Commit 7347e89e authored by Ralf Jung's avatar Ralf Jung

experiment a little with notation for our language

parent ad9aa6eb
......@@ -17,6 +17,41 @@ 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?
Also find better notation for function application. Or maybe
we can make "App" a coercion from expr to (expr → expr)? *)
(* The colons indicate binders. *)
Notation "'rec::' e" := (Rec e) (at level 100) : lang_scope.
Notation "'λ:' e" := (Lam e) (at level 100) : lang_scope.
Infix "$" := App : 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 10) : lang_scope.
Notation "'#1'" := (Var 1) (at level 10) : lang_scope.
Notation "'#2'" := (Var 2) (at level 10) : lang_scope.
Notation "'#3'" := (Var 3) (at level 10) : lang_scope.
Notation "'#4'" := (Var 4) (at level 10) : lang_scope.
Notation "'#5'" := (Var 5) (at level 10) : lang_scope.
Notation "'#6'" := (Var 6) (at level 10) : lang_scope.
Notation "'#7'" := (Var 7) (at level 10) : lang_scope.
Notation "'#8'" := (Var 8) (at level 10) : lang_scope.
Notation "'#9'" := (Var 9) (at level 10) : 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 Loc : loc >-> expr.
Section suger.
Context {Σ : iFunctor}.
Implicit Types P : iProp heap_lang Σ.
......
......@@ -5,14 +5,15 @@ 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.
......@@ -22,10 +23,10 @@ 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.
Definition e3 : expr := #0.
(* FIXME: Fix levels so that we do not need the parenthesis here. *)
Definition e2 : expr := (#0 <- #0 + 1) ; e3.
Definition e : expr := let: new 1 in e2.
Goal σ E, (ownP σ : iProp heap_lang Σ) (wp E e (λ v, (v = LitNatV 2))).
Proof.
move=> σ E. rewrite /e.
......@@ -34,11 +35,13 @@ 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.
......@@ -52,15 +55,15 @@ 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))
).
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))
......@@ -73,7 +76,7 @@ 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' (LitNat n1) (Var 0) (LitNat n2) (FindPred (LitNat n2)))).
rewrite -wp_plus. asimpl.
rewrite -(wp_bindi (CaseCtx _ _)).
rewrite -!later_intro /=.
......@@ -94,7 +97,7 @@ Module LiftingTests.
Qed.
Lemma Pred_spec n E Q :
Q (LitNatV $ pred n) wp E (App Pred (LitNat n)) Q.
Q (LitNatV (pred n)) wp E (App Pred (LitNat n)) Q.
Proof.
rewrite -wp_lam //. asimpl.
rewrite -(wp_bindi (CaseCtx _ _)).
......@@ -109,7 +112,8 @@ 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 = LitNatV 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? *)
......
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