clutch.meas_lang.class_instances
From Stdlib Require Import Reals Psatz.
From clutch.common Require Export language.
From clutch.meas_lang Require Export lang tactics notation.
From iris.prelude Require Import options.
(*
Global Instance into_val_val v : IntoVal (Val v) v.
Proof. done. Qed.
Global Instance as_val_val v : AsVal (Val v).
Proof. by eexists. Qed.
(** * Instances of the Atomic class *)
Section atomic.
Local Ltac solve_atomic :=
apply strongly_atomic_atomic, ectx_language_atomic;
intros ????; simpl; by inv_head_step |apply ectxi_language_sub_redexes_are_values; intros [] **; naive_solver.
Global Instance rec_atomic s f x e : Atomic s (Rec f x e).
Proof. solve_atomic. Qed.
Global Instance injl_atomic s v : Atomic s (InjL (Val v)).
Proof. solve_atomic. Qed.
Global Instance injr_atomic s v : Atomic s (InjR (Val v)).
Proof. solve_atomic. Qed.
(** The instance below is a more general version of Skip *)
Global Instance beta_atomic s f x v1 v2 : Atomic s (App (RecV f x (Val v1)) (Val v2)).
Proof. destruct f,x; solve_atomic. Qed.
Global Instance unop_atomic s op v : Atomic s (UnOp op (Val v)).
Proof. solve_atomic. Qed.
Global Instance binop_atomic s op v1 v2 : Atomic s (BinOp op (Val v1) (Val v2)).
Proof. solve_atomic. Qed.
Global Instance if_true_atomic s v1 e2 :
Atomic s (If (Val LitBool true) (Val v1) e2).
Proof. solve_atomic. Qed.
Global Instance if_false_atomic s e1 v2 :
Atomic s (If (Val LitBool false) e1 (Val v2)).
Proof. solve_atomic. Qed.
Global Instance fst_atomic s v : Atomic s (Fst (Val v)).
Proof. solve_atomic. Qed.
Global Instance snd_atomic s v : Atomic s (Snd (Val v)).
Proof. solve_atomic. Qed.
Global Instance alloc_atomic s v : Atomic s (Alloc (Val v)).
Proof. solve_atomic. Qed.
Global Instance load_atomic s v : Atomic s (Load (Val v)).
Proof. solve_atomic. Qed.
Global Instance store_atomic s v1 v2 : Atomic s (Store (Val v1) (Val v2)).
Proof. solve_atomic. Qed.
Global Instance rand_atomic s z l : Atomic s (Rand (Val (LitV (LitInt z))) (Val (LitV (LitLbl l)))).
Proof. solve_atomic. Qed.
Global Instance rand_atomic_int s z : Atomic s (Rand (Val (LitV (LitInt z))) (Val (LitV LitUnit))).
Proof. solve_atomic. Qed.
Global Instance alloc_tape_atomic s z : Atomic s (AllocTape (Val (LitV (LitInt z)))).
Proof. solve_atomic. Qed.
Global Instance tick_atomic s z : Atomic s (Tick (Val (LitV (LitInt z)))).
Proof. solve_atomic. Qed.
End atomic.
(** * Instances of the PureExec class *)
(** The behavior of the various wp_ tactics with regard to lambda differs in
the following way:
- wp_pures does *not* reduce lambdas/recs that are hidden behind a definition.
- wp_rec and wp_lam reduce lambdas/recs that are hidden behind a definition.
To realize this behavior, we define the class AsRecV v f x erec, which takes a
value v as its input, and turns it into a RecV f x erec via the instance
AsRecV_recv : AsRecV (RecV f x e) f x e. We register this instance via
Hint Extern so that it is only used if v is syntactically a lambda/rec, and
not if v contains a lambda/rec that is hidden behind a definition.
To make sure that wp_rec and wp_lam do reduce lambdas/recs that are hidden
behind a definition, we activate AsRecV_recv by hand in these tactics. *)
Class AsRecV (v : val) (f x : binder) (erec : expr) :=
as_recv : v = RecV f x erec.
Global Hint Mode AsRecV ! - - - : typeclass_instances.
Definition AsRecV_recv f x e : AsRecV (RecV f x e) f x e := eq_refl.
Global Hint Extern 0 (AsRecV (RecV _ _ _) _ _ _) =>
apply AsRecV_recv : typeclass_instances.
Section pure_exec.
Local Ltac solve_exec_safe := intros; subst; eexists; eapply head_step_support_equiv_rel; eauto with head_step.
Local Ltac solve_exec_puredet :=
intros; simpl;
(repeat case_match); simplify_eq;
rewrite dret_1_1 //.
Local Ltac solve_pure_exec :=
subst; intros ?; apply nsteps_once, pure_head_step_pure_step;
constructor; solve_exec_safe | solve_exec_puredet.
