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Update for Coq 8.9
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7 changed files with 23 additions and 23 deletions
2
.gitignore
vendored
2
.gitignore
vendored
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@ -12,7 +12,7 @@
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Makefile.coq
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Makefile.coq.conf
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*.glob
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*.v.d
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*.d
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*.vo
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frap.tgz
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.coq-native
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@ -886,7 +886,7 @@ Module DeeperWithFail.
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| Stepped (h : heap) (c : cmd result)
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| Failed.
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Implicit Arguments Failed [result].
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Arguments Failed {result}.
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Fixpoint step {result} (c : cmd result) (h : heap) : stepResult result :=
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match c with
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@ -731,7 +731,7 @@ Module DeeperWithFail.
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| Stepped (h : heap) (c : cmd result)
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| Failed.
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Implicit Arguments Failed [result].
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Arguments Failed {result}.
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Fixpoint step {result} (c : cmd result) (h : heap) : stepResult result :=
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match c with
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@ -1217,7 +1217,7 @@ Section split.
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Defined.
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End split.
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Implicit Arguments split [P1 P2].
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Arguments split {P1 P2}.
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(* And now, a few more boring lemmas. Rejoin at "BOREDOM VANQUISHED", if you
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* like. *)
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@ -599,7 +599,7 @@ Section split.
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Defined.
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End split.
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Implicit Arguments split [P1 P2].
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Arguments split {P1 P2}.
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(* And now, a few more boring lemmas. Rejoin at "BOREDOM VANQUISHED", if you
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* like. *)
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@ -1,5 +1,5 @@
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Require Import Eqdep String Arith Omega Program Sets Relations Map Var Invariant Bool ModelCheck.
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Export String Arith Sets Relations Map Var Invariant Bool ModelCheck.
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Export Ascii String Arith Sets Relations Map Var Invariant Bool ModelCheck.
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Require Import List.
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Export List ListNotations.
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Open Scope string_scope.
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@ -776,25 +776,25 @@ Inductive boundRunningTime : cmd -> nat -> Prop :=
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(* Perhaps surprisingly, there exist commands that have no finite time bounds!
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* Mixed-embedding languages often have these counterintuitive properties. *)
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Theorem boundRunningTime_not_total : exists c, forall n, ~boundRunningTime c n.
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Proof.
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Fixpoint scribbly (n : nat) : cmd :=
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Fixpoint scribbly (n : nat) : cmd :=
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match n with
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| O => Return 0
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| S n' => _ <- Write n' 0; scribbly n'
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end.
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Lemma scribbly_time : forall n m,
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Lemma scribbly_time : forall n m,
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boundRunningTime (scribbly n) m
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-> m >= n.
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Proof.
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Proof.
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induct n; invert 1; auto.
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invert H2.
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specialize (H4 n0).
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apply IHn in H4.
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linear_arithmetic.
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Qed.
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Qed.
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Theorem boundRunningTime_not_total : exists c, forall n, ~boundRunningTime c n.
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Proof.
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exists (n <- Read 0; scribbly n); propositional.
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invert H.
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specialize (H4 (S n2)).
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