# HG changeset patch # User Adam Chlipala # Date 1380223572 14400 # Node ID 3b21f43951789a808d1c34ee6482e40b5629037f # Parent a4b3386ae140b29aea4e31dfe7373e2ca055a644 Fix a word that was only included in LaTeX version diff -r a4b3386ae140 -r 3b21f4395178 src/GeneralRec.v --- a/src/GeneralRec.v Thu Sep 19 17:28:32 2013 -0400 +++ b/src/GeneralRec.v Thu Sep 26 15:26:12 2013 -0400 @@ -169,7 +169,7 @@ red; intro; eapply lengthOrder_wf'; eauto. Defined. - (** Notice that we end these proofs with %\index{Vernacular commands!Defined}%[Defined], not [Qed]. Recall that [Defined] marks the theorems as %\emph{transparent}%, so that the details of their proofs may be used during program execution. Why could such details possibly matter for computation? It turns out that [Fix] satisfies the primitive recursion restriction by declaring itself as _recursive in the structure of [Acc] proofs_. This is possible because [Acc] proofs follow a predictable inductive structure. We must do work, as in the last theorem's proof, to establish that all elements of a type belong to [Acc], but the automatic unwinding of those proofs during recursion is straightforward. If we ended the proof with [Qed], the proof details would be hidden from computation, in which case the unwinding process would get stuck. + (** Notice that we end these proofs with %\index{Vernacular commands!Defined}%[Defined], not [Qed]. Recall that [Defined] marks the theorems as %\emph{%##transparent##%}%, so that the details of their proofs may be used during program execution. Why could such details possibly matter for computation? It turns out that [Fix] satisfies the primitive recursion restriction by declaring itself as _recursive in the structure of [Acc] proofs_. This is possible because [Acc] proofs follow a predictable inductive structure. We must do work, as in the last theorem's proof, to establish that all elements of a type belong to [Acc], but the automatic unwinding of those proofs during recursion is straightforward. If we ended the proof with [Qed], the proof details would be hidden from computation, in which case the unwinding process would get stuck. To justify our two recursive [mergeSort] calls, we will also need to prove that [split] respects the [lengthOrder] relation. These proofs, too, must be kept transparent, to avoid stuckness of [Fix] evaluation. We use the syntax [@foo] to reference identifier [foo] with its implicit argument behavior turned off. (The proof details below use Ltac features not introduced yet, and they are safe to skip for now.) *)