src/Doc/Datatypes/Datatypes.thy
author traytel
Tue, 01 Oct 2013 17:06:35 +0200
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child 54023 cede3c1d2417
permissions -rw-r--r--
base the fset bnf on the new FSet theory
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(*  Title:      Doc/Datatypes/Datatypes.thy
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    Author:     Jasmin Blanchette, TU Muenchen
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    Author:     Lorenz Panny, TU Muenchen
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    Author:     Andrei Popescu, TU Muenchen
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    Author:     Dmitriy Traytel, TU Muenchen
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Tutorial for (co)datatype definitions with the new package.
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*)
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theory Datatypes
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imports Setup
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keywords
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  "primcorec_notyet" :: thy_decl
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begin
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(*<*)
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(* FIXME: Temporary setup until "primcorec" and "primcorecursive" are fully implemented. *)
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ML_command {*
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fun add_dummy_cmd _ _ lthy = lthy;
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val _ = Outer_Syntax.local_theory @{command_spec "primcorec_notyet"} ""
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  (Parse.fixes -- Parse_Spec.where_alt_specs >> uncurry add_dummy_cmd);
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*}
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(*>*)
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section {* Introduction
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  \label{sec:introduction} *}
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text {*
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The 2013 edition of Isabelle introduced a new definitional package for freely
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generated datatypes and codatatypes. The datatype support is similar to that
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provided by the earlier package due to Berghofer and Wenzel
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\cite{Berghofer-Wenzel:1999:TPHOL}, documented in the Isar reference manual
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\cite{isabelle-isar-ref}; indeed, replacing the keyword \keyw{datatype} by
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@{command datatype_new} is usually all that is needed to port existing theories
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to use the new package.
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Perhaps the main advantage of the new package is that it supports recursion
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through a large class of non-datatypes, such as finite sets:
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*}
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    datatype_new 'a tree\<^sub>f\<^sub>s = Node\<^sub>f\<^sub>s (lbl\<^sub>f\<^sub>s: 'a) (sub\<^sub>f\<^sub>s: "'a tree\<^sub>f\<^sub>s fset")
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text {*
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\noindent
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Another strong point is the support for local definitions:
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*}
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    context linorder
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    begin
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    datatype_new flag = Less | Eq | Greater
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    end
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text {*
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\noindent
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The package also provides some convenience, notably automatically generated
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discriminators and selectors.
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In addition to plain inductive datatypes, the new package supports coinductive
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datatypes, or \emph{codatatypes}, which may have infinite values. For example,
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the following command introduces the type of lazy lists, which comprises both
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finite and infinite values:
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*}
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(*<*)
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    locale early
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(*>*)
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    codatatype (*<*)(in early) (*>*)'a llist = LNil | LCons 'a "'a llist"
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text {*
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\noindent
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Mixed inductive--coinductive recursion is possible via nesting. Compare the
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following four Rose tree examples:
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*}
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    datatype_new (*<*)(in early) (*>*)'a tree\<^sub>f\<^sub>f = Node\<^sub>f\<^sub>f 'a "'a tree\<^sub>f\<^sub>f list"
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    datatype_new (*<*)(in early) (*>*)'a tree\<^sub>f\<^sub>i = Node\<^sub>f\<^sub>i 'a "'a tree\<^sub>f\<^sub>i llist"
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    codatatype (*<*)(in early) (*>*)'a tree\<^sub>i\<^sub>f = Node\<^sub>i\<^sub>f 'a "'a tree\<^sub>i\<^sub>f list"
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    codatatype (*<*)(in early) (*>*)'a tree\<^sub>i\<^sub>i = Node\<^sub>i\<^sub>i 'a "'a tree\<^sub>i\<^sub>i llist"
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text {*
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The first two tree types allow only finite branches, whereas the last two allow
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branches of infinite length. Orthogonally, the nodes in the first and third
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types have finite branching, whereas those of the second and fourth may have
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infinitely many direct subtrees.
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To use the package, it is necessary to import the @{theory BNF} theory, which
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can be precompiled into the \texttt{HOL-BNF} image. The following commands show
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how to launch jEdit/PIDE with the image loaded and how to build the image
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without launching jEdit:
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*}
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text {*
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\noindent
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\ \ \ \ \texttt{isabelle jedit -l HOL-BNF} \\
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\noindent
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\hbox{}\ \ \ \ \texttt{isabelle build -b HOL-BNF}
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*}
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text {*
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The package, like its predecessor, fully adheres to the LCF philosophy
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\cite{mgordon79}: The characteristic theorems associated with the specified
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(co)datatypes are derived rather than introduced axiomatically.%
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\footnote{If the @{text quick_and_dirty} option is enabled, some of the
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internal constructions and most of the internal proof obligations are skipped.}
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The package's metatheory is described in a pair of papers
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\cite{traytel-et-al-2012,blanchette-et-al-wit}. The central notion is that of a
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\emph{bounded natural functor} (BNF)---a well-behaved type constructor for which
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nested (co)recursion is supported.
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This tutorial is organized as follows:
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\begin{itemize}
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\setlength{\itemsep}{0pt}
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\item Section \ref{sec:defining-datatypes}, ``Defining Datatypes,''
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describes how to specify datatypes using the @{command datatype_new} command.
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\item Section \ref{sec:defining-recursive-functions}, ``Defining Recursive
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Functions,'' describes how to specify recursive functions using
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@{command primrec_new}, \keyw{fun}, and \keyw{function}.
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\item Section \ref{sec:defining-codatatypes}, ``Defining Codatatypes,''
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describes how to specify codatatypes using the @{command codatatype} command.
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\item Section \ref{sec:defining-corecursive-functions}, ``Defining Corecursive
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Functions,'' describes how to specify corecursive functions using the
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@{command primcorec} and @{command primcorecursive} commands.
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\item Section \ref{sec:registering-bounded-natural-functors}, ``Registering
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Bounded Natural Functors,'' explains how to use the @{command bnf} command
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to register arbitrary type constructors as BNFs.
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\item Section
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\ref{sec:deriving-destructors-and-theorems-for-free-constructors},
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``Deriving Destructors and Theorems for Free Constructors,'' explains how to
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use the command @{command wrap_free_constructors} to derive destructor constants
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and theorems for freely generated types, as performed internally by @{command
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datatype_new} and @{command codatatype}.
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%\item Section \ref{sec:standard-ml-interface}, ``Standard ML Interface,''
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%describes the package's programmatic interface.
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%\item Section \ref{sec:interoperability}, ``Interoperability,''
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%is concerned with the packages' interaction with other Isabelle packages and
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%tools, such as the code generator and the counterexample generators.
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%\item Section \ref{sec:known-bugs-and-limitations}, ``Known Bugs and
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%Limitations,'' concludes with known open issues at the time of writing.
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\end{itemize}
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\newbox\boxA
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\setbox\boxA=\hbox{\texttt{nospam}}
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\newcommand\authoremaili{\texttt{blan{\color{white}nospam}\kern-\wd\boxA{}chette@\allowbreak
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in.\allowbreak tum.\allowbreak de}}
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\newcommand\authoremailii{\texttt{lore{\color{white}nospam}\kern-\wd\boxA{}nz.panny@\allowbreak
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\allowbreak tum.\allowbreak de}}
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\newcommand\authoremailiii{\texttt{pope{\color{white}nospam}\kern-\wd\boxA{}scua@\allowbreak
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in.\allowbreak tum.\allowbreak de}}
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\newcommand\authoremailiv{\texttt{tray{\color{white}nospam}\kern-\wd\boxA{}tel@\allowbreak
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in.\allowbreak tum.\allowbreak de}}
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The commands @{command datatype_new} and @{command primrec_new} are expected to
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replace \keyw{datatype} and \keyw{primrec} in a future release. Authors of new
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theories are encouraged to use the new commands, and maintainers of older
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theories may want to consider upgrading.
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Comments and bug reports concerning either the tool or this tutorial should be
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directed to the authors at \authoremaili, \authoremailii, \authoremailiii,
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and \authoremailiv.
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\begin{framed}
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\noindent
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\textbf{Warning:}\enskip This tutorial and the package it describes are under
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construction. Please forgive their appearance. Should you have suggestions
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or comments regarding either, please let the authors know.
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\end{framed}
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*}
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section {* Defining Datatypes
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  \label{sec:defining-datatypes} *}
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text {*
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Datatypes can be specified using the @{command datatype_new} command.
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*}
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subsection {* Introductory Examples
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  \label{ssec:datatype-introductory-examples} *}
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text {*
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Datatypes are illustrated through concrete examples featuring different flavors
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of recursion. More examples can be found in the directory
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\verb|~~/src/HOL/BNF/Examples|.
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*}
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subsubsection {* Nonrecursive Types
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  \label{sssec:datatype-nonrecursive-types} *}
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text {*
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Datatypes are introduced by specifying the desired names and argument types for
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their constructors. \emph{Enumeration} types are the simplest form of datatype.
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All their constructors are nullary:
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*}
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    datatype_new trool = Truue | Faalse | Perhaaps
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text {*
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\noindent
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Here, @{const Truue}, @{const Faalse}, and @{const Perhaaps} have the type @{typ trool}.
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Polymorphic types are possible, such as the following option type, modeled after
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its homologue from the @{theory Option} theory:
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*}
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(*<*)
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    hide_const None Some
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(*>*)
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    datatype_new 'a option = None | Some 'a
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text {*
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\noindent
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The constructors are @{text "None :: 'a option"} and
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@{text "Some :: 'a \<Rightarrow> 'a option"}.
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The next example has three type parameters:
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*}
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    datatype_new ('a, 'b, 'c) triple = Triple 'a 'b 'c
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text {*
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\noindent
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The constructor is
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@{text "Triple :: 'a \<Rightarrow> 'b \<Rightarrow> 'c \<Rightarrow> ('a, 'b, 'c) triple"}.
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Unlike in Standard ML, curried constructors are supported. The uncurried variant
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is also possible:
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*}
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    datatype_new ('a, 'b, 'c) triple\<^sub>u = Triple\<^sub>u "'a * 'b * 'c"
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text {*
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\noindent
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Occurrences of nonatomic types on the right-hand side of the equal sign must be
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enclosed in double quotes, as is customary in Isabelle.
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*}
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subsubsection {* Simple Recursion
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  \label{sssec:datatype-simple-recursion} *}
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text {*
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Natural numbers are the simplest example of a recursive type:
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*}
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    datatype_new nat = Zero | Suc nat
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text {*
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\noindent
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Lists were shown in the introduction. Terminated lists are a variant:
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*}
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    datatype_new (*<*)(in early) (*>*)('a, 'b) tlist = TNil 'b | TCons 'a "('a, 'b) tlist"
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subsubsection {* Mutual Recursion
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  \label{sssec:datatype-mutual-recursion} *}
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text {*
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\emph{Mutually recursive} types are introduced simultaneously and may refer to
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each other. The example below introduces a pair of types for even and odd
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natural numbers:
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*}
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    datatype_new even_nat = Even_Zero | Even_Suc odd_nat
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    and odd_nat = Odd_Suc even_nat
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text {*
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\noindent
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Arithmetic expressions are defined via terms, terms via factors, and factors via
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expressions:
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*}
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    datatype_new ('a, 'b) exp =
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      Term "('a, 'b) trm" | Sum "('a, 'b) trm" "('a, 'b) exp"
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    and ('a, 'b) trm =
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      Factor "('a, 'b) fct" | Prod "('a, 'b) fct" "('a, 'b) trm"
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    and ('a, 'b) fct =
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      Const 'a | Var 'b | Expr "('a, 'b) exp"
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subsubsection {* Nested Recursion
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  \label{sssec:datatype-nested-recursion} *}
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text {*
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\emph{Nested recursion} occurs when recursive occurrences of a type appear under
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a type constructor. The introduction showed some examples of trees with nesting
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through lists. A more complex example, that reuses our @{type option} type,
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follows:
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*}
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    datatype_new 'a btree =
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      BNode 'a "'a btree option" "'a btree option"
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text {*
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\noindent
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Not all nestings are admissible. For example, this command will fail:
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*}
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    datatype_new 'a wrong = Wrong (*<*)'a
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    typ (*>*)"'a wrong \<Rightarrow> 'a"
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text {*
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\noindent
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The issue is that the function arrow @{text "\<Rightarrow>"} allows recursion
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only through its right-hand side. This issue is inherited by polymorphic
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datatypes defined in terms of~@{text "\<Rightarrow>"}:
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*}
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    datatype_new ('a, 'b) fn = Fn "'a \<Rightarrow> 'b"
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    datatype_new 'a also_wrong = Also_Wrong (*<*)'a
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    typ (*>*)"('a also_wrong, 'a) fn"
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text {*
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\noindent
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This is legal:
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*}
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    datatype_new 'a ftree = FTLeaf 'a | FTNode "'a \<Rightarrow> 'a ftree"
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text {*
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\noindent
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In general, type constructors @{text "('a\<^sub>1, \<dots>, 'a\<^sub>m) t"}
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allow recursion on a subset of their type arguments @{text 'a\<^sub>1}, \ldots,
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@{text 'a\<^sub>m}. These type arguments are called \emph{live}; the remaining
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type arguments are called \emph{dead}. In @{typ "'a \<Rightarrow> 'b"} and
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@{typ "('a, 'b) fn"}, the type variable @{typ 'a} is dead and @{typ 'b} is live.
