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Th2.3: prove If rule

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Théophile Bastian 2017-12-06 01:15:10 +01:00
parent 93336c705e
commit 55eef82c54
1 changed files with 12 additions and 4 deletions
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16
wp.v
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@ -83,8 +83,8 @@ Fixpoint interp (inst: Instr) (mem: MemCpo) : MemCpo :=
| seq instr1 instr2 => interp instr2 (interp instr1 (MemElem mem0)) | seq instr1 instr2 => interp instr2 (interp instr1 (MemElem mem0))
| ifelse guard instrIf instrElse => | ifelse guard instrIf instrElse =>
if ((guard mem0) =? 0) % Z if ((guard mem0) =? 0) % Z
then interp instrIf mem then interp instrElse mem
else interp instrElse mem else interp instrIf mem
| while guard body => | while guard body =>
let fix while_chain (mem: MemCpo) (n: nat): MemCpo := let fix while_chain (mem: MemCpo) (n: nat): MemCpo :=
match n with match n with
@ -155,7 +155,7 @@ Notation "a [[ x <- 'expr' z ]]" := (substAssertExpr a x z)
(at level 50, left associativity). (at level 50, left associativity).
Definition assertOfExpr : Expr -> Assert := Definition assertOfExpr : Expr -> Assert :=
fun expr mem => expr mem <> 0%Z. fun expr mem => (expr mem <> 0)%Z.
Definition assertImplLogical (a1 a2: Assert): Prop := Definition assertImplLogical (a1 a2: Assert): Prop :=
forall (m: Mem), (a1 m) -> (a2 m). forall (m: Mem), (a1 m) -> (a2 m).
@ -240,4 +240,12 @@ Proof.
apply (IHdeduction2 m). unfold hoare_consequence in IHdeduction1. apply (IHdeduction2 m). unfold hoare_consequence in IHdeduction1.
specialize IHdeduction1 with mem as IH1_mem. specialize IHdeduction1 with mem as IH1_mem.
rewrite mRel in IH1_mem. apply IH1_mem. assumption. rewrite mRel in IH1_mem. apply IH1_mem. assumption.
- - destruct (expr mem =? 0)%Z eqn:branchEqn.
* apply (IHdeduction2 mem). unfold assertOfExpr.
unfold assertAnd. split.
+ assumption.
+ unfold assertNot. rewrite <- Z.eqb_eq. congruence.
* apply (IHdeduction1 mem). unfold assertOfExpr.
unfold assertAnd. split.
+ assumption.
+ rewrite <- Z.eqb_eq. congruence.