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Revising before class
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1 changed files with 10 additions and 8 deletions
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@ -8,6 +8,8 @@ Require Import Frap.
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Require Import Program Setoids.Setoid Classes.RelationClasses Classes.Morphisms Morphisms_Prop.
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Require Import Eqdep.
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Set Warnings "-cannot-define-projection".
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Ltac inv_pair :=
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match goal with
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| [ H : existT _ _ _ = existT _ _ _ |- _ ] => apply inj_pair2 in H; invert H
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@ -325,7 +327,7 @@ Inductive RefineMethods {state1 state2} (R : state1 -> state2 -> Prop)
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-> RefineMethods R (MethodsCons {| MethodName := name; MethodBody := f1 |} ms1)
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(MethodsCons {| MethodName := name; MethodBody := f2 |} ms2).
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Hint Constructors RefineMethods.
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Hint Constructors RefineMethods : core.
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(* When does [adt2] refine [adt1]? When there exists a simulation relation,
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* with respect to which the constructors and methods all satisfy the usual
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@ -358,7 +360,7 @@ Definition split_counter := ADT {
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and method "value"[[self, _]] = ret (self, fst self + snd self)
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}.
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Hint Extern 1 (@eq nat _ _) => simplify; linear_arithmetic.
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Hint Extern 1 (@eq nat _ _) => simplify; linear_arithmetic : core.
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(* Here is why the new implementation is correct. *)
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Theorem split_counter_ok : adt_refine counter split_counter.
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@ -389,9 +391,9 @@ Proof.
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constructor.
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cases m; constructor; first_order.
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subst; eauto.
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Qed.
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Qed.
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Hint Immediate RefineMethods_refl.
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Hint Immediate RefineMethods_refl : core.
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Theorem refine_refl : forall names (adt1 : adt names),
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adt_refine adt1 adt1.
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@ -420,7 +422,7 @@ Proof.
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first_order.
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Qed.
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Hint Resolve RefineMethods_trans.
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Hint Resolve RefineMethods_trans : core.
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Theorem refine_trans : forall names (adt1 adt2 adt3 : adt names),
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adt_refine adt1 adt2
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@ -551,7 +553,7 @@ Proof.
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eauto.
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Qed.
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Hint Resolve RepChangeMethods_ok.
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Hint Resolve RepChangeMethods_ok : core.
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Theorem refine_rep : forall state1 state2 (absfunc : state2 -> state1)
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names (ms1 : methods state1 names) (ms2 : methods state2 names)
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@ -648,7 +650,7 @@ Inductive CachingMethods {state} (name : string) (func : state -> nat)
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CachingMethods name func ms1 ms2
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-> CachingMethods name func
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(MethodsCons {| MethodName := name; MethodBody := (fun s _ => ret (s, func s)) |} ms1)
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(MethodsCons {| MethodName := name; MethodBody := (fun s arg => ret (s, snd s)) |} ms2)
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(MethodsCons {| MethodName := name; MethodBody := (fun s _ => ret (s, snd s)) |} ms2)
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(* Any other method now picks up an obligation to recompute the cache value
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* whenever changing the state. We express that recomputation with a pick, to
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@ -686,7 +688,7 @@ Proof.
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eauto.
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Qed.
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Hint Resolve CachingMethods_ok.
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Hint Resolve CachingMethods_ok : core.
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Theorem refine_cache : forall state name (func : state -> nat)
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names (ms1 : methods state names) (ms2 : methods (state * nat) names)
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