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Type constructors must be registered as BNFs to have live arguments. This is
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done automatically for datatypes and codatatypes introduced by the @{command
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datatype_new} and @{command codatatype} commands.
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Section~\ref{sec:registering-bounded-natural-functors} explains how to register
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arbitrary type constructors as BNFs.
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*}
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subsubsection {* Custom Names and Syntaxes
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  \label{sssec:datatype-custom-names-and-syntaxes} *}
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text {*
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The @{command datatype_new} command introduces various constants in addition to
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the constructors. With each datatype are associated set functions, a map
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function, a relator, discriminators, and selectors, all of which can be given
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custom names. In the example below, the traditional names
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@{text set}, @{text map}, @{text list_all2}, @{text null}, @{text hd}, and
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@{text tl} override the default names @{text list_set}, @{text list_map}, @{text
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list_rel}, @{text is_Nil}, @{text un_Cons1}, and @{text un_Cons2}:
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*}
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(*<*)
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    no_translations
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      "[x, xs]" == "x # [xs]"
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      "[x]" == "x # []"
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    no_notation
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      Nil ("[]") and
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      Cons (infixr "#" 65)
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    hide_type list
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    hide_const Nil Cons hd tl set map list_all2 list_case list_rec
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    context early begin
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(*>*)
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    datatype_new (set: 'a) list (map: map rel: list_all2) =
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      null: Nil (defaults tl: Nil)
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    | Cons (hd: 'a) (tl: "'a list")
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text {*
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\noindent
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The command introduces a discriminator @{const null} and a pair of selectors
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@{const hd} and @{const tl} characterized as follows:
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%
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\[@{thm list.collapse(1)[of xs, no_vars]}
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  \qquad @{thm list.collapse(2)[of xs, no_vars]}\]
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%
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For two-constructor datatypes, a single discriminator constant suffices. The
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discriminator associated with @{const Cons} is simply
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@{term "\<lambda>xs. \<not> null xs"}.
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The @{text defaults} clause following the @{const Nil} constructor specifies a
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default value for selectors associated with other constructors. Here, it is used
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to ensure that the tail of the empty list is itself (instead of being left
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unspecified).
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Because @{const Nil} is nullary, it is also possible to use
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@{term "\<lambda>xs. xs = Nil"} as a discriminator. This is specified by
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entering ``@{text "="}'' instead of the identifier @{const null}. Although this
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may look appealing, the mixture of constructors and selectors in the
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characteristic theorems can lead Isabelle's automation to switch between the
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constructor and the destructor view in surprising ways.
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The usual mixfix syntax annotations are available for both types and
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constructors. For example:
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*}
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(*<*)
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    end
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(*>*)
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    datatype_new ('a, 'b) prod (infixr "*" 20) = Pair 'a 'b
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text {* \blankline *}
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    datatype_new (set: 'a) list (map: map rel: list_all2) =
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      null: Nil ("[]")
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    | Cons (hd: 'a) (tl: "'a list") (infixr "#" 65)
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text {*
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\noindent
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Incidentally, this is how the traditional syntax can be set up:
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*}
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    syntax "_list" :: "args \<Rightarrow> 'a list" ("[(_)]")
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text {* \blankline *}
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    translations
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      "[x, xs]" == "x # [xs]"
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      "[x]" == "x # []"
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subsection {* Command Syntax
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  \label{ssec:datatype-command-syntax} *}
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subsubsection {* \keyw{datatype\_new}
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  \label{sssec:datatype-new} *}
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text {*
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\begin{matharray}{rcl}
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  @{command_def "datatype_new"} & : & @{text "local_theory \<rightarrow> local_theory"}
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\end{matharray}
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@{rail "
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  @@{command datatype_new} target? @{syntax dt_options}? \\
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    (@{syntax dt_name} '=' (@{syntax ctor} + '|') + @'and')
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  ;
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  @{syntax_def dt_options}: '(' (('no_discs_sels' | 'rep_compat') + ',') ')'
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"}
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The syntactic entity \synt{target} can be used to specify a local
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context---e.g., @{text "(in linorder)"}. It is documented in the Isar reference
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manual \cite{isabelle-isar-ref}.
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%
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The optional target is optionally followed by datatype-specific options:
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\begin{itemize}
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\setlength{\itemsep}{0pt}
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\item
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The @{text "no_discs_sels"} option indicates that no discriminators or selectors
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should be generated.
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\item
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The @{text "rep_compat"} option indicates that the generated names should
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contain optional (and normally not displayed) ``@{text "new."}'' components to
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prevent clashes with a later call to \keyw{rep\_datatype}. See
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Section~\ref{ssec:datatype-compatibility-issues} for details.
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\end{itemize}
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The left-hand sides of the datatype equations specify the name of the type to
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define, its type parameters, and additional information:
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@{rail "
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  @{syntax_def dt_name}: @{syntax tyargs}? name @{syntax map_rel}? mixfix?
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  ;
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  @{syntax_def tyargs}: typefree | '(' ((name ':')? typefree + ',') ')'
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  ;
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  @{syntax_def map_rel}: '(' ((('map' | 'rel') ':' name) +) ')'
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"}
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\noindent
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The syntactic entity \synt{name} denotes an identifier, \synt{typefree}
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denotes fixed type variable (@{typ 'a}, @{typ 'b}, \ldots), and \synt{mixfix}
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denotes the usual parenthesized mixfix notation. They are documented in the Isar
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reference manual \cite{isabelle-isar-ref}.
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The optional names preceding the type variables allow to override the default
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names of the set functions (@{text t_set1}, \ldots, @{text t_setM}).
53647
e78ebb290dd6 more (co)data docs
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parents: 53646
diff changeset
   492
Inside a mutually recursive specification, all defined datatypes must
e78ebb290dd6 more (co)data docs
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parents: 53646
diff changeset
   493
mention exactly the same type variables in the same order.
52822
ae938ac9a721 more (co)datatype docs
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parents: 52806
diff changeset
   494
52824
b7a83845bc93 more (co)datatype documentation
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parents: 52822
diff changeset
   495
@{rail "
53534
de2027f9aff3 more (co)datatype documentation
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parents: 53491
diff changeset
   496
  @{syntax_def ctor}: (name ':')? name (@{syntax ctor_arg} * ) \\
de2027f9aff3 more (co)datatype documentation
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parents: 53491
diff changeset
   497
    @{syntax dt_sel_defaults}? mixfix?
52824
b7a83845bc93 more (co)datatype documentation
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parents: 52822
diff changeset
   498
"}
b7a83845bc93 more (co)datatype documentation
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parents: 52822
diff changeset
   499
53535
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parents: 53534
diff changeset
   500
\medskip
d0c163c6c725 more (co)data docs
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parents: 53534
diff changeset
   501
52827
395d3df496ed more (co)datatype documentation
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parents: 52824
diff changeset
   502
\noindent
53863
c7364dca96f2 textual improvements following Christian Sternagel's feedback
blanchet
parents: 53857
diff changeset
   503
The main constituents of a constructor specification are the name of the
52827
395d3df496ed more (co)datatype documentation
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parents: 52824
diff changeset
   504
constructor and the list of its argument types. An optional discriminator name
53554
78fe0002024d more (co)data docs
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parents: 53553
diff changeset
   505
can be supplied at the front to override the default name
78fe0002024d more (co)data docs
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parents: 53553
diff changeset
   506
(@{text t.is_C\<^sub>j}).
52822
ae938ac9a721 more (co)datatype docs
blanchet
parents: 52806
diff changeset
   507
52824
b7a83845bc93 more (co)datatype documentation
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parents: 52822
diff changeset
   508
@{rail "
53534
de2027f9aff3 more (co)datatype documentation
blanchet
parents: 53491
diff changeset
   509
  @{syntax_def ctor_arg}: type | '(' name ':' type ')'
52827
395d3df496ed more (co)datatype documentation
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parents: 52824
diff changeset
   510
"}
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
   511
53535
d0c163c6c725 more (co)data docs
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parents: 53534
diff changeset
   512
\medskip
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   513
52827
395d3df496ed more (co)datatype documentation
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parents: 52824
diff changeset
   514
\noindent
395d3df496ed more (co)datatype documentation
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parents: 52824
diff changeset
   515
In addition to the type of a constructor argument, it is possible to specify a
395d3df496ed more (co)datatype documentation
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parents: 52824
diff changeset
   516
name for the corresponding selector to override the default name
53554
78fe0002024d more (co)data docs
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parents: 53553
diff changeset
   517
(@{text un_C\<^sub>ji}). The same selector names can be reused for several
78fe0002024d more (co)data docs
blanchet
parents: 53553
diff changeset
   518
constructors as long as they share the same type.
52827
395d3df496ed more (co)datatype documentation
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parents: 52824
diff changeset
   519
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
   520
@{rail "
53621
9c3a80af72ff more (co)data doc
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parents: 53619
diff changeset
   521
  @{syntax_def dt_sel_defaults}: '(' 'defaults' (name ':' term +) ')'
52824
b7a83845bc93 more (co)datatype documentation
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parents: 52822
diff changeset
   522
"}
52827
395d3df496ed more (co)datatype documentation
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parents: 52824
diff changeset
   523
395d3df496ed more (co)datatype documentation
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parents: 52824
diff changeset
   524
\noindent
395d3df496ed more (co)datatype documentation
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parents: 52824
diff changeset
   525
Given a constructor
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
   526
@{text "C \<Colon> \<sigma>\<^sub>1 \<Rightarrow> \<dots> \<Rightarrow> \<sigma>\<^sub>p \<Rightarrow> \<sigma>"},
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
   527
default values can be specified for any selector
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
   528
@{text "un_D \<Colon> \<sigma> \<Rightarrow> \<tau>"}
53535
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   529
associated with other constructors. The specified default value must be of type
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
   530
@{text "\<sigma>\<^sub>1 \<Rightarrow> \<dots> \<Rightarrow> \<sigma>\<^sub>p \<Rightarrow> \<tau>"}
53863
c7364dca96f2 textual improvements following Christian Sternagel's feedback
blanchet
parents: 53857
diff changeset
   531
(i.e., it may depend on @{text C}'s arguments).
52822
ae938ac9a721 more (co)datatype docs
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parents: 52806
diff changeset
   532
*}
ae938ac9a721 more (co)datatype docs
blanchet
parents: 52806
diff changeset
   533
53617
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parents: 53565
diff changeset
   534
53621
9c3a80af72ff more (co)data doc
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parents: 53619
diff changeset
   535
subsubsection {* \keyw{datatype\_new\_compat}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   536
  \label{sssec:datatype-new-compat} *}
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   537
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   538
text {*
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
   539
\begin{matharray}{rcl}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
   540
  @{command_def "datatype_new_compat"} & : & @{text "local_theory \<rightarrow> local_theory"}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
   541
\end{matharray}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
   542
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
   543
@{rail "
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
   544
  @@{command datatype_new_compat} names
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
   545
"}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
   546
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
   547
\noindent
53621
9c3a80af72ff more (co)data doc
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parents: 53619
diff changeset
   548
The old datatype package provides some functionality that is not yet replicated
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   549
in the new package:
9c3a80af72ff more (co)data doc
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parents: 53619
diff changeset
   550
9c3a80af72ff more (co)data doc
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parents: 53619
diff changeset
   551
\begin{itemize}
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
   552
\setlength{\itemsep}{0pt}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
   553
53621
9c3a80af72ff more (co)data doc
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parents: 53619
diff changeset
   554
\item It is integrated with \keyw{fun} and \keyw{function}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   555
\cite{isabelle-function}, Nitpick \cite{isabelle-nitpick}, Quickcheck,
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   556
and other packages.
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   557
9c3a80af72ff more (co)data doc
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parents: 53619
diff changeset
   558
\item It is extended by various add-ons, notably to produce instances of the
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   559
@{const size} function.
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   560
\end{itemize}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   561
9c3a80af72ff more (co)data doc
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parents: 53619
diff changeset
   562
\noindent
53863
c7364dca96f2 textual improvements following Christian Sternagel's feedback
blanchet
parents: 53857
diff changeset
   563
New-style datatypes can in most cases be registered as old-style datatypes using
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
   564
@{command datatype_new_compat}. The \textit{names} argument is a space-separated
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
   565
list of type names that are mutually recursive. For example:
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   566
*}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   567
53623
501e2091182b more (co)data docs
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parents: 53621
diff changeset
   568
    datatype_new_compat even_nat odd_nat
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   569
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   570
text {* \blankline *}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   571
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
   572
    thm even_nat_odd_nat.size
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   573
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   574
text {* \blankline *}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   575
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
   576
    ML {* Datatype_Data.get_info @{theory} @{type_name even_nat} *}
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   577
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   578
text {*
53748
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   579
A few remarks concern nested recursive datatypes only:
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   580
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   581
\begin{itemize}
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
   582
\setlength{\itemsep}{0pt}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
   583
53748
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   584
\item The old-style, nested-as-mutual induction rule, iterator theorems, and
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   585
recursor theorems are generated under their usual names but with ``@{text
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   586
"compat_"}'' prefixed (e.g., @{text compat_tree.induct}).
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   587
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   588
\item All types through which recursion takes place must be new-style datatypes
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   589
or the function type. In principle, it should be possible to support old-style
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   590
datatypes as well, but the command does not support this yet (and there is
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   591
currently no way to register old-style datatypes as new-style datatypes).
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   592
\end{itemize}
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   593
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   594
An alternative to @{command datatype_new_compat} is to use the old package's
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   595
\keyw{rep\_datatype} command. The associated proof obligations must then be
be0ddf3dd01b updated docs
blanchet
parents: 53722
diff changeset
   596
discharged manually.
53617
da5e1887d7a7 more (co)data doc
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parents: 53565
diff changeset
   597
*}
da5e1887d7a7 more (co)data doc
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parents: 53565
diff changeset
   598
da5e1887d7a7 more (co)data doc
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parents: 53565
diff changeset
   599
da5e1887d7a7 more (co)data doc
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parents: 53565
diff changeset
   600
subsection {* Generated Constants
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   601
  \label{ssec:datatype-generated-constants} *}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   602
da5e1887d7a7 more (co)data doc
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parents: 53565
diff changeset
   603
text {*
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
   604
Given a datatype @{text "('a\<^sub>1, \<dots>, 'a\<^sub>m) t"}
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   605
with $m > 0$ live type variables and $n$ constructors
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   606
@{text "t.C\<^sub>1"}, \ldots, @{text "t.C\<^sub>n"}, the
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   607
following auxiliary constants are introduced:
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   608
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   609
\begin{itemize}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   610
\setlength{\itemsep}{0pt}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   611
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   612
\item \relax{Case combinator}: @{text t_case} (rendered using the familiar
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   613
@{text case}--@{text of} syntax)
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   614
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   615
\item \relax{Discriminators}: @{text "t.is_C\<^sub>1"}, \ldots,
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   616
@{text "t.is_C\<^sub>n"}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   618
\item \relax{Selectors}:
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   619
@{text t.un_C\<^sub>11}$, \ldots, @{text t.un_C\<^sub>1k\<^sub>1}, \\
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   620
\phantom{\relax{Selectors:}} \quad\vdots \\
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   621
\phantom{\relax{Selectors:}} @{text t.un_C\<^sub>n1}$, \ldots, @{text t.un_C\<^sub>nk\<^sub>n}.
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   622
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   623
\item \relax{Set functions} (or \relax{natural transformations}):
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   624
@{text t_set1}, \ldots, @{text t_setm}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   625
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   626
\item \relax{Map function} (or \relax{functorial action}): @{text t_map}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   627
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   628
\item \relax{Relator}: @{text t_rel}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   629
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   630
\item \relax{Iterator}: @{text t_fold}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   631
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   632
\item \relax{Recursor}: @{text t_rec}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   633
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   634
\end{itemize}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   635
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   636
\noindent
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   637
The case combinator, discriminators, and selectors are collectively called
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   638
\emph{destructors}. The prefix ``@{text "t."}'' is an optional component of the
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   639
name and is normally hidden. 
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   640
*}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   641
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   642
52840
a0da63cec918 more (co)datatype documentation
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parents: 52829
diff changeset
   643
subsection {* Generated Theorems
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
   644
  \label{ssec:datatype-generated-theorems} *}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
   645
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
   646
text {*
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   647
The characteristic theorems generated by @{command datatype_new} are grouped in
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
   648
three broad categories:
53535
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   649
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   650
\begin{itemize}
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
   651
\setlength{\itemsep}{0pt}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
   652
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   653
\item The \emph{free constructor theorems} are properties about the constructors
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   654
and destructors that can be derived for any freely generated type. Internally,
53542
14000a283ce0 more (co)data docs
blanchet
parents: 53535
diff changeset
   655
the derivation is performed by @{command wrap_free_constructors}.
53535
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   656
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   657
\item The \emph{functorial theorems} are properties of datatypes related to
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   658
their BNF nature.
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   659
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   660
\item The \emph{inductive theorems} are properties of datatypes related to
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   661
their inductive nature.
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   662
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   663
\end{itemize}
53535
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   664
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   665
\noindent
53542
14000a283ce0 more (co)data docs
blanchet
parents: 53535
diff changeset
   666
The full list of named theorems can be obtained as usual by entering the
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   667
command \keyw{print\_theorems} immediately after the datatype definition.
53542
14000a283ce0 more (co)data docs
blanchet
parents: 53535
diff changeset
   668
This list normally excludes low-level theorems that reveal internal
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   669
constructions. To make these accessible, add the line
53542
14000a283ce0 more (co)data docs
blanchet
parents: 53535
diff changeset
   670
*}
53535
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   671
53542
14000a283ce0 more (co)data docs
blanchet
parents: 53535
diff changeset
   672
    declare [[bnf_note_all]]
14000a283ce0 more (co)data docs
blanchet
parents: 53535
diff changeset
   673
(*<*)
14000a283ce0 more (co)data docs
blanchet
parents: 53535
diff changeset
   674
    declare [[bnf_note_all = false]]
14000a283ce0 more (co)data docs
blanchet
parents: 53535
diff changeset
   675
(*>*)
53535
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   676
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   677
text {*
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   678
\noindent
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   679
to the top of the theory file.
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   680
*}
53535
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   681
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   682
subsubsection {* Free Constructor Theorems
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   683
  \label{sssec:free-constructor-theorems} *}
53535
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   684
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   685
(*<*)
53837
65c775430caa updated docs
blanchet
parents: 53831
diff changeset
   686
    consts nonnull :: 'a
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   687
(*>*)
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   688
53535
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   689
text {*
53863
c7364dca96f2 textual improvements following Christian Sternagel's feedback
blanchet
parents: 53857
diff changeset
   690
The first subgroup of properties is concerned with the constructors.
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   691
They are listed below for @{typ "'a list"}:
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   692
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   693
\begin{indentblock}
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   694
\begin{description}
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   695
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
   696
\item[@{text "t."}\hthm{inject} @{text "[iff, induct_simp]"}\rm:] ~ \\
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   697
@{thm list.inject[no_vars]}
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   698
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
   699
\item[@{text "t."}\hthm{distinct} @{text "[simp, induct_simp]"}\rm:] ~ \\
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   700
@{thm list.distinct(1)[no_vars]} \\
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   701
@{thm list.distinct(2)[no_vars]}
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   702
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
   703
\item[@{text "t."}\hthm{exhaust} @{text "[cases t, case_names C\<^sub>1 \<dots> C\<^sub>n]"}\rm:] ~ \\
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   704
@{thm list.exhaust[no_vars]}
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   705
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
   706
\item[@{text "t."}\hthm{nchotomy}\rm:] ~ \\
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   707
@{thm list.nchotomy[no_vars]}
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   708
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   709
\end{description}
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   710
\end{indentblock}
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   711
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   712
\noindent
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   713
In addition, these nameless theorems are registered as safe elimination rules:
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   714
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   715
\begin{indentblock}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   716
\begin{description}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   717
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
   718
\item[@{text "t."}\hthm{list.distinct {\upshape[}THEN notE}@{text ", elim!"}\hthm{\upshape]}\rm:] ~ \\
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   719
@{thm list.distinct(1)[THEN notE, elim!, no_vars]} \\
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   720
@{thm list.distinct(2)[THEN notE, elim!, no_vars]}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   721
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   722
\end{description}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   723
\end{indentblock}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   724
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   725
\noindent
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   726
The next subgroup is concerned with the case combinator:
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   727
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   728
\begin{indentblock}
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   729
\begin{description}
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   730
53798
6a4e3299dfd1 set [code] on case equations
blanchet
parents: 53753
diff changeset
   731
\item[@{text "t."}\hthm{case} @{text "[simp, code]"}\rm:] ~ \\
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   732
@{thm list.case(1)[no_vars]} \\
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   733
@{thm list.case(2)[no_vars]}
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   734
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
   735
\item[@{text "t."}\hthm{case\_cong}\rm:] ~ \\
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   736
@{thm list.case_cong[no_vars]}
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   737
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
   738
\item[@{text "t."}\hthm{weak\_case\_cong} @{text "[cong]"}\rm:] ~ \\
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   739
@{thm list.weak_case_cong[no_vars]}
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   740
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
   741
\item[@{text "t."}\hthm{split}\rm:] ~ \\
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   742
@{thm list.split[no_vars]}
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   743
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
   744
\item[@{text "t."}\hthm{split\_asm}\rm:] ~ \\
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   745
@{thm list.split_asm[no_vars]}
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   746
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   747
\item[@{text "t."}\hthm{splits} = @{text "split split_asm"}]
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   748
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   749
\end{description}
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   750
\end{indentblock}
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   751
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   752
\noindent
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   753
The third and last subgroup revolves around discriminators and selectors:
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   754
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   755
\begin{indentblock}
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   756
\begin{description}
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   757
53694
7b453b619b5f use singular to avoid confusion
blanchet
parents: 53691
diff changeset
   758
\item[@{text "t."}\hthm{disc} @{text "[simp]"}\rm:] ~ \\
7b453b619b5f use singular to avoid confusion
blanchet
parents: 53691
diff changeset
   759
@{thm list.disc(1)[no_vars]} \\
7b453b619b5f use singular to avoid confusion
blanchet
parents: 53691
diff changeset
   760
@{thm list.disc(2)[no_vars]}
7b453b619b5f use singular to avoid confusion
blanchet
parents: 53691
diff changeset
   761
53703
0c565fec9c78 updated docs
blanchet
parents: 53694
diff changeset
   762
\item[@{text "t."}\hthm{discI}\rm:] ~ \\
0c565fec9c78 updated docs
blanchet
parents: 53694
diff changeset
   763
@{thm list.discI(1)[no_vars]} \\
0c565fec9c78 updated docs
blanchet
parents: 53694
diff changeset
   764
@{thm list.discI(2)[no_vars]}
0c565fec9c78 updated docs
blanchet
parents: 53694
diff changeset
   765
53805
4163160853fd added [code] to selectors
blanchet
parents: 53798
diff changeset
   766
\item[@{text "t."}\hthm{sel} @{text "[simp, code]"}\rm:] ~ \\
53694
7b453b619b5f use singular to avoid confusion
blanchet
parents: 53691
diff changeset
   767
@{thm list.sel(1)[no_vars]} \\
7b453b619b5f use singular to avoid confusion
blanchet
parents: 53691
diff changeset
   768
@{thm list.sel(2)[no_vars]}
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   769
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
   770
\item[@{text "t."}\hthm{collapse} @{text "[simp]"}\rm:] ~ \\
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   771
@{thm list.collapse(1)[no_vars]} \\
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   772
@{thm list.collapse(2)[no_vars]}
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   773
53837
65c775430caa updated docs
blanchet
parents: 53831
diff changeset
   774
\item[@{text "t."}\hthm{disc\_exclude} @{text "[dest]"}\rm:] ~ \\
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   775
These properties are missing for @{typ "'a list"} because there is only one
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   776
proper discriminator. Had the datatype been introduced with a second
53837
65c775430caa updated docs
blanchet
parents: 53831
diff changeset
   777
discriminator called @{const nonnull}, they would have read thusly: \\[\jot]
65c775430caa updated docs
blanchet
parents: 53831
diff changeset
   778
@{prop "null list \<Longrightarrow> \<not> nonnull list"} \\
65c775430caa updated docs
blanchet
parents: 53831
diff changeset
   779
@{prop "nonnull list \<Longrightarrow> \<not> null list"}
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   780
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
   781
\item[@{text "t."}\hthm{disc\_exhaust} @{text "[case_names C\<^sub>1 \<dots> C\<^sub>n]"}\rm:] ~ \\
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   782
@{thm list.disc_exhaust[no_vars]}
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   783
53916
37c31a619eee generate "sel_exhaust" theorem
blanchet
parents: 53863
diff changeset
   784
\item[@{text "t."}\hthm{sel\_exhaust} @{text "[case_names C\<^sub>1 \<dots> C\<^sub>n]"}\rm:] ~ \\
37c31a619eee generate "sel_exhaust" theorem
blanchet
parents: 53863
diff changeset
   785
@{thm list.sel_exhaust[no_vars]}
37c31a619eee generate "sel_exhaust" theorem
blanchet
parents: 53863
diff changeset
   786
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
   787
\item[@{text "t."}\hthm{expand}\rm:] ~ \\
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   788
@{thm list.expand[no_vars]}
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   789
53917
bf74357f91f8 generate "sel_splits(_asm)" theorems
blanchet
parents: 53916
diff changeset
   790
\item[@{text "t."}\hthm{sel\_split}\rm:] ~ \\
bf74357f91f8 generate "sel_splits(_asm)" theorems
blanchet
parents: 53916
diff changeset
   791
@{thm list.sel_split[no_vars]}
bf74357f91f8 generate "sel_splits(_asm)" theorems
blanchet
parents: 53916
diff changeset
   792
bf74357f91f8 generate "sel_splits(_asm)" theorems
blanchet
parents: 53916
diff changeset
   793
\item[@{text "t."}\hthm{sel\_split\_asm}\rm:] ~ \\
bf74357f91f8 generate "sel_splits(_asm)" theorems
blanchet
parents: 53916
diff changeset
   794
@{thm list.sel_split_asm[no_vars]}
bf74357f91f8 generate "sel_splits(_asm)" theorems
blanchet
parents: 53916
diff changeset
   795
53857
c9aefa1fc451 renamed generated property
blanchet
parents: 53837
diff changeset
   796
\item[@{text "t."}\hthm{case\_conv\_if}\rm:] ~ \\
c9aefa1fc451 renamed generated property
blanchet
parents: 53837
diff changeset
   797
@{thm list.case_conv_if[no_vars]}
53543
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   798
c6c8dce7e9ab more (co)data docs
blanchet
parents: 53542
diff changeset
   799
\end{description}
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   800
\end{indentblock}
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   801
*}
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   802
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   803
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   804
subsubsection {* Functorial Theorems
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   805
  \label{sssec:functorial-theorems} *}
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   806
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   807
text {*
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
   808
The BNF-related theorem are as follows:
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   809
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   810
\begin{indentblock}
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   811
\begin{description}
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   812
53798
6a4e3299dfd1 set [code] on case equations
blanchet
parents: 53753
diff changeset
   813
\item[@{text "t."}\hthm{set} @{text "[simp, code]"}\rm:] ~ \\
53694
7b453b619b5f use singular to avoid confusion
blanchet
parents: 53691
diff changeset
   814
@{thm list.set(1)[no_vars]} \\
7b453b619b5f use singular to avoid confusion
blanchet
parents: 53691
diff changeset
   815
@{thm list.set(2)[no_vars]}
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   816
53798
6a4e3299dfd1 set [code] on case equations
blanchet
parents: 53753
diff changeset
   817
\item[@{text "t."}\hthm{map} @{text "[simp, code]"}\rm:] ~ \\
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   818
@{thm list.map(1)[no_vars]} \\
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   819
@{thm list.map(2)[no_vars]}
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   820
53798
6a4e3299dfd1 set [code] on case equations
blanchet
parents: 53753
diff changeset
   821
\item[@{text "t."}\hthm{rel\_inject} @{text "[simp, code]"}\rm:] ~ \\
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   822
@{thm list.rel_inject(1)[no_vars]} \\
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   823
@{thm list.rel_inject(2)[no_vars]}
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   824
53798
6a4e3299dfd1 set [code] on case equations
blanchet
parents: 53753
diff changeset
   825
\item[@{text "t."}\hthm{rel\_distinct} @{text "[simp, code]"}\rm:] ~ \\
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   826
@{thm list.rel_distinct(1)[no_vars]} \\
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   827
@{thm list.rel_distinct(2)[no_vars]}
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   828
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   829
\end{description}
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   830
\end{indentblock}
53535
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   831
*}
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   832
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   833
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   834
subsubsection {* Inductive Theorems
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   835
  \label{sssec:inductive-theorems} *}
53535
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   836
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
   837
text {*
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
   838
The inductive theorems are as follows:
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   839
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   840
\begin{indentblock}
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   841
\begin{description}
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   842
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
   843
\item[@{text "t."}\hthm{induct} @{text "[induct t, case_names C\<^sub>1 \<dots> C\<^sub>n]"}\rm:] ~ \\
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   844
@{thm list.induct[no_vars]}
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   845
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
   846
\item[@{text "t\<^sub>1_\<dots>_t\<^sub>m."}\hthm{induct} @{text "[case_names C\<^sub>1 \<dots> C\<^sub>n]"}\rm:] ~ \\
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   847
Given $m > 1$ mutually recursive datatypes, this induction rule can be used to
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   848
prove $m$ properties simultaneously.
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
   849
53798
6a4e3299dfd1 set [code] on case equations
blanchet
parents: 53753
diff changeset
   850
\item[@{text "t."}\hthm{fold} @{text "[simp, code]"}\rm:] ~ \\
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   851
@{thm list.fold(1)[no_vars]} \\
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   852
@{thm list.fold(2)[no_vars]}
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   853
53798
6a4e3299dfd1 set [code] on case equations
blanchet
parents: 53753
diff changeset
   854
\item[@{text "t."}\hthm{rec} @{text "[simp, code]"}\rm:] ~ \\
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   855
@{thm list.rec(1)[no_vars]} \\
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   856
@{thm list.rec(2)[no_vars]}
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   857
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   858
\end{description}
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   859
\end{indentblock}
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   860
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   861
\noindent
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   862
For convenience, @{command datatype_new} also provides the following collection:
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   863
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   864
\begin{indentblock}
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   865
\begin{description}
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   866
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   867
\item[@{text "t."}\hthm{simps} = @{text t.inject} @{text t.distinct} @{text t.case} @{text t.rec} @{text t.fold} @{text t.map} @{text t.rel_inject}] ~ \\
53694
7b453b619b5f use singular to avoid confusion
blanchet
parents: 53691
diff changeset
   868
@{text t.rel_distinct} @{text t.set}
53544
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   869
2176a7e40786 more (co)data docs
blanchet
parents: 53543
diff changeset
   870
\end{description}
53552
eed6efba4e3f more (co)datatype docs
blanchet
parents: 53544
diff changeset
   871
\end{indentblock}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
   872
*}
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
   873
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
   874
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
   875
subsection {* Compatibility Issues
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
   876
  \label{ssec:datatype-compatibility-issues} *}
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
   877
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
   878
text {*
53997
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
   879
The command @{command datatype_new} has been designed to be highly compatible
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
   880
with the old \keyw{datatype}, to ease migration. There are nonetheless a few
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   881
incompatibilities that may arise when porting to the new package:
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   882
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   883
\begin{itemize}
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
   884
\setlength{\itemsep}{0pt}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
   885
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   886
\item \emph{The Standard ML interfaces are different.} Tools and extensions
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   887
written to call the old ML interfaces will need to be adapted to the new
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   888
interfaces. Little has been done so far in this direction. Whenever possible, it
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   889
is recommended to use @{command datatype_new_compat} or \keyw{rep\_datatype}
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   890
to register new-style datatypes as old-style datatypes.
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   891
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   892
\item \emph{The recursor @{text "t_rec"} has a different signature for nested
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   893
recursive datatypes.} In the old package, nested recursion was internally
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   894
reduced to mutual recursion. This reduction was visible in the type of the
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   895
recursor, used by \keyw{primrec}. In the new package, nested recursion is
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   896
handled in a more modular fashion. The old-style recursor can be generated on
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   897
demand using @{command primrec_new}, as explained in
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   898
Section~\ref{sssec:primrec-nested-as-mutual-recursion}, if the recursion is via
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   899
new-style datatypes.
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   900
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   901
\item \emph{Accordingly, the induction principle is different for nested
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   902
recursive datatypes.} Again, the old-style induction principle can be generated
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   903
on demand using @{command primrec_new}, as explained in
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   904
Section~\ref{sssec:primrec-nested-as-mutual-recursion}, if the recursion is via
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   905
new-style datatypes.
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
   906
53863
c7364dca96f2 textual improvements following Christian Sternagel's feedback
blanchet
parents: 53857
diff changeset
   907
\item \emph{The internal constructions are completely different.} Proof texts
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   908
that unfold the definition of constants introduced by \keyw{datatype} will be
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   909
difficult to port.
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   910
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   911
\item \emph{A few theorems have different names.}
53997
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
   912
The properties @{text t.cases} and @{text t.recs} have been renamed
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   913
@{text t.case} and @{text t.rec}. For non-mutually recursive datatypes,
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   914
@{text t.inducts} is available as @{text t.induct}.
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   915
For $m > 1$ mutually recursive datatypes,
53997
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
   916
@{text "t\<^sub>1_\<dots>_t\<^sub>m.inducts(i)"} has been renamed
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   917
@{text "t\<^sub>i.induct"}.
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   918
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   919
\item \emph{The @{text t.simps} collection has been extended.}
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   920
Previously available theorems are available at the same index.
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   921
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   922
\item \emph{Variables in generated properties have different names.} This is
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   923
rarely an issue, except in proof texts that refer to variable names in the
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   924
@{text "[where \<dots>]"} attribute. The solution is to use the more robust
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   925
@{text "[of \<dots>]"} syntax.
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   926
\end{itemize}
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   927
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   928
In the other direction, there is currently no way to register old-style
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   929
datatypes as new-style datatypes. If the goal is to define new-style datatypes
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   930
with nested recursion through old-style datatypes, the old-style
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   931
datatypes can be registered as a BNF
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   932
(Section~\ref{sec:registering-bounded-natural-functors}). If the goal is
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   933
to derive discriminators and selectors, this can be achieved using @{command
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   934
wrap_free_constructors}
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
   935
(Section~\ref{sec:deriving-destructors-and-theorems-for-free-constructors}).
