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OperationalSemantics: a model-checking example
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2 changed files with 25 additions and 6 deletions
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Frap.v
4
Frap.v
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@ -107,10 +107,10 @@ Ltac singletoner :=
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Ltac model_check_step :=
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eapply MscStep; [
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repeat ((apply oneStepClosure_empty; simplify)
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repeat (apply oneStepClosure_empty
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|| (apply oneStepClosure_split; [ simplify;
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repeat match goal with
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| [ H : _ |- _ ] => invert H; try congruence
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| [ H : _ |- _ ] => invert H; simplify; try congruence
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end; solve [ singletoner ] | ]))
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| simplify ].
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@ -36,15 +36,15 @@ Infix "-" := Minus : arith_scope.
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Infix "*" := Times : arith_scope.
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Delimit Scope arith_scope with arith.
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Notation "x <- e" := (Assign x e%arith) (at level 75).
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Infix ";" := Sequence (at level 76).
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Infix ";;" := Sequence (at level 76). (* This one changed slightly, to avoid parsing clashes. *)
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Notation "'when' e 'do' then_ 'else' else_ 'done'" := (If e%arith then_ else_) (at level 75, e at level 0).
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Notation "'while' e 'do' body 'done'" := (While e%arith body) (at level 75).
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(* Here's an adaptation of our factorial example from Chapter 3. *)
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Example factorial :=
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"output" <- 1;
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"output" <- 1;;
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while "input" do
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"output" <- "output" * "input";
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"output" <- "output" * "input";;
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"input" <- "input" - 1
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done.
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@ -160,7 +160,7 @@ Fixpoint fact (n : nat) : nat :=
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Example factorial_loop :=
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while "input" do
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"output" <- "output" * "input";
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"output" <- "output" * "input";;
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"input" <- "input" - 1
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done.
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@ -497,3 +497,22 @@ Theorem small_big_snazzy : forall v c v', step^* (v, c) (v', Skip)
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Proof.
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eauto.
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Qed.
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(** * Small-step semantics gives rise to transition systems. *)
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Definition trsys_of (v : valuation) (c : cmd) : trsys (valuation * cmd) := {|
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Initial := {(v, c)};
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Step := step
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|}.
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Theorem simple_invariant :
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invariantFor (trsys_of ($0 $+ ("a", 1)) ("b" <- "a" + 1;; "c" <- "b" + "b"))
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(fun s => snd s = Skip -> fst s $? "c" = Some 4).
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Proof.
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model_check.
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Qed.
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(* We'll return to these systems and their abstractions in the next few
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* chapters. *)
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