Commit 6a054461 authored by Ralf Jung's avatar Ralf Jung

heap_lang: Separate derived notions and notations into different files

parent f0e60e9d
...@@ -69,5 +69,6 @@ program_logic/ghost_ownership.v ...@@ -69,5 +69,6 @@ program_logic/ghost_ownership.v
heap_lang/heap_lang.v heap_lang/heap_lang.v
heap_lang/heap_lang_tactics.v heap_lang/heap_lang_tactics.v
heap_lang/lifting.v heap_lang/lifting.v
heap_lang/sugar.v heap_lang/derived.v
heap_lang/notation.v
heap_lang/tests.v heap_lang/tests.v
Require Export heap_lang.heap_lang heap_lang.lifting. Require Export heap_lang.lifting.
Import uPred heap_lang. Import uPred.
(** Define some syntactic sugar. *) (** Define some derived forms, and derived lemmas about them. *)
Notation Lam x e := (Rec "" x e). Notation Lam x e := (Rec "" x e).
Notation Let x e1 e2 := (App (Lam x e2) e1). Notation Let x e1 e2 := (App (Lam x e2) e1).
Notation Seq e1 e2 := (Let "" e1 e2). Notation Seq e1 e2 := (Let "" e1 e2).
...@@ -9,53 +9,7 @@ Notation LamV x e := (RecV "" x e). ...@@ -9,53 +9,7 @@ Notation LamV x e := (RecV "" x e).
Notation LetCtx x e2 := (AppRCtx (LamV x e2)). Notation LetCtx x e2 := (AppRCtx (LamV x e2)).
Notation SeqCtx e2 := (LetCtx "" e2). Notation SeqCtx e2 := (LetCtx "" e2).
Module notations. Section derived.
Delimit Scope lang_scope with L.
Bind Scope lang_scope with expr val.
Arguments wp {_ _} _ _%L _.
Coercion LitNat : nat >-> base_lit.
Coercion LitBool : bool >-> base_lit.
(** No coercion from base_lit to expr. This makes is slightly easier to tell
apart language and Coq expressions. *)
Coercion Var : string >-> expr.
Coercion App : expr >-> Funclass.
Coercion of_val : val >-> expr.
(** Syntax inspired by Coq/Ocaml. Constructions with higher precedence come
first. *)
(* What about Arguments for hoare triples?. *)
Notation "' l" := (LitV l) (at level 8, format "' l") : lang_scope.
Notation "! e" := (Load e%L) (at level 10, format "! e") : lang_scope.
Notation "'ref' e" := (Alloc e%L) (at level 30) : lang_scope.
Notation "e1 + e2" := (BinOp PlusOp e1%L e2%L)
(at level 50, left associativity) : lang_scope.
Notation "e1 - e2" := (BinOp MinusOp e1%L e2%L)
(at level 50, left associativity) : lang_scope.
Notation "e1 ≤ e2" := (BinOp LeOp e1%L e2%L) (at level 70) : lang_scope.
Notation "e1 < e2" := (BinOp LtOp e1%L e2%L) (at level 70) : lang_scope.
Notation "e1 = e2" := (BinOp EqOp e1%L e2%L) (at level 70) : lang_scope.
(* The unicode ← is already part of the notation "_ ← _; _" for bind. *)
Notation "e1 <- e2" := (Store e1%L e2%L) (at level 80) : lang_scope.
Notation "'rec:' f x := e" := (Rec f x e%L)
(at level 102, f at level 1, x at level 1, e at level 200) : lang_scope.
Notation "'if' e1 'then' e2 'else' e3" := (If e1%L e2%L e3%L)
(at level 200, e1, e2, e3 at level 200) : lang_scope.
(** Derived notions, in order of declaration. The notations for let and seq
are stated explicitly instead of relying on the Notations Let and Seq as
defined above. This is needed because App is now a coercion, and these
notations are otherwise not pretty printed back accordingly. *)
Notation "λ: x , e" := (Lam x e%L)
(at level 102, x at level 1, e at level 200) : lang_scope.
Notation "'let:' x := e1 'in' e2" := (Lam x e2%L e1%L)
(at level 102, x at level 1, e1, e2 at level 200) : lang_scope.
Notation "e1 ; e2" := (Lam "" e2%L e1%L)
(at level 100, e2 at level 200) : lang_scope.
End notations.
Export notations.
Section sugar.
Context {Σ : iFunctor}. Context {Σ : iFunctor}.
Implicit Types P : iProp heap_lang Σ. Implicit Types P : iProp heap_lang Σ.
Implicit Types Q : val iProp heap_lang Σ. Implicit Types Q : val iProp heap_lang Σ.
...@@ -79,30 +33,30 @@ Proof. ...@@ -79,30 +33,30 @@ Proof.
Qed. Qed.
Lemma wp_le E (n1 n2 : nat) P Q : Lemma wp_le E (n1 n2 : nat) P Q :
(n1 n2 P Q (LitV true)) (n1 n2 P Q (LitV $ LitBool true))
(n2 < n1 P Q (LitV false)) (n2 < n1 P Q (LitV $ LitBool false))
P wp E ('n1 'n2) Q. P wp E (BinOp LeOp (Lit $ LitNat n1) (Lit $ LitNat n2)) Q.
Proof. Proof.
intros. rewrite -wp_bin_op //; []. intros. rewrite -wp_bin_op //; [].
destruct (bool_decide_reflect (n1 n2)); by eauto with omega. destruct (bool_decide_reflect (n1 n2)); by eauto with omega.