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
   936
*}
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
   937
52792
3e651be14fcd sketched documentation for new (co)datatype package
blanchet
parents:
diff changeset
   938
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
   939
section {* Defining Recursive Functions
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
   940
  \label{sec:defining-recursive-functions} *}
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
   941
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
   942
text {*
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
   943
Recursive functions over datatypes can be specified using @{command
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
   944
primrec_new}, which supports primitive recursion, or using the more general
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
   945
\keyw{fun} and \keyw{function} commands. Here, the focus is on @{command
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
   946
primrec_new}; the other two commands are described in a separate tutorial
53646
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
   947
\cite{isabelle-function}.
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
   948
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   949
%%% TODO: partial_function
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
   950
*}
52792
3e651be14fcd sketched documentation for new (co)datatype package
blanchet
parents:
diff changeset
   951
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
   952
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   953
subsection {* Introductory Examples
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
   954
  \label{ssec:primrec-introductory-examples} *}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
   955
53646
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
   956
text {*
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
   957
Primitive recursion is illustrated through concrete examples based on the
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
   958
datatypes defined in Section~\ref{ssec:datatype-introductory-examples}. More
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
   959
examples can be found in the directory \verb|~~/src/HOL/BNF/Examples|.
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
   960
*}
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
   961
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   962
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   963
subsubsection {* Nonrecursive Types
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   964
  \label{sssec:primrec-nonrecursive-types} *}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
   965
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
   966
text {*
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   967
Primitive recursion removes one layer of constructors on the left-hand side in
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   968
each equation. For example:
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
   969
*}
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
   970
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
   971
    primrec_new bool_of_trool :: "trool \<Rightarrow> bool" where
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   972
      "bool_of_trool Faalse \<longleftrightarrow> False" |
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   973
      "bool_of_trool Truue \<longleftrightarrow> True"
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
   974
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   975
text {* \blankline *}
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
   976
53025
c820c9e9e8f4 more work on (co)datatype docs
blanchet
parents: 53018
diff changeset
   977
    primrec_new the_list :: "'a option \<Rightarrow> 'a list" where
c820c9e9e8f4 more work on (co)datatype docs
blanchet
parents: 53018
diff changeset
   978
      "the_list None = []" |
c820c9e9e8f4 more work on (co)datatype docs
blanchet
parents: 53018
diff changeset
   979
      "the_list (Some a) = [a]"
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
   980
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   981
text {* \blankline *}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   982
53025
c820c9e9e8f4 more work on (co)datatype docs
blanchet
parents: 53018
diff changeset
   983
    primrec_new the_default :: "'a \<Rightarrow> 'a option \<Rightarrow> 'a" where
c820c9e9e8f4 more work on (co)datatype docs
blanchet
parents: 53018
diff changeset
   984
      "the_default d None = d" |
c820c9e9e8f4 more work on (co)datatype docs
blanchet
parents: 53018
diff changeset
   985
      "the_default _ (Some a) = a"
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
   986
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   987
text {* \blankline *}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   988
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
   989
    primrec_new mirrror :: "('a, 'b, 'c) triple \<Rightarrow> ('c, 'b, 'a) triple" where
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
   990
      "mirrror (Triple a b c) = Triple c b a"
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
   991
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   992
text {*
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   993
\noindent
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   994
The equations can be specified in any order, and it is acceptable to leave out
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   995
some cases, which are then unspecified. Pattern matching on the left-hand side
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   996
is restricted to a single datatype, which must correspond to the same argument
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   997
in all equations.
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
   998
*}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
   999
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1000
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1001
subsubsection {* Simple Recursion
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1002
  \label{sssec:primrec-simple-recursion} *}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1003
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1004
text {*
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1005
For simple recursive types, recursive calls on a constructor argument are
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1006
allowed on the right-hand side:
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1007
*}
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1008
53330
77da8d3c46e0 fixed docs w.r.t. availability of "primrec_new" and friends
blanchet
parents: 53262
diff changeset
  1009
    primrec_new replicate :: "nat \<Rightarrow> 'a \<Rightarrow> 'a list" where
77da8d3c46e0 fixed docs w.r.t. availability of "primrec_new" and friends
blanchet
parents: 53262
diff changeset
  1010
      "replicate Zero _ = []" |
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1011
      "replicate (Suc n) x = x # replicate n x"
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1012
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1013
text {* \blankline *}
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1014
53332
c97a05a26dd6 Doc improvements
traytel
parents: 53331
diff changeset
  1015
    primrec_new at :: "'a list \<Rightarrow> nat \<Rightarrow> 'a" where
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1016
      "at (x # xs) j =
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1017
         (case j of
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1018
            Zero \<Rightarrow> x
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1019
          | Suc j' \<Rightarrow> at xs j')"
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1020
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1021
text {* \blankline *}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1022
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1023
    primrec_new (*<*)(in early) (*>*)tfold :: "('a \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> ('a, 'b) tlist \<Rightarrow> 'b" where
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1024
      "tfold _ (TNil y) = y" |
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1025
      "tfold f (TCons x xs) = f x (tfold f xs)"
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1026
53025
c820c9e9e8f4 more work on (co)datatype docs
blanchet
parents: 53018
diff changeset
  1027
text {*
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1028
\noindent
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1029
The next example is not primitive recursive, but it can be defined easily using
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1030
\keyw{fun}. The @{command datatype_new_compat} command is needed to register
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1031
new-style datatypes for use with \keyw{fun} and \keyw{function}
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1032
(Section~\ref{sssec:datatype-new-compat}):
53025
c820c9e9e8f4 more work on (co)datatype docs
blanchet
parents: 53018
diff changeset
  1033
*}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1034
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1035
    datatype_new_compat nat
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1036
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1037
text {* \blankline *}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1038
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1039
    fun at_least_two :: "nat \<Rightarrow> bool" where
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1040
      "at_least_two (Suc (Suc _)) \<longleftrightarrow> True" |
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1041
      "at_least_two _ \<longleftrightarrow> False"
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1042
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1043
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1044
subsubsection {* Mutual Recursion
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1045
  \label{sssec:primrec-mutual-recursion} *}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1046
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1047
text {*
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1048
The syntax for mutually recursive functions over mutually recursive datatypes
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1049
is straightforward:
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1050
*}
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1051
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1052
    primrec_new
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1053
      nat_of_even_nat :: "even_nat \<Rightarrow> nat" and
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1054
      nat_of_odd_nat :: "odd_nat \<Rightarrow> nat"
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1055
    where
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1056
      "nat_of_even_nat Even_Zero = Zero" |
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1057
      "nat_of_even_nat (Even_Suc n) = Suc (nat_of_odd_nat n)" |
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1058
      "nat_of_odd_nat (Odd_Suc n) = Suc (nat_of_even_nat n)"
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1059
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1060
text {* \blankline *}
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1061
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1062
    primrec_new
53330
77da8d3c46e0 fixed docs w.r.t. availability of "primrec_new" and friends
blanchet
parents: 53262
diff changeset
  1063
      eval\<^sub>e :: "('a \<Rightarrow> int) \<Rightarrow> ('b \<Rightarrow> int) \<Rightarrow> ('a, 'b) exp \<Rightarrow> int" and
77da8d3c46e0 fixed docs w.r.t. availability of "primrec_new" and friends
blanchet
parents: 53262
diff changeset
  1064
      eval\<^sub>t :: "('a \<Rightarrow> int) \<Rightarrow> ('b \<Rightarrow> int) \<Rightarrow> ('a, 'b) trm \<Rightarrow> int" and
77da8d3c46e0 fixed docs w.r.t. availability of "primrec_new" and friends
blanchet
parents: 53262
diff changeset
  1065
      eval\<^sub>f :: "('a \<Rightarrow> int) \<Rightarrow> ('b \<Rightarrow> int) \<Rightarrow> ('a, 'b) fct \<Rightarrow> int"
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1066
    where
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1067
      "eval\<^sub>e \<gamma> \<xi> (Term t) = eval\<^sub>t \<gamma> \<xi> t" |
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1068
      "eval\<^sub>e \<gamma> \<xi> (Sum t e) = eval\<^sub>t \<gamma> \<xi> t + eval\<^sub>e \<gamma> \<xi> e" |
53330
77da8d3c46e0 fixed docs w.r.t. availability of "primrec_new" and friends
blanchet
parents: 53262
diff changeset
  1069
      "eval\<^sub>t \<gamma> \<xi> (Factor f) = eval\<^sub>f \<gamma> \<xi> f" |
52841
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1070
      "eval\<^sub>t \<gamma> \<xi> (Prod f t) = eval\<^sub>f \<gamma> \<xi> f + eval\<^sub>t \<gamma> \<xi> t" |
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1071
      "eval\<^sub>f \<gamma> _ (Const a) = \<gamma> a" |
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1072
      "eval\<^sub>f _ \<xi> (Var b) = \<xi> b" |
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1073
      "eval\<^sub>f \<gamma> \<xi> (Expr e) = eval\<^sub>e \<gamma> \<xi> e"
87a66bad0796 more (co)datatype documentation
blanchet
parents: 52840
diff changeset
  1074
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1075
text {*
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1076
\noindent
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1077
Mutual recursion is possible within a single type, using \keyw{fun}:
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1078
*}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1079
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1080
    fun
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1081
      even :: "nat \<Rightarrow> bool" and
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1082
      odd :: "nat \<Rightarrow> bool"
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1083
    where
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1084
      "even Zero = True" |
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1085
      "even (Suc n) = odd n" |
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1086
      "odd Zero = False" |
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1087
      "odd (Suc n) = even n"
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1088
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1089
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1090
subsubsection {* Nested Recursion
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1091
  \label{sssec:primrec-nested-recursion} *}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1092
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1093
text {*
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1094
In a departure from the old datatype package, nested recursion is normally
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1095
handled via the map functions of the nesting type constructors. For example,
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1096
recursive calls are lifted to lists using @{const map}:
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1097
*}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1098
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1099
(*<*)
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1100
    datatype_new 'a tree\<^sub>f\<^sub>f = Node\<^sub>f\<^sub>f (lbl\<^sub>f\<^sub>f: 'a) (sub\<^sub>f\<^sub>f: "'a tree\<^sub>f\<^sub>f list")
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1101
(*>*)
53028
a1e64c804c35 more (co)datatype documentation
blanchet
parents: 53025
diff changeset
  1102
    primrec_new at\<^sub>f\<^sub>f :: "'a tree\<^sub>f\<^sub>f \<Rightarrow> nat list \<Rightarrow> 'a" where
a1e64c804c35 more (co)datatype documentation
blanchet
parents: 53025
diff changeset
  1103
      "at\<^sub>f\<^sub>f (Node\<^sub>f\<^sub>f a ts) js =
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1104
         (case js of
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1105
            [] \<Rightarrow> a
53028
a1e64c804c35 more (co)datatype documentation
blanchet
parents: 53025
diff changeset
  1106
          | j # js' \<Rightarrow> at (map (\<lambda>t. at\<^sub>f\<^sub>f t js') ts) j)"
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1107
53025
c820c9e9e8f4 more work on (co)datatype docs
blanchet
parents: 53018
diff changeset
  1108
text {*
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1109
\noindent
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1110
The next example features recursion through the @{text option} type. Although
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1111
@{text option} is not a new-style datatype, it is registered as a BNF with the
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1112
map function @{const option_map}:
53025
c820c9e9e8f4 more work on (co)datatype docs
blanchet
parents: 53018
diff changeset
  1113
*}
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1114
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1115
    primrec_new (*<*)(in early) (*>*)sum_btree :: "('a\<Colon>{zero,plus}) btree \<Rightarrow> 'a" where
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1116
      "sum_btree (BNode a lt rt) =
53330
77da8d3c46e0 fixed docs w.r.t. availability of "primrec_new" and friends
blanchet
parents: 53262
diff changeset
  1117
         a + the_default 0 (option_map sum_btree lt) +
77da8d3c46e0 fixed docs w.r.t. availability of "primrec_new" and friends
blanchet
parents: 53262
diff changeset
  1118
           the_default 0 (option_map sum_btree rt)"
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1119
53136
98a2c33d5d1b ideas for (co)datatype docs
blanchet
parents: 53028
diff changeset
  1120
text {*
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1121
\noindent
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1122
The same principle applies for arbitrary type constructors through which
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1123
recursion is possible. Notably, the map function for the function type
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1124
(@{text \<Rightarrow>}) is simply composition (@{text "op \<circ>"}):
53136
98a2c33d5d1b ideas for (co)datatype docs
blanchet
parents: 53028
diff changeset
  1125
*}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1126
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1127
    primrec_new ftree_map :: "('a \<Rightarrow> 'a) \<Rightarrow> 'a ftree \<Rightarrow> 'a ftree" where
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1128
      "ftree_map f (FTLeaf x) = FTLeaf (f x)" |
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1129
      "ftree_map f (FTNode g) = FTNode (ftree_map f \<circ> g)"
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1130
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1131
text {*
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1132
\noindent
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1133
(No such function is defined by the package because @{typ 'a} is dead in
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1134
@{typ "'a ftree"}, but we can easily do it ourselves.)
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1135
*}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1136
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1137
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1138
subsubsection {* Nested-as-Mutual Recursion
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1139
  \label{sssec:primrec-nested-as-mutual-recursion} *}
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1140
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1141
(*<*)
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1142
    locale n2m begin
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1143
(*>*)
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1144
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1145
text {*
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1146
For compatibility with the old package, but also because it is sometimes
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1147
convenient in its own right, it is possible to treat nested recursive datatypes
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1148
as mutually recursive ones if the recursion takes place though new-style
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1149
datatypes. For example:
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1150
*}
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1151
53331
20440c789759 prove theorem in the right context (that knows about local variables)
traytel
parents: 53330
diff changeset
  1152
    primrec_new
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1153
      at\<^sub>f\<^sub>f :: "'a tree\<^sub>f\<^sub>f \<Rightarrow> nat list \<Rightarrow> 'a" and
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1154
      ats\<^sub>f\<^sub>f :: "'a tree\<^sub>f\<^sub>f list \<Rightarrow> nat \<Rightarrow> nat list \<Rightarrow> 'a"
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1155
    where
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1156
      "at\<^sub>f\<^sub>f (Node\<^sub>f\<^sub>f a ts) js =
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1157
         (case js of
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1158
            [] \<Rightarrow> a
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1159
          | j # js' \<Rightarrow> ats\<^sub>f\<^sub>f ts j js')" |
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1160
      "ats\<^sub>f\<^sub>f (t # ts) j =
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1161
         (case j of
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1162
            Zero \<Rightarrow> at\<^sub>f\<^sub>f t
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1163
          | Suc j' \<Rightarrow> ats\<^sub>f\<^sub>f ts j')"
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1164
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1165
text {*
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1166
\noindent
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1167
Appropriate induction principles are generated under the names
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1168
@{thm [source] "at\<^sub>f\<^sub>f.induct"},
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1169
@{thm [source] "ats\<^sub>f\<^sub>f.induct"}, and
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1170
@{thm [source] "at\<^sub>f\<^sub>f_ats\<^sub>f\<^sub>f.induct"}.
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1171
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1172
%%% TODO: Add recursors.
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1173
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1174
Here is a second example:
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1175
*}
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1176
53331
20440c789759 prove theorem in the right context (that knows about local variables)
traytel
parents: 53330
diff changeset
  1177
    primrec_new
53330
77da8d3c46e0 fixed docs w.r.t. availability of "primrec_new" and friends
blanchet
parents: 53262
diff changeset
  1178
      sum_btree :: "('a\<Colon>{zero,plus}) btree \<Rightarrow> 'a" and
77da8d3c46e0 fixed docs w.r.t. availability of "primrec_new" and friends
blanchet
parents: 53262
diff changeset
  1179
      sum_btree_option :: "'a btree option \<Rightarrow> 'a"
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1180
    where
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1181
      "sum_btree (BNode a lt rt) =
53025
c820c9e9e8f4 more work on (co)datatype docs
blanchet
parents: 53018
diff changeset
  1182
         a + sum_btree_option lt + sum_btree_option rt" |
53330
77da8d3c46e0 fixed docs w.r.t. availability of "primrec_new" and friends
blanchet
parents: 53262
diff changeset
  1183
      "sum_btree_option None = 0" |
53025
c820c9e9e8f4 more work on (co)datatype docs
blanchet
parents: 53018
diff changeset
  1184
      "sum_btree_option (Some t) = sum_btree t"
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1185
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1186
text {*
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1187
%  * can pretend a nested type is mutually recursive (if purely inductive)
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1188
%  * avoids the higher-order map
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1189
%  * e.g.
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1190
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1191
%  * this can always be avoided;
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1192
%     * e.g. in our previous example, we first mapped the recursive
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1193
%       calls, then we used a generic at function to retrieve the result
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1194
%
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1195
%  * there's no hard-and-fast rule of when to use one or the other,
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1196
%    just like there's no rule when to use fold and when to use
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1197
%    primrec_new
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1198
%
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1199
%  * higher-order approach, considering nesting as nesting, is more
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1200
%    compositional -- e.g. we saw how we could reuse an existing polymorphic
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1201
%    at or the_default, whereas @{const ats\<^sub>f\<^sub>f} is much more specific
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1202
%
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1203
%  * but:
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1204
%     * is perhaps less intuitive, because it requires higher-order thinking
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1205
%     * may seem inefficient, and indeed with the code generator the
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1206
%       mutually recursive version might be nicer
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1207
%     * is somewhat indirect -- must apply a map first, then compute a result
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1208
%       (cannot mix)
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1209
%     * the auxiliary functions like @{const ats\<^sub>f\<^sub>f} are sometimes useful in own right
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1210
%
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1211
%  * impact on automation unclear
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1212
%
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1213
*}
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1214
(*<*)
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1215
    end
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1216
(*>*)
52843
ea95702328cf more (co)datatype docs
blanchet
parents: 52841
diff changeset
  1217
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  1218
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1219
subsection {* Command Syntax
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1220
  \label{ssec:primrec-command-syntax} *}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1221
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1222
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1223
subsubsection {* \keyw{primrec\_new}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1224
  \label{sssec:primrec-new} *}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1225
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1226
text {*
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1227
\begin{matharray}{rcl}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1228
  @{command_def "primrec_new"} & : & @{text "local_theory \<rightarrow> local_theory"}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1229
\end{matharray}
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  1230
52840
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  1231
@{rail "
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1232
  @@{command primrec_new} target? fixes \\ @'where' (@{syntax pr_equation} + '|')
52840
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  1233
  ;
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1234
  @{syntax_def pr_equation}: thmdecl? prop
52840
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  1235
"}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1236
*}
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1237
52840
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  1238
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  1239
(*
52840
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  1240
subsection {* Generated Theorems
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  1241
  \label{ssec:primrec-generated-theorems} *}
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  1242
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1243
text {*
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1244
%  * synthesized nonrecursive definition
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1245
%  * user specification is rederived from it, exactly as entered
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1246
%
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1247
%  * induct
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1248
%    * mutualized
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1249
%    * without some needless induction hypotheses if not used
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1250
%  * fold, rec
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1251
%    * mutualized
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1252
*}
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  1253
*)
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  1254
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  1255
52840
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  1256
subsection {* Recursive Default Values for Selectors
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1257
  \label{ssec:primrec-recursive-default-values-for-selectors} *}
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1258
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1259
text {*
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1260
A datatype selector @{text un_D} can have a default value for each constructor
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1261
on which it is not otherwise specified. Occasionally, it is useful to have the
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1262
default value be defined recursively. This produces a chicken-and-egg situation
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1263
that may seem unsolvable, because the datatype is not introduced yet at the
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1264
moment when the selectors are introduced. Of course, we can always define the
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1265
selectors manually afterward, but we then have to state and prove all the
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1266
characteristic theorems ourselves instead of letting the package do it.
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1267
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1268
Fortunately, there is a fairly elegant workaround that relies on overloading and
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1269
that avoids the tedium of manual derivations:
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1270
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1271
\begin{enumerate}
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1272
\setlength{\itemsep}{0pt}
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1273
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1274
\item
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1275
Introduce a fully unspecified constant @{text "un_D\<^sub>0 \<Colon> 'a"} using
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1276
@{keyword consts}.
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1277
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1278
\item
53535
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
  1279
Define the datatype, specifying @{text "un_D\<^sub>0"} as the selector's default
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
  1280
value.
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1281
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1282
\item
53535
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
  1283
Define the behavior of @{text "un_D\<^sub>0"} on values of the newly introduced
d0c163c6c725 more (co)data docs
blanchet
parents: 53534
diff changeset
  1284
datatype using the \keyw{overloading} command.
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1285
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1286
\item
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1287
Derive the desired equation on @{text un_D} from the characteristic equations
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1288
for @{text "un_D\<^sub>0"}.
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1289
\end{enumerate}
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1290
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  1291
\noindent
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1292
The following example illustrates this procedure:
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1293
*}
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1294
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1295
    consts termi\<^sub>0 :: 'a
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1296
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  1297
text {* \blankline *}
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  1298
53491
2479b39d9d09 more docs
blanchet
parents: 53335
diff changeset
  1299
    datatype_new ('a, 'b) tlist =
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1300
      TNil (termi: 'b) (defaults ttl: TNil)
53491
2479b39d9d09 more docs
blanchet
parents: 53335
diff changeset
  1301
    | TCons (thd: 'a) (ttl : "('a, 'b) tlist") (defaults termi: "\<lambda>_ xs. termi\<^sub>0 xs")
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1302
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  1303
text {* \blankline *}
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  1304
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1305
    overloading
53491
2479b39d9d09 more docs
blanchet
parents: 53335
diff changeset
  1306
      termi\<^sub>0 \<equiv> "termi\<^sub>0 \<Colon> ('a, 'b) tlist \<Rightarrow> 'b"
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1307
    begin
53491
2479b39d9d09 more docs
blanchet
parents: 53335
diff changeset
  1308
    primrec_new termi\<^sub>0 :: "('a, 'b) tlist \<Rightarrow> 'b" where
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1309
      "termi\<^sub>0 (TNil y) = y" |
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1310
      "termi\<^sub>0 (TCons x xs) = termi\<^sub>0 xs"
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1311
    end
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1312
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  1313
text {* \blankline *}
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  1314
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1315
    lemma terminal_TCons[simp]: "termi (TCons x xs) = termi xs"
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1316
    by (cases xs) auto
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1317
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1318
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1319
subsection {* Compatibility Issues
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1320
  \label{ssec:primrec-compatibility-issues} *}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1321
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1322
text {*
53997
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1323
The command @{command primrec_new} has been designed to be highly compatible
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1324
with the old \keyw{primrec}, to ease migration. There is nonetheless at least
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1325
one incompatibility that may arise when porting to the new package:
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1326
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1327
\begin{itemize}
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1328
\setlength{\itemsep}{0pt}
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1329
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1330
\item \emph{Theorems sometimes have different names.}
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1331
For $m > 1$ mutually recursive functions,
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1332
@{text "f\<^sub>1_\<dots>_f\<^sub>m.simps(k\<^sub>i,\<dots>,k\<^sub>i+n\<^sub>i-1)"} have
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1333
been renamed @{text "f\<^sub>i.simps(1,\<dots>,n\<^sub>i-1)"}.
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1334
\end{itemize}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1335
*}
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  1336
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  1337
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1338
section {* Defining Codatatypes
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1339
  \label{sec:defining-codatatypes} *}
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1340
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1341
text {*
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1342
Codatatypes can be specified using the @{command codatatype} command. The
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1343
command is first illustrated through concrete examples featuring different
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1344
flavors of corecursion. More examples can be found in the directory
53997
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1345
\verb|~~/src/HOL/|\allowbreak\verb|BNF/Examples|. The
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1346
\emph{Archive of Formal Proofs} also includes some useful codatatypes, notably
8ff43f638da2 more "primrec_new" documentation
blanchet
parents: 53917
diff changeset
  1347
for lazy lists \cite{lochbihler-2010}.