Global Instance pure_recc f x (erec : expr) :
PureExec True 1 (Rec f x erec) (Val PairV v1 v2).
Proof. solve_pure_exec. Qed.
Global Instance pure_injlc (v : val) :
PureExec True 1 (InjL InjLV v).
Proof. solve_pure_exec. Qed.
Global Instance pure_injrc (v : val) :
PureExec True 1 (InjR InjRV v).
Proof. solve_pure_exec. Qed.
Global Instance pure_beta f x (erec : expr) (v1 v2 : val) `{!AsRecV v1 f x erec} :
PureExec True 1 (App (Val v1) (Val v2)) (subst' x v2 (subst' f v1 erec)).
Proof. unfold AsRecV in *. subst. solve_pure_exec. Qed.
Global Instance pure_unop op v v' :
PureExec (un_op_eval op v = Some v') 1 (UnOp op (Val v)) (Val v').
Proof. solve_pure_exec. Qed.
Global Instance pure_binop op v1 v2 v' :
PureExec (bin_op_eval op v1 v2 = Some v') 1 (BinOp op (Val v1) (Val v2)) (Val v') | 10.
Proof. solve_pure_exec. Qed.
(* Lower-cost instance for EqOp. *)
Global Instance pure_eqop v1 v2 :
PureExec (vals_compare_safe v1 v2) 1
(BinOp EqOp (Val v1) (Val v2))
(Val LitBool LitV bool_decide (v1 = v2)).
{ intros. revert Hcompare. solve_pure_exec. }
rewrite /bin_op_eval /= decide_True //.
Qed.
Global Instance pure_if_true e1 e2 :
PureExec True 1 (If (Val LitBool true) e1 e2) e1.
Proof. solve_pure_exec. Qed.
Global Instance pure_if_false e1 e2 :
PureExec True 1 (If (Val LitBool false) e1 e2) e2.
Proof. solve_pure_exec. Qed.
Global Instance pure_fst v1 v2 :
PureExec True 1 (Fst (Val PairV v1 v2)) (Val v2).
Proof. solve_pure_exec. Qed.
Global Instance pure_case_inl v e1 e2 :
PureExec True 1 (Case (Val InjRV v) e1 e2) (App e2 (Val v)).
Proof. solve_pure_exec. Qed.
Global Instance pure_tick (z : Z) :
PureExec True 1 (Tick z) ().
Proof. solve_pure_exec. Qed.
End pure_exec.
*)
From clutch.common Require Export language.
From clutch.meas_lang Require Export lang tactics notation.
From iris.prelude Require Import options.
(*
Global Instance into_val_val v : IntoVal (Val v) v.
Proof. done. Qed.
Global Instance as_val_val v : AsVal (Val v).
Proof. by eexists. Qed.
(** * Instances of the Atomic class *)
Section atomic.
Local Ltac solve_atomic :=
apply strongly_atomic_atomic, ectx_language_atomic;
intros ????; simpl; by inv_head_step |apply ectxi_language_sub_redexes_are_values; intros [] **; naive_solver.
Global Instance rec_atomic s f x e : Atomic s (Rec f x e).
Proof. solve_atomic. Qed.
Global Instance injl_atomic s v : Atomic s (InjL (Val v)).
Proof. solve_atomic. Qed.
Global Instance injr_atomic s v : Atomic s (InjR (Val v)).
Proof. solve_atomic. Qed.
(** The instance below is a more general version of Skip *)
Global Instance beta_atomic s f x v1 v2 : Atomic s (App (RecV f x (Val v1)) (Val v2)).
Proof. destruct f,x; solve_atomic. Qed.
Global Instance unop_atomic s op v : Atomic s (UnOp op (Val v)).
Proof. solve_atomic. Qed.
Global Instance binop_atomic s op v1 v2 : Atomic s (BinOp op (Val v1) (Val v2)).
Proof. solve_atomic. Qed.
Global Instance if_true_atomic s v1 e2 :
Atomic s (If (Val LitBool true) (Val v1) e2).
Proof. solve_atomic. Qed.
Global Instance if_false_atomic s e1 v2 :
Atomic s (If (Val LitBool false) e1 (Val v2)).
Proof. solve_atomic. Qed.
Global Instance fst_atomic s v : Atomic s (Fst (Val v)).
Proof. solve_atomic. Qed.
Global Instance snd_atomic s v : Atomic s (Snd (Val v)).
Proof. solve_atomic. Qed.
Global Instance alloc_atomic s v : Atomic s (Alloc (Val v)).
Proof. solve_atomic. Qed.
Global Instance load_atomic s v : Atomic s (Load (Val v)).
Proof. solve_atomic. Qed.
Global Instance store_atomic s v1 v2 : Atomic s (Store (Val v1) (Val v2)).
Proof. solve_atomic. Qed.