Qed. Qed.
Lemma wp_lt E (n1 n2 : nat) P Q : Lemma wp_lt E (n1 n2 : nat) P Q :
(n1 < n2 P Q (LitV true)) (n1 < n2 P Q (LitV $ LitBool true))
(n2 n1 P Q (LitV false)) (n2 n1 P Q (LitV $ LitBool false))
P wp E ('n1 < 'n2) Q. P wp E (BinOp LtOp (Lit $ LitNat n1) (Lit $ LitNat n2)) Q.
Proof. Proof.
intros. rewrite -wp_bin_op //; []. intros. rewrite -wp_bin_op //; [].
destruct (bool_decide_reflect (n1 < n2)); by eauto with omega. destruct (bool_decide_reflect (n1 < n2)); by eauto with omega.
Qed. Qed.
Lemma wp_eq E (n1 n2 : nat) P Q : Lemma wp_eq E (n1 n2 : nat) P Q :
(n1 = n2 P Q (LitV true)) (n1 = n2 P Q (LitV $ LitBool true))
(n1 n2 P Q (LitV false)) (n1 n2 P Q (LitV $ LitBool false))
P wp E ('n1 = 'n2) Q. P wp E (BinOp EqOp (Lit $ LitNat n1) (Lit $ LitNat n2)) Q.
Proof. Proof.
intros. rewrite -wp_bin_op //; []. intros. rewrite -wp_bin_op //; [].
destruct (bool_decide_reflect (n1 = n2)); by eauto with omega. destruct (bool_decide_reflect (n1 = n2)); by eauto with omega.
Qed. Qed.
End sugar. End derived.
Require Import prelude.gmap program_logic.lifting program_logic.ownership. Require Import prelude.gmap program_logic.lifting program_logic.ownership.
Require Export program_logic.weakestpre heap_lang.heap_lang_tactics. Require Export program_logic.weakestpre heap_lang.heap_lang_tactics.
Import uPred heap_lang. Export heap_lang. (* Prefer heap_lang names over language names. *)
Import uPred.
Local Hint Extern 0 (language.reducible _ _) => do_step ltac:(eauto 2). Local Hint Extern 0 (language.reducible _ _) => do_step ltac:(eauto 2).
(** The substitution operation [gsubst e x ev] behaves just as [subst] but (** The substitution operation [gsubst e x ev] behaves just as [subst] but
......
Require Export heap_lang.derived.
Delimit Scope lang_scope with L.
Bind Scope lang_scope with expr val.
Arguments wp {_ _} _ _%L _.
Coercion LitNat : nat >-> base_lit.
Coercion LitBool : bool >-> base_lit.
(** No coercion from base_lit to expr. This makes is slightly easier to tell
apart language and Coq expressions. *)
Coercion Var : string >-> expr.
Coercion App : expr >-> Funclass.
Coercion of_val : val >-> expr.
(** Syntax inspired by Coq/Ocaml. Constructions with higher precedence come
first. *)
(* What about Arguments for hoare triples?. *)
Notation "' l" := (LitV l) (at level 8, format "' l") : lang_scope.
Notation "! e" := (Load e%L) (at level 10, format "! e") : lang_scope.
Notation "'ref' e" := (Alloc e%L) (at level 30) : lang_scope.
Notation "e1 + e2" := (BinOp PlusOp e1%L e2%L)
(at level 50, left associativity) : lang_scope.
Notation "e1 - e2" := (BinOp MinusOp e1%L e2%L)
(at level 50, left associativity) : lang_scope.
Notation "e1 ≤ e2" := (BinOp LeOp e1%L e2%L) (at level 70) : lang_scope.
Notation "e1 < e2" := (BinOp LtOp e1%L e2%L) (at level 70) : lang_scope.
Notation "e1 = e2" := (BinOp EqOp e1%L e2%L) (at level 70) : lang_scope.
(* The unicode ← is already part of the notation "_ ← _; _" for bind. *)
Notation "e1 <- e2" := (Store e1%L e2%L) (at level 80) : lang_scope.
Notation "'rec:' f x := e" := (Rec f x e%L)
(at level 102, f at level 1, x at level 1, e at level 200) : lang_scope.
Notation "'if' e1 'then' e2 'else' e3" := (If e1%L e2%L e3%L)
(at level 200, e1, e2, e3 at level 200) : lang_scope.
(** Derived notions, in order of declaration. The notations for let and seq
are stated explicitly instead of relying on the Notations Let and Seq as
defined above. This is needed because App is now a coercion, and these
notations are otherwise not pretty printed back accordingly. *)
Notation "λ: x , e" := (Lam x e%L)
(at level 102, x at level 1, e at level 200) : lang_scope.
Notation "'let:' x := e1 'in' e2" := (Lam x e2%L e1%L)
(at level 102, x at level 1, e1, e2 at level 200) : lang_scope.
Notation "e1 ; e2" := (Lam "" e2%L e1%L)
(at level 100, e2 at level 200) : lang_scope.
(** This file is essentially a bunch of testcases. *) (** This file is essentially a bunch of testcases. *)
Require Import program_logic.ownership. Require Import program_logic.ownership.
Require Import heap_lang.lifting heap_lang.sugar. Require Import heap_lang.notation.
Import heap_lang uPred. Import uPred.
Module LangTests. Module LangTests.
Definition add := ('21 + '21)%L. Definition add := ('21 + '21)%L.
......
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