Why not Agda/Epigram?

book/src/Intro.v

@@ -93,7 +93,7 @@ ACL2 and PVS do not meet the de Bruijn criterion, employing fancy decision proce
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 A commitment to a kernel proof language opens up wide possibilities for user extension of proof automation systems, without allowing user mistakes to trick the overall system into accepting invalid proofs.  Almost any interesting verification problem is undecidable, so it is important to help users build their own procedures for solving the restricted problems that they encounter in particular implementations.
 
-Twelf features no proof automation marked as a bonafide part of the latest release; there is some code included for testing purposes.  The Twelf style is based on writing out all proofs in full detail.  Because Twelf is specialized to the domain of syntactic metatheory proofs about programming languages and logics, it is feasible to use it to write those kinds of proofs manually.  Outside that domain, the lack of automation can be a serious obstacle to productivity.  Most kinds of program verification fall outside Twelf's forte.
+Twelf features no proof automation marked as a bonafide part of the latest release; there is some automation code included for testing purposes.  The Twelf style is based on writing out all proofs in full detail.  Because Twelf is specialized to the domain of syntactic metatheory proofs about programming languages and logics, it is feasible to use it to write those kinds of proofs manually.  Outside that domain, the lack of automation can be a serious obstacle to productivity.  Most kinds of program verification fall outside Twelf's forte.
 
 Of the remaining tools, all can support user extension with new decision procedures by hacking directly in the tool's implementation language (such as OCaml for Coq).  Since ACL2 and PVS do not satisfy the de Bruijn criterion, overall correctness is at the mercy of the authors of new procedures.
 
@@ -109,6 +109,17 @@ The critical ingredient for this technique, many of whose instances are referred
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+(** * Why Not a Different Dependently-Typed Language? *)
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+The logic and programming language behind Coq belongs to a type-theory ecosystem with a good number of other thriving members.  %Agda\footnote{\url{http://appserv.cs.chalmers.se/users/ulfn/wiki/agda.php}}%#<a href="http://appserv.cs.chalmers.se/users/ulfn/wiki/agda.php">Agda</a># and %Epigram\footnote{\url{http://www.e-pig.org/}}%#<a href="http://www.e-pig.org/">Epigram</a># are the most developed tools among the alternatives to Coq, and there are others that are earlier in their lifecycles.  All of the languages in this family feel sort of like different historical offshoots of Latin.  The hardest conceptual epiphanies are, for the most part, portable among all the languages.  Given this, why choose Coq for certified programming?
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+I think the answer is simple.  None of the competition has well-developed systems for tactic-based theorem proving.  Agda and Epigram are designed and marketed more as programming languages than proof assistants.  Dependent types are great, because they often help you prove deep theorems without doing anything that feels like proving.  Nonetheless, almost any interesting certified programming project will benefit from some activity that deserves to be called proving, and many interesting projects absolutely require semi-automated proving, if the sanity of the programmer is to be safeguarded.  Informally, proving is unavoidable when any correctness proof for a program has a structure that does not mirror the structure of the program itself.  An example is a compiler correctness proof, which probably proceeds by induction on program execution traces, which have no simple relationship with the structure of the compiler or the structure of the programs it compiles.  In building such proofs, a mature system for scripted proof automation is invaluable.
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+On the other hand, Agda, Epigram, and similar tools have less implementation baggage associated with them, and so they tend to be the default first homes of innovations in practical type theory.  Some significant kinds of dependently-typed programs are much easier to write in Agda and Epigram than in Coq.  The former tools may very well be superior choices for projects that do not involve any "proving."  Anecdotally, I have gotten the impression that manual proving is orders of magnitudes more costly then manual coping with Coq's lack of programming bells and whistles.  In this book, I will devote significant time to patterns for programming with dependent types in Coq as it is today, and I will also try to mention related innovations in Agda and Epigram.  We can hope that the type theory community is tending towards convergence on the right set of features for practical programming with dependent types, and that we will eventually have a single tool embodying those features.
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 (** * Engineering with a Proof Assistant *)
 
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