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Revising for next Wednesday's lecture
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2 changed files with 17 additions and 17 deletions
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@ -908,7 +908,7 @@ Proof.
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Qed.
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Qed.
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(* Fancy theorem to help us rewrite within preconditions and postconditions *)
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(* Fancy theorem to help us rewrite within preconditions and postconditions *)
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Instance hoare_triple_morphism : forall A,
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Global Instance hoare_triple_morphism : forall A,
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Proper (heq ==> eq ==> (eq ==> heq) ==> iff) (@hoare_triple A).
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Proper (heq ==> eq ==> (eq ==> heq) ==> iff) (@hoare_triple A).
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Proof.
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Proof.
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Transparent himp.
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Transparent himp.
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@ -1133,13 +1133,13 @@ Qed.
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* memory. *)
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* memory. *)
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Fixpoint linkedList (p : nat) (ls : list nat) :=
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Fixpoint linkedList (p : nat) (ls : list nat) :=
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match ls with
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match ls with
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| nil => [| p = 0 |]
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| nil => [| p = 0 |]
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(* An empty list is associated with a null pointer and no memory
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(* An empty list is associated with a null pointer and no memory
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* contents. *)
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* contents. *)
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| x :: ls' => [| p <> 0 |]
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| x :: ls' => [| p <> 0 |]
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* exists p', p |--> [x; p'] * linkedList p' ls'
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* exists p', p |--> [x; p'] * linkedList p' ls'
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(* A nonempty list is associated with a nonnull pointer and a two-cell
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(* A nonempty list is associated with a nonnull pointer and a two-cell
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* struct, which points to a further list. *)
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* struct, which points to a further list. *)
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end%sep.
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end%sep.
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(* The definition of [linkedList] is recursive in the list. Let's also prove
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(* The definition of [linkedList] is recursive in the list. Let's also prove
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@ -1266,8 +1266,8 @@ Qed.
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* *list segments* that end with some pointer beside null. *)
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* *list segments* that end with some pointer beside null. *)
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Fixpoint linkedListSegment (p : nat) (ls : list nat) (q : nat) :=
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Fixpoint linkedListSegment (p : nat) (ls : list nat) (q : nat) :=
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match ls with
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match ls with
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| nil => [| p = q |]
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| nil => [| p = q |]
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| x :: ls' => [| p <> 0 |] * exists p', p |--> [x; p'] * linkedListSegment p' ls' q
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| x :: ls' => [| p <> 0 |] * exists p', p |--> [x; p'] * linkedListSegment p' ls' q
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end%sep.
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end%sep.
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(* Next, two [linkedListSegment] lemmas analogous to those for [linkedList]
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(* Next, two [linkedListSegment] lemmas analogous to those for [linkedList]
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@ -515,13 +515,13 @@ Admitted.
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* memory. *)
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* memory. *)
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Fixpoint linkedList (p : nat) (ls : list nat) :=
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Fixpoint linkedList (p : nat) (ls : list nat) :=
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match ls with
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match ls with
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| nil => [| p = 0 |]
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| nil => [| p = 0 |]
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(* An empty list is associated with a null pointer and no memory
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(* An empty list is associated with a null pointer and no memory
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* contents. *)
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* contents. *)
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| x :: ls' => [| p <> 0 |]
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| x :: ls' => [| p <> 0 |]
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* exists p', p |--> [x; p'] * linkedList p' ls'
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* exists p', p |--> [x; p'] * linkedList p' ls'
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(* A nonempty list is associated with a nonnull pointer and a two-cell
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(* A nonempty list is associated with a nonnull pointer and a two-cell
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* struct, which points to a further list. *)
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* struct, which points to a further list. *)
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end%sep.
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end%sep.
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(* The definition of [linkedList] is recursive in the list. Let's also prove
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(* The definition of [linkedList] is recursive in the list. Let's also prove
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