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1348
*}
52792
3e651be14fcd sketched documentation for new (co)datatype package
blanchet
parents:
diff changeset
  1349
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  1350
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1351
subsection {* Introductory Examples
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1352
  \label{ssec:codatatype-introductory-examples} *}
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  1353
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1354
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1355
subsubsection {* Simple Corecursion
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1356
  \label{sssec:codatatype-simple-corecursion} *}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1357
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1358
text {*
53863
c7364dca96f2 textual improvements following Christian Sternagel's feedback
blanchet
parents: 53857
diff changeset
  1359
Noncorecursive codatatypes coincide with the corresponding datatypes, so they
c7364dca96f2 textual improvements following Christian Sternagel's feedback
blanchet
parents: 53857
diff changeset
  1360
are useless in practice. \emph{Corecursive codatatypes} have the same syntax
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1361
as recursive datatypes, except for the command name. For example, here is the
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1362
definition of lazy lists:
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1363
*}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1364
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1365
    codatatype (lset: 'a) llist (map: lmap rel: llist_all2) =
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1366
      lnull: LNil (defaults ltl: LNil)
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1367
    | LCons (lhd: 'a) (ltl: "'a llist")
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1368
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1369
text {*
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1370
\noindent
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1371
Lazy lists can be infinite, such as @{text "LCons 0 (LCons 0 (\<dots>))"} and
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1372
@{text "LCons 0 (LCons 1 (LCons 2 (\<dots>)))"}. Here is a related type, that of
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1373
infinite streams:
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1374
*}
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1375
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1376
    codatatype (sset: 'a) stream (map: smap rel: stream_all2) =
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1377
      SCons (shd: 'a) (stl: "'a stream")
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1378
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1379
text {*
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1380
\noindent
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1381
Another interesting type that can
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1382
be defined as a codatatype is that of the extended natural numbers:
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1383
*}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1384
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1385
    codatatype enat = EZero | ESuc enat
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1386
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1387
text {*
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1388
\noindent
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1389
This type has exactly one infinite element, @{text "ESuc (ESuc (ESuc (\<dots>)))"},
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1390
that represents $\infty$. In addition, it has finite values of the form
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1391
@{text "ESuc (\<dots> (ESuc EZero)\<dots>)"}.
53675
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1392
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1393
Here is an example with many constructors:
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1394
*}
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1395
53675
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1396
    codatatype 'a process =
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1397
      Fail
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1398
    | Skip (cont: "'a process")
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1399
    | Action (prefix: 'a) (cont: "'a process")
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1400
    | Choice (left: "'a process") (right: "'a process")
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1401
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1402
text {*
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1403
\noindent
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1404
Notice that the @{const cont} selector is associated with both @{const Skip}
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1405
and @{const Choice}.
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1406
*}
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1407
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1408
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1409
subsubsection {* Mutual Corecursion
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1410
  \label{sssec:codatatype-mutual-corecursion} *}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1411
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1412
text {*
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1413
\noindent
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1414
The example below introduces a pair of \emph{mutually corecursive} types:
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1415
*}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1416
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1417
    codatatype even_enat = Even_EZero | Even_ESuc odd_enat
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1418
    and odd_enat = Odd_ESuc even_enat
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1419
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1420
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1421
subsubsection {* Nested Corecursion
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1422
  \label{sssec:codatatype-nested-corecursion} *}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1423
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1424
text {*
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1425
\noindent
53675
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1426
The next examples feature \emph{nested corecursion}:
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1427
*}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1428
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1429
    codatatype 'a tree\<^sub>i\<^sub>i = Node\<^sub>i\<^sub>i (lbl\<^sub>i\<^sub>i: 'a) (sub\<^sub>i\<^sub>i: "'a tree\<^sub>i\<^sub>i llist")
53675
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1430
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1431
text {* \blankline *}
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1432
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1433
    codatatype 'a tree\<^sub>i\<^sub>s = Node\<^sub>i\<^sub>s (lbl\<^sub>i\<^sub>s: 'a) (sub\<^sub>i\<^sub>s: "'a tree\<^sub>i\<^sub>s fset")
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1434
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1435
text {* \blankline *}
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1436
53675
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1437
    codatatype 'a state_machine =
53751
7a994dc08cea added primcorec examples with lambdas
blanchet
parents: 53750
diff changeset
  1438
      State_Machine (accept: bool) (trans: "'a \<Rightarrow> 'a state_machine")
53675
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1439
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  1440
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1441
subsection {* Command Syntax
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1442
  \label{ssec:codatatype-command-syntax} *}
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1443
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  1444
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1445
subsubsection {* \keyw{codatatype}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  1446
  \label{sssec:codatatype} *}
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  1447
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  1448
text {*
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1449
\begin{matharray}{rcl}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1450
  @{command_def "codatatype"} & : & @{text "local_theory \<rightarrow> local_theory"}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1451
\end{matharray}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1452
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1453
@{rail "
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1454
  @@{command codatatype} target? \\
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1455
    (@{syntax dt_name} '=' (@{syntax ctor} + '|') + @'and')
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1456
"}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1457
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1458
\noindent
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1459
Definitions of codatatypes have almost exactly the same syntax as for datatypes
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1460
(Section~\ref{ssec:datatype-command-syntax}). The @{text "no_discs_sels"} option
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1461
is not available, because destructors are a crucial notion for codatatypes.
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1462
*}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1463
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1464
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1465
subsection {* Generated Constants
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1466
  \label{ssec:codatatype-generated-constants} *}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1467
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1468
text {*
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1469
Given a codatatype @{text "('a\<^sub>1, \<dots>, 'a\<^sub>m) t"}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1470
with $m > 0$ live type variables and $n$ constructors @{text "t.C\<^sub>1"},
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1471
\ldots, @{text "t.C\<^sub>n"}, the same auxiliary constants are generated as for
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1472
datatypes (Section~\ref{ssec:datatype-generated-constants}), except that the
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1473
iterator and the recursor are replaced by dual concepts:
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1474
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1475
\begin{itemize}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1476
\setlength{\itemsep}{0pt}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1477
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1478
\item \relax{Coiterator}: @{text t_unfold}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1479
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1480
\item \relax{Corecursor}: @{text t_corec}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1481
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1482
\end{itemize}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1483
*}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1484
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1485
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1486
subsection {* Generated Theorems
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1487
  \label{ssec:codatatype-generated-theorems} *}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1488
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1489
text {*
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1490
The characteristic theorems generated by @{command codatatype} are grouped in
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1491
three broad categories:
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1492
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1493
\begin{itemize}
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1494
\setlength{\itemsep}{0pt}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1495
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1496
\item The \emph{free constructor theorems} are properties about the constructors
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1497
and destructors that can be derived for any freely generated type.
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1498
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1499
\item The \emph{functorial theorems} are properties of datatypes related to
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1500
their BNF nature.
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1501
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1502
\item The \emph{coinductive theorems} are properties of datatypes related to
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1503
their coinductive nature.
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1504
\end{itemize}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1505
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1506
\noindent
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1507
The first two categories are exactly as for datatypes and are described in
53642
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
  1508
Sections
05ca82603671 more (co)data docs
blanchet
parents: 53623
diff changeset
  1509
\ref{sssec:free-constructor-theorems}~and~\ref{sssec:functorial-theorems}.
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  1510
*}
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  1511
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1512
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1513
subsubsection {* Coinductive Theorems
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1514
  \label{sssec:coinductive-theorems} *}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1515
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1516
text {*
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1517
The coinductive theorems are as follows:
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1518
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1519
\begin{indentblock}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1520
\begin{description}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1521
53643
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1522
\item[\begin{tabular}{@ {}l@ {}}
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1523
  @{text "t."}\hthm{coinduct} @{text "[coinduct t, consumes m, case_names t\<^sub>1 \<dots> t\<^sub>m,"} \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1524
  \phantom{@{text "t."}\hthm{coinduct} @{text "["}}@{text "case_conclusion D\<^sub>1 \<dots> D\<^sub>n]"}\rm:
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1525
\end{tabular}] ~ \\
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1526
@{thm llist.coinduct[no_vars]}
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1527
53643
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1528
\item[\begin{tabular}{@ {}l@ {}}
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1529
  @{text "t."}\hthm{strong\_coinduct} @{text "[consumes m, case_names t\<^sub>1 \<dots> t\<^sub>m,"} \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1530
  \phantom{@{text "t."}\hthm{strong\_coinduct} @{text "["}}@{text "case_conclusion D\<^sub>1 \<dots> D\<^sub>n]"}\rm:
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1531
\end{tabular}] ~ \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1532
@{thm llist.strong_coinduct[no_vars]}
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1533
53643
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1534
\item[\begin{tabular}{@ {}l@ {}}
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1535
  @{text "t\<^sub>1_\<dots>_t\<^sub>m."}\hthm{coinduct} @{text "[case_names t\<^sub>1 \<dots> t\<^sub>m, case_conclusion D\<^sub>1 \<dots> D\<^sub>n]"} \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1536
  @{text "t\<^sub>1_\<dots>_t\<^sub>m."}\hthm{strong\_coinduct} @{text "[case_names t\<^sub>1 \<dots> t\<^sub>m,"} \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1537
  \phantom{@{text "t\<^sub>1_\<dots>_t\<^sub>m."}\hthm{strong\_coinduct} @{text "["}}@{text "case_conclusion D\<^sub>1 \<dots> D\<^sub>n]"}\rm:
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1538
\end{tabular}] ~ \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1539
Given $m > 1$ mutually corecursive codatatypes, these coinduction rules can be
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1540
used to prove $m$ properties simultaneously.
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1541
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1542
\item[@{text "t."}\hthm{unfold} \rm(@{text "[simp]"})\rm:] ~ \\
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1543
@{thm llist.unfold(1)[no_vars]} \\
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1544
@{thm llist.unfold(2)[no_vars]}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1545
53643
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1546
\item[@{text "t."}\hthm{corec} (@{text "[simp]"})\rm:] ~ \\
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1547
@{thm llist.corec(1)[no_vars]} \\
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1548
@{thm llist.corec(2)[no_vars]}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1549
53703
0c565fec9c78 updated docs
blanchet
parents: 53694
diff changeset
  1550
\item[@{text "t."}\hthm{disc\_unfold}\rm:] ~ \\
53643
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1551
@{thm llist.disc_unfold(1)[no_vars]} \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1552
@{thm llist.disc_unfold(2)[no_vars]}
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1553
53703
0c565fec9c78 updated docs
blanchet
parents: 53694
diff changeset
  1554
\item[@{text "t."}\hthm{disc\_corec}\rm:] ~ \\
53643
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1555
@{thm llist.disc_corec(1)[no_vars]} \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1556
@{thm llist.disc_corec(2)[no_vars]}
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1557
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1558
\item[@{text "t."}\hthm{disc\_unfold\_iff} @{text "[simp]"}\rm:] ~ \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1559
@{thm llist.disc_unfold_iff(1)[no_vars]} \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1560
@{thm llist.disc_unfold_iff(2)[no_vars]}
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1561
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1562
\item[@{text "t."}\hthm{disc\_corec\_iff} @{text "[simp]"}\rm:] ~ \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1563
@{thm llist.disc_corec_iff(1)[no_vars]} \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1564
@{thm llist.disc_corec_iff(2)[no_vars]}
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1565
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1566
\item[@{text "t."}\hthm{sel\_unfold} @{text "[simp]"}\rm:] ~ \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1567
@{thm llist.sel_unfold(1)[no_vars]} \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1568
@{thm llist.sel_unfold(2)[no_vars]}
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1569
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1570
\item[@{text "t."}\hthm{sel\_corec} @{text "[simp]"}\rm:] ~ \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1571
@{thm llist.sel_corec(1)[no_vars]} \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1572
@{thm llist.sel_corec(2)[no_vars]}
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1573
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1574
\end{description}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1575
\end{indentblock}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1576
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1577
\noindent
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  1578
For convenience, @{command codatatype} also provides the following collection:
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1579
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1580
\begin{indentblock}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1581
\begin{description}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1582
53643
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1583
\item[@{text "t."}\hthm{simps} = @{text t.inject} @{text t.distinct} @{text t.case} @{text t.corec}$^*$ @{text t.disc_corec}] ~ \\
673cb2c9d695 more (co)data docs
blanchet
parents: 53642
diff changeset
  1584
@{text t.disc_corec_iff} @{text t.sel_corec} @{text t.unfold}$^*$ @{text t.disc_unfold} @{text t.disc_unfold_iff} ~ \\
53694
7b453b619b5f use singular to avoid confusion
blanchet
parents: 53691
diff changeset
  1585
@{text t.sel_unfold} @{text t.map} @{text t.rel_inject} @{text t.rel_distinct} @{text t.set}
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1586
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1587
\end{description}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1588
\end{indentblock}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  1589
*}
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1590
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1591
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  1592
section {* Defining Corecursive Functions
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1593
  \label{sec:defining-corecursive-functions} *}
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1594
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1595
text {*
53753
ae7f50e70c09 renamed "primcorec" to "primcorecursive", to open the door to a 'theory -> theory' command called "primcorec" (cf. "fun" vs. "function")
blanchet
parents: 53752
diff changeset
  1596
Corecursive functions can be specified using @{command primcorec} and
ae7f50e70c09 renamed "primcorec" to "primcorecursive", to open the door to a 'theory -> theory' command called "primcorec" (cf. "fun" vs. "function")
blanchet
parents: 53752
diff changeset
  1597
@{command primcorecursive}, which support primitive corecursion, or using the
ae7f50e70c09 renamed "primcorec" to "primcorecursive", to open the door to a 'theory -> theory' command called "primcorec" (cf. "fun" vs. "function")
blanchet
parents: 53752
diff changeset
  1598
more general \keyw{partial\_function} command. Here, the focus is on
ae7f50e70c09 renamed "primcorec" to "primcorecursive", to open the door to a 'theory -> theory' command called "primcorec" (cf. "fun" vs. "function")
blanchet
parents: 53752
diff changeset
  1599
the former two. More examples can be found in the directory
ae7f50e70c09 renamed "primcorec" to "primcorecursive", to open the door to a 'theory -> theory' command called "primcorec" (cf. "fun" vs. "function")
blanchet
parents: 53752
diff changeset
  1600
\verb|~~/src/HOL/BNF/Examples|.
