.
Require Export program_logic.upred program_logic.resources.
Require Import algebra.cofe_solver.
Module iProp.
......
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment