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For Coq 8.5 compatibility, use [Admitted] instead of [admit]
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2 changed files with 10 additions and 16 deletions
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@ -38,8 +38,7 @@ Compute size ex2.
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* Size is an upper bound on depth. *)
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Theorem depth_le_size : forall e, depth e <= size e.
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Proof.
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admit.
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Qed.
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Admitted.
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(* A silly recursive function: swap the operand orders of all binary operators. *)
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Fixpoint commuter (e : arith) : arith :=
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@ -56,18 +55,16 @@ Compute commuter ex2.
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Theorem size_commuter : forall e, size (commuter e) = size e.
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Proof.
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admit.
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Qed.
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Admitted.
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Theorem depth_commuter : forall e, depth (commuter e) = depth e.
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Proof.
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admit.
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Qed.
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Admitted.
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Theorem commuter_inverse : forall e, commuter (commuter e) = e.
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Proof.
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admit.
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Qed.
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Admitted.
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@ -67,8 +67,7 @@ Fixpoint commuter (e : arith) : arith :=
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* *meanings* of expressions! *)
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Theorem commuter_ok : forall v e, interp (commuter e) v = interp e v.
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Proof.
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admit.
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Qed.
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Admitted.
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(* Let's also revisit substitution. *)
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Fixpoint substitute (inThis : arith) (replaceThis : var) (withThis : arith) : arith :=
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@ -102,8 +101,7 @@ Fixpoint doSomeArithmetic (e : arith) : arith :=
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Theorem doSomeArithmetic_ok : forall e v, interp (doSomeArithmetic e) v = interp e v.
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Proof.
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admit.
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Qed.
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Admitted.
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@ -183,8 +181,8 @@ Fixpoint compile (e : arith) : list instruction :=
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Theorem compile_ok : forall e v, run (compile e) v nil = interp e v :: nil.
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Proof.
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admit.
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Qed.
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Admitted.
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@ -279,8 +277,7 @@ Theorem factorial_ok : forall v input,
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v $? "input" = Some input
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-> exec factorial v $? "output" = Some (fact input).
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Proof.
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admit.
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Qed.
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Admitted.
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