Mercurial > cpdt > repo
diff src/LogicProg.v @ 410:b4c37245502e
Typesetting pass over LogicProg
author | Adam Chlipala <adam@chlipala.net> |
---|---|
date | Fri, 08 Jun 2012 15:09:11 -0400 |
parents | 05efde66559d |
children | 610568369aee |
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--- a/src/LogicProg.v Fri Jun 08 15:00:59 2012 -0400 +++ b/src/LogicProg.v Fri Jun 08 15:09:11 2012 -0400 @@ -143,7 +143,7 @@ auto 6. -(** Sometimes it is useful to see a description of the proof tree that [auto] finds, with the %\index{tactics!info}%[info] tactical. *) +(** Sometimes it is useful to see a description of the proof tree that [auto] finds, with the %\index{tactics!info}%[info] tactical. (This tactical is not available in Coq 8.4 as of this writing, but I hope it reappears soon.) *) Restart. info auto 6. @@ -155,7 +155,7 @@ Qed. (* end thide *) -(** The two key components of logic programming are %\index{backtracking}%_backtracking_ and %\index{unification}%_unification_. To see these techniques in action, consider this further silly example. Here our candidate proof steps will be reflexivity and quantifier instantiation. *) +(** The two key components of logic programming are%\index{backtracking}% _backtracking_ and%\index{unification}% _unification_. To see these techniques in action, consider this further silly example. Here our candidate proof steps will be reflexivity and quantifier instantiation. *) Example seven_minus_three : exists x, x + 3 = 7. (* begin thide *) @@ -185,7 +185,7 @@ Example seven_minus_three' : exists x, plusR x 3 7. (* begin thide *) -(** We could attempt to guess the quantifier instantiation manually as before, but here there is no need. Instead of [apply], we use %\index{tactics!eapply}%[eapply] instead, which proceeds with placeholder %\index{unification variable}%_unification variables_ standing in for those parameters we wish to postpone guessing. *) +(** We could attempt to guess the quantifier instantiation manually as before, but here there is no need. Instead of [apply], we use %\index{tactics!eapply}%[eapply] instead, which proceeds with placeholder%\index{unification variable}% _unification variables_ standing in for those parameters we wish to postpone guessing. *) eapply ex_intro. (** [[ @@ -380,7 +380,7 @@ Abort. End slow. -(** Sometimes, though, transitivity is just what is needed to get a proof to go through automatically with [eauto]. For those cases, we can use named %\index{hint databases}%_hint databases_ to segragate hints into different groups that may be called on as needed. Here we put [eq_trans] into the database [slow]. *) +(** Sometimes, though, transitivity is just what is needed to get a proof to go through automatically with [eauto]. For those cases, we can use named%\index{hint databases}% _hint databases_ to segragate hints into different groups that may be called on as needed. Here we put [eq_trans] into the database [slow]. *) (* begin thide *) Hint Resolve eq_trans : slow. @@ -791,7 +791,7 @@ (* begin thide *) auto. - (** [crush] would have discharged this goal, but the default hint database for [auto] contains no hint that applies. *) + (** A call to [crush] would have discharged this goal, but the default hint database for [auto] contains no hint that applies. *) Abort. @@ -804,7 +804,7 @@ Qed. (* end thide *) -(** [Extern] hints may be implemented with the full Ltac language. This example shows a case where a hint uses a [match]. *) +(** A [Hint Extern] may be implemented with the full Ltac language. This example shows a case where a hint uses a [match]. *) Section forall_and. Variable A : Set. @@ -842,7 +842,7 @@ User error: Bound head variable >> - Coq's [auto] hint databases work as tables mapping %\index{head symbol}%_head symbols_ to lists of tactics to try. Because of this, the constant head of an [Extern] pattern must be determinable statically. In our first [Extern] hint, the head symbol was [not], since [x <> y] desugars to [not (eq x y)]; and, in the second example, the head symbol was [P]. + Coq's [auto] hint databases work as tables mapping%\index{head symbol}% _head symbols_ to lists of tactics to try. Because of this, the constant head of an [Extern] pattern must be determinable statically. In our first [Extern] hint, the head symbol was [not], since [x <> y] desugars to [not (eq x y)]; and, in the second example, the head symbol was [P]. Fortunately, a more basic form of [Hint Extern] also applies. We may simply leave out the pattern to the left of the [=>], incorporating the corresponding logic into the Ltac script. *) @@ -948,12 +948,8 @@ Qed. End garden_path. - (** remove printing * *) - (** It can also be useful to apply the [autorewrite with db in *] form, which does rewriting in hypotheses, as well as in the conclusion. *) - (** printing * $*$ *) - Lemma in_star : forall x y, f (f (f (f x))) = f (f y) -> f x = f (f (f y)). (* begin thide *)