Global Instance rand_atomic s z l : Atomic s (Rand (Val (LitV (LitInt z))) (Val (LitV (LitLbl l)))).
Proof. solve_atomic. Qed.
Global Instance rand_atomic_int s z : Atomic s (Rand (Val (LitV (LitInt z))) (Val (LitV LitUnit))).
Proof. solve_atomic. Qed.
Global Instance alloc_tape_atomic s z : Atomic s (AllocTape (Val (LitV (LitInt z)))).
Proof. solve_atomic. Qed.
Global Instance tick_atomic s z : Atomic s (Tick (Val (LitV (LitInt z)))).
Proof. solve_atomic. Qed.
End atomic.
(** * Instances of the PureExec class *)
(** The behavior of the various wp_ tactics with regard to lambda differs in
the following way:
- wp_pures does *not* reduce lambdas/recs that are hidden behind a definition.
- wp_rec and wp_lam reduce lambdas/recs that are hidden behind a definition.
To realize this behavior, we define the class AsRecV v f x erec, which takes a
value v as its input, and turns it into a RecV f x erec via the instance
AsRecV_recv : AsRecV (RecV f x e) f x e. We register this instance via
Hint Extern so that it is only used if v is syntactically a lambda/rec, and
not if v contains a lambda/rec that is hidden behind a definition.
To make sure that wp_rec and wp_lam do reduce lambdas/recs that are hidden
behind a definition, we activate AsRecV_recv by hand in these tactics. *)
Class AsRecV (v : val) (f x : binder) (erec : expr) :=
as_recv : v = RecV f x erec.
Global Hint Mode AsRecV ! - - - : typeclass_instances.
Definition AsRecV_recv f x e : AsRecV (RecV f x e) f x e := eq_refl.
Global Hint Extern 0 (AsRecV (RecV _ _ _) _ _ _) =>
apply AsRecV_recv : typeclass_instances.
Section pure_exec.
Local Ltac solve_exec_safe := intros; subst; eexists; eapply head_step_support_equiv_rel; eauto with head_step.
Local Ltac solve_exec_puredet :=
intros; simpl;
(repeat case_match); simplify_eq;
rewrite dret_1_1 //.
Local Ltac solve_pure_exec :=
subst; intros ?; apply nsteps_once, pure_head_step_pure_step;
constructor; solve_exec_safe | solve_exec_puredet.
Global Instance pure_recc f x (erec : expr) :
PureExec True 1 (Rec f x erec) (Val PairV v1 v2).
Proof. solve_pure_exec. Qed.
Global Instance pure_injlc (v : val) :
PureExec True 1 (InjL InjLV v).
Proof. solve_pure_exec. Qed.
Global Instance pure_injrc (v : val) :
PureExec True 1 (InjR InjRV v).
Proof. solve_pure_exec. Qed.
Global Instance pure_beta f x (erec : expr) (v1 v2 : val) `{!AsRecV v1 f x erec} :
PureExec True 1 (App (Val v1) (Val v2)) (subst' x v2 (subst' f v1 erec)).
Proof. unfold AsRecV in *. subst. solve_pure_exec. Qed.
Global Instance pure_unop op v v' :
PureExec (un_op_eval op v = Some v') 1 (UnOp op (Val v)) (Val v').
Proof. solve_pure_exec. Qed.
Global Instance pure_binop op v1 v2 v' :
PureExec (bin_op_eval op v1 v2 = Some v') 1 (BinOp op (Val v1) (Val v2)) (Val v') | 10.
Proof. solve_pure_exec. Qed.
(* Lower-cost instance for EqOp. *)
Global Instance pure_eqop v1 v2 :
PureExec (vals_compare_safe v1 v2) 1
(BinOp EqOp (Val v1) (Val v2))
(Val LitBool LitV bool_decide (v1 = v2)).
{ intros. revert Hcompare. solve_pure_exec. }
rewrite /bin_op_eval /= decide_True //.
Qed.
Global Instance pure_if_true e1 e2 :
PureExec True 1 (If (Val LitBool true) e1 e2) e1.
Proof. solve_pure_exec. Qed.
Global Instance pure_if_false e1 e2 :
PureExec True 1 (If (Val LitBool false) e1 e2) e2.
Proof. solve_pure_exec. Qed.
Global Instance pure_fst v1 v2 :
PureExec True 1 (Fst (Val PairV v1 v2)) (Val v2).
Proof. solve_pure_exec. Qed.
Global Instance pure_case_inl v e1 e2 :
PureExec True 1 (Case (Val InjRV v) e1 e2) (App e2 (Val v)).
Proof. solve_pure_exec. Qed.
Global Instance pure_tick (z : Z) :
PureExec True 1 (Tick z) ().
Proof. solve_pure_exec. Qed.
End pure_exec.
*)