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1601
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1602
Whereas recursive functions consume datatypes one constructor at a time,
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1603
corecursive functions construct codatatypes one constructor at a time.
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1604
Partly reflecting a lack of agreement among proponents of coalgebraic methods,
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1605
Isabelle supports three competing syntaxes for specifying a function $f$:
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1606
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1607
\begin{itemize}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1608
\setlength{\itemsep}{0pt}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1609
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1610
\abovedisplayskip=.5\abovedisplayskip
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1611
\belowdisplayskip=.5\belowdisplayskip
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1612
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1613
\item The \emph{destructor view} specifies $f$ by implications of the form
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1614
\[@{text "\<dots> \<Longrightarrow> is_C\<^sub>j (f x\<^sub>1 \<dots> x\<^sub>n)"}\] and
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1615
equations of the form
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1616
\[@{text "un_C\<^sub>ji (f x\<^sub>1 \<dots> x\<^sub>n) = \<dots>"}\]
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1617
This style is popular in the coalgebraic literature.
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1618
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1619
\item The \emph{constructor view} specifies $f$ by equations of the form
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1620
\[@{text "\<dots> \<Longrightarrow> f x\<^sub>1 \<dots> x\<^sub>n = C \<dots>"}\]
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1621
This style is often more concise than the previous one.
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1622
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1623
\item The \emph{code view} specifies $f$ by a single equation of the form
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1624
\[@{text "f x\<^sub>1 \<dots> x\<^sub>n = \<dots>"}\]
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1625
with restrictions on the format of the right-hand side. Lazy functional
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1626
programming languages such as Haskell support a generalized version of this
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1627
style.
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1628
\end{itemize}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1629
53753
ae7f50e70c09 renamed "primcorec" to "primcorecursive", to open the door to a 'theory -> theory' command called "primcorec" (cf. "fun" vs. "function")
blanchet
parents: 53752
diff changeset
  1630
All three styles are available as input syntax. Whichever syntax is chosen,
ae7f50e70c09 renamed "primcorec" to "primcorecursive", to open the door to a 'theory -> theory' command called "primcorec" (cf. "fun" vs. "function")
blanchet
parents: 53752
diff changeset
  1631
characteristic theorems for all three styles are generated.
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1632
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1633
\begin{framed}
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1634
\noindent
53753
ae7f50e70c09 renamed "primcorec" to "primcorecursive", to open the door to a 'theory -> theory' command called "primcorec" (cf. "fun" vs. "function")
blanchet
parents: 53752
diff changeset
  1635
\textbf{Warning:}\enskip The @{command primcorec} and @{command primcorecursive}
ae7f50e70c09 renamed "primcorec" to "primcorecursive", to open the door to a 'theory -> theory' command called "primcorec" (cf. "fun" vs. "function")
blanchet
parents: 53752
diff changeset
  1636
commands are under development. Some of the functionality described here is
ae7f50e70c09 renamed "primcorec" to "primcorecursive", to open the door to a 'theory -> theory' command called "primcorec" (cf. "fun" vs. "function")
blanchet
parents: 53752
diff changeset
  1637
vaporware. An alternative is to define corecursive functions directly using the
ae7f50e70c09 renamed "primcorec" to "primcorecursive", to open the door to a 'theory -> theory' command called "primcorec" (cf. "fun" vs. "function")
blanchet
parents: 53752
diff changeset
  1638
generated @{text t_unfold} or @{text t_corec} combinators.
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1639
\end{framed}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1640
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1641
%%% TODO: partial_function? E.g. for defining tail recursive function on lazy
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  1642
%%% lists (cf. terminal0 in TLList.thy)
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1643
*}
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1644
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  1645
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1646
subsection {* Introductory Examples
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  1647
  \label{ssec:primcorec-introductory-examples} *}
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1648
53646
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1649
text {*
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1650
Primitive corecursion is illustrated through concrete examples based on the
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1651
codatatypes defined in Section~\ref{ssec:codatatype-introductory-examples}. More
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1652
examples can be found in the directory \verb|~~/src/HOL/BNF/Examples|. The code
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1653
view is favored in the examples below. Sections
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1654
\ref{ssec:primrec-constructor-view} and \ref{ssec:primrec-destructor-view}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1655
present the same examples expressed using the constructor and destructor views.
53646
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1656
*}
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1657
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1658
(*<*)
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1659
    locale code_view
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1660
    begin
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1661
(*>*)
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1662
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1663
subsubsection {* Simple Corecursion
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1664
  \label{sssec:primcorec-simple-corecursion} *}
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1665
53646
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1666
text {*
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1667
Following the code view, corecursive calls are allowed on the right-hand side as
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1668
long as they occur under a constructor, which itself appears either directly to
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1669
the right of the equal sign or in a conditional expression:
53646
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1670
*}
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1671
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1672
    primcorec literate :: "('a \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> 'a llist" where
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1673
      "literate f x = LCons x (literate f (f x))"
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1674
53677
b51ebeda414d more (co)data docs
blanchet
parents: 53675
diff changeset
  1675
text {* \blankline *}
b51ebeda414d more (co)data docs
blanchet
parents: 53675
diff changeset
  1676
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1677
    primcorec siterate :: "('a \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> 'a stream" where
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1678
      "siterate f x = SCons x (siterate f (f x))"
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1679
53646
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1680
text {*
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1681
\noindent
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1682
The constructor ensures that progress is made---i.e., the function is
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1683
\emph{productive}. The above functions compute the infinite lazy list or stream
53646
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1684
@{text "[x, f x, f (f x), \<dots>]"}. Productivity guarantees that prefixes
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1685
@{text "[x, f x, f (f x), \<dots>, (f ^^ k) x]"} of arbitrary finite length
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1686
@{text k} can be computed by unfolding the code equation a finite number of
53863
c7364dca96f2 textual improvements following Christian Sternagel's feedback
blanchet
parents: 53857
diff changeset
  1687
times.
53646
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1688
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1689
Corecursive functions construct codatatype values, but nothing prevents them
53863
c7364dca96f2 textual improvements following Christian Sternagel's feedback
blanchet
parents: 53857
diff changeset
  1690
from also consuming such values. The following function drops every second
53675
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1691
element in a stream:
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1692
*}
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1693
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1694
    primcorec every_snd :: "'a stream \<Rightarrow> 'a stream" where
53675
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1695
      "every_snd s = SCons (shd s) (stl (stl s))"
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1696
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1697
text {*
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1698
\noindent
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1699
Constructs such as @{text "let"}---@{text "in"}, @{text
53646
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1700
"if"}---@{text "then"}---@{text "else"}, and @{text "case"}---@{text "of"} may
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1701
appear around constructors that guard corecursive calls:
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1702
*}
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1703
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1704
    primcorec_notyet lappend :: "'a llist \<Rightarrow> 'a llist \<Rightarrow> 'a llist" where
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1705
      "lappend xs ys =
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1706
         (case xs of
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1707
            LNil \<Rightarrow> ys
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1708
          | LCons x xs' \<Rightarrow> LCons x (lappend xs' ys))"
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1709
53646
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1710
text {*
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1711
\noindent
53646
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1712
Corecursion is useful to specify not only functions but also infinite objects:
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1713
*}
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1714
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1715
    primcorec infty :: enat where
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1716
      "infty = ESuc infty"
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1717
53646
ac6e0a28489f more (co)data docs
blanchet
parents: 53644
diff changeset
  1718
text {*
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1719
\noindent
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1720
The example below constructs a pseudorandom process value. It takes a stream of
53675
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1721
actions (@{text s}), a pseudorandom function generator (@{text f}), and a
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1722
pseudorandom seed (@{text n}):
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1723
*}
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1724
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1725
    primcorec_notyet
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1726
      random_process :: "'a stream \<Rightarrow> (int \<Rightarrow> int) \<Rightarrow> int \<Rightarrow> 'a process"
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1727
    where
53675
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1728
      "random_process s f n =
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1729
         (if n mod 4 = 0 then
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1730
            Fail
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1731
          else if n mod 4 = 1 then
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1732
            Skip (random_process s f (f n))
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1733
          else if n mod 4 = 2 then
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1734
            Action (shd s) (random_process (stl s) f (f n))
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1735
          else
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1736
            Choice (random_process (every_snd s) (f \<circ> f) (f n))
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1737
              (random_process (every_snd (stl s)) (f \<circ> f) (f (f n))))"
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1738
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1739
text {*
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1740
\noindent
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1741
The main disadvantage of the code view is that the conditions are tested
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1742
sequentially. This is visible in the generated theorems. The constructor and
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1743
destructor views offer nonsequential alternatives.
53675
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1744
*}
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1745
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1746
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1747
subsubsection {* Mutual Corecursion
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1748
  \label{sssec:primcorec-mutual-corecursion} *}
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1749
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1750
text {*
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1751
The syntax for mutually corecursive functions over mutually corecursive
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1752
datatypes is unsurprising:
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1753
*}
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1754
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1755
    primcorec
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1756
      even_infty :: even_enat and
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1757
      odd_infty :: odd_enat
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1758
    where
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1759
      "even_infty = Even_ESuc odd_infty" |
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1760
      "odd_infty = Odd_ESuc even_infty"
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1761
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1762
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1763
subsubsection {* Nested Corecursion
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1764
  \label{sssec:primcorec-nested-corecursion} *}
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1765
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1766
text {*
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1767
The next pair of examples generalize the @{const literate} and @{const siterate}
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1768
functions (Section~\ref{sssec:primcorec-nested-corecursion}) to possibly
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1769
infinite trees in which subnodes are organized either as a lazy list (@{text
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1770
tree\<^sub>i\<^sub>i}) or as a finite set (@{text tree\<^sub>i\<^sub>s}):
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1771
*}
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1772
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1773
    primcorec iterate\<^sub>i\<^sub>i :: "('a \<Rightarrow> 'a llist) \<Rightarrow> 'a \<Rightarrow> 'a tree\<^sub>i\<^sub>i" where
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1774
      "iterate\<^sub>i\<^sub>i f x = Node\<^sub>i\<^sub>i x (lmap (iterate\<^sub>i\<^sub>i f