theory HOLCF_Specific

 imports HOLCF

 begin

 chapter {* Isabelle/HOLCF \label{ch:holcf} *}

 section {* Mixfix syntax for continuous operations *}

 text {*

   \begin{matharray}{rcl}

     @{command_def (HOLCF) "consts"} & : & @{text "theory \<rightarrow> theory"} \\

   \end{matharray}

   HOLCF provides a separate type for continuous functions @{text "\<alpha> \<rightarrow>

   \<beta>"}, with an explicit application operator @{term "f \<cdot> x"}.

   Isabelle mixfix syntax normally refers directly to the pure

   meta-level function type @{text "\<alpha> \<Rightarrow> \<beta>"}, with application @{text "f

   x"}.

   The HOLCF variant of @{command (HOLCF) "consts"} modifies that of

   Pure Isabelle (cf.\ \secref{sec:consts}) such that declarations

   involving continuous function types are treated specifically.  Any

   given syntax template is transformed internally, generating

   translation rules for the abstract and concrete representation of

   continuous application.  Note that mixing of HOLCF and Pure

   application is \emph{not} supported!

 *}

 section {* Recursive domains *}

 text {*

   \begin{matharray}{rcl}

     @{command_def (HOLCF) "domain"} & : & @{text "theory \<rightarrow> theory"} \\

   \end{matharray}

   @{rail "

     @@{command (HOLCF) domain} @{syntax parname}? (dmspec + @'and')

     ;

     dmspec: @{syntax typespec} '=' (cons + '|')

     ;

     cons: @{syntax name} (@{syntax type} * ) @{syntax mixfix}?

     ;

     dtrules: @'distinct' @{syntax thmrefs} @'inject' @{syntax thmrefs}

       @'induction' @{syntax thmrefs}

   "}

   Recursive domains in HOLCF are analogous to datatypes in classical

   HOL (cf.\ \secref{sec:hol-datatype}).  Mutual recursion is

   supported, but no nesting nor arbitrary branching.  Domain

   constructors may be strict (default) or lazy, the latter admits to

   introduce infinitary objects in the typical LCF manner (e.g.\ lazy

   lists).  See also \cite{MuellerNvOS99} for a general discussion of

   HOLCF domains.

 *}

 end