Mercurial > cpdt > repo
comparison src/Match.v @ 394:cc8d0503619f
Citations for continuations and unification
| author | Adam Chlipala <adam@chlipala.net> |
|---|---|
| date | Sun, 22 Apr 2012 15:51:03 -0400 |
| parents | b911d0df5eee |
| children | 05efde66559d |
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| 393:d40b05266306 | 394:cc8d0503619f |
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| 469 | 469 |
| 470 (** What is going wrong here? The answer has to do with the dual status of Ltac as both a purely functional and an imperative programming language. The basic programming language is purely functional, but tactic scripts are one %``%#"#datatype#"#%''% that can be returned by such programs, and Coq will run such a script using an imperative semantics that mutates proof states. Readers familiar with %\index{monad}\index{Haskell}%monadic programming in Haskell%~\cite{Monads,IO}% may recognize a similarity. Side-effecting Haskell programs can be thought of as pure programs that return %\emph{%#<i>#the code of programs in an imperative language#</i>#%}%, where some out-of-band mechanism takes responsibility for running these derived programs. In this way, Haskell remains pure, while supporting usual input-output side effects and more. Ltac uses the same basic mechanism, but in a dynamically typed setting. Here the embedded imperative language includes all the tactics we have been applying so far. | 470 (** What is going wrong here? The answer has to do with the dual status of Ltac as both a purely functional and an imperative programming language. The basic programming language is purely functional, but tactic scripts are one %``%#"#datatype#"#%''% that can be returned by such programs, and Coq will run such a script using an imperative semantics that mutates proof states. Readers familiar with %\index{monad}\index{Haskell}%monadic programming in Haskell%~\cite{Monads,IO}% may recognize a similarity. Side-effecting Haskell programs can be thought of as pure programs that return %\emph{%#<i>#the code of programs in an imperative language#</i>#%}%, where some out-of-band mechanism takes responsibility for running these derived programs. In this way, Haskell remains pure, while supporting usual input-output side effects and more. Ltac uses the same basic mechanism, but in a dynamically typed setting. Here the embedded imperative language includes all the tactics we have been applying so far. |
| 471 | 471 |
| 472 Even basic [idtac] is an embedded imperative program, so we may not automatically mix it with purely functional code. In fact, a semicolon operator alone marks a span of Ltac code as an embedded tactic script. This makes some amount of sense, since pure functional languages have no need for sequencing: since they lack side effects, there is no reason to run an expression and then just throw away its value and move on to another expression. | 472 Even basic [idtac] is an embedded imperative program, so we may not automatically mix it with purely functional code. In fact, a semicolon operator alone marks a span of Ltac code as an embedded tactic script. This makes some amount of sense, since pure functional languages have no need for sequencing: since they lack side effects, there is no reason to run an expression and then just throw away its value and move on to another expression. |
| 473 | 473 |
| 474 The solution is like in Haskell: we must %``%#"#monadify#"#%''% our pure program to give it access to side effects. The trouble is that the embedded tactic language has no [return] construct. Proof scripts are about proving theorems, not calculating results. We can apply a somewhat awkward workaround that requires translating our program into %\index{continuation-passing style}\emph{%#<i>#continuation-passing style#</i>#%}%, a program structuring idea popular in functional programming. *) | 474 The solution is like in Haskell: we must %``%#"#monadify#"#%''% our pure program to give it access to side effects. The trouble is that the embedded tactic language has no [return] construct. Proof scripts are about proving theorems, not calculating results. We can apply a somewhat awkward workaround that requires translating our program into %\index{continuation-passing style}\emph{%#<i>#continuation-passing style#</i>#%}~\cite{continuations}%, a program structuring idea popular in functional programming. *) |
| 475 | 475 |
| 476 (* begin hide *) | 476 (* begin hide *) |
| 477 Reset length. | 477 Reset length. |
| 478 (* end hide *) | 478 (* end hide *) |
| 479 (** %\noindent\coqdockw{%#<tt>#Reset#</tt>#%}% [length.] *) | 479 (** %\noindent\coqdockw{%#<tt>#Reset#</tt>#%}% [length.] *) |