First draft of full prose for GeneralRec

latex/cpdt.bib

@@ -267,3 +267,22 @@
   publisher    = "MIT Press",
   chapter      = "8"
 }
+
+@article{Capretta,
+  author     = {Venanzio Capretta},
+  title      = {General Recursion via Coinductive Types},
+  journal    = {Logical Methods in Computer Science},
+  volume     = 1,
+  number     = 2,
+  year       = 2005,
+  pages      = {1--18},
+}
+
+@inproceedings{Megacz,
+ author = {Adam Megacz},
+ title = {A coinductive monad for prop-bounded recursion},
+ booktitle =   {Proceedings of the {ACM} Workshop Programming
+                Languages meets Program Verification},
+ pages = {11--20},
+ year = {2007},
+}

src/Match.v

@@ -465,7 +465,7 @@ Error: variable n should be bound to a term.
 >> *)
 Abort.
 
-(** 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{monads}\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.
+(** 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.
 
    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.