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Fix Epigram URL
author Adam Chlipala <adam@chlipala.net>
date Thu, 15 Oct 2015 07:42:00 -0400
parents dac7a2705b00
children 16d701d4bd82
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117 (** * Why Not a Different Dependently Typed Language? *) 117 (** * Why Not a Different Dependently Typed Language? *)
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119 (** 119 (**
120 The logic and programming language behind Coq belongs to a type-theory ecosystem with a good number of other thriving members. %\index{Agda}%{{http://appserv.cs.chalmers.se/users/ulfn/wiki/agda.php}Agda} and %\index{Epigram}%{{http://www.e-pig.org/}Epigram} 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? 120 The logic and programming language behind Coq belongs to a type-theory ecosystem with a good number of other thriving members. %\index{Agda}%{{http://appserv.cs.chalmers.se/users/ulfn/wiki/agda.php}Agda} and %\index{Epigram}%{{https://code.google.com/p/epigram/}Epigram} 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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122 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, to protect the sanity of the programmer. 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. 122 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, to protect the sanity of the programmer. 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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124 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 than manual coping with Coq's lack of programming bells and whistles. In this book, I will devote significant space to patterns for programming with dependent types in Coq as it is today. 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. 124 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 than manual coping with Coq's lack of programming bells and whistles. In this book, I will devote significant space to patterns for programming with dependent types in Coq as it is today. 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.
125 *) 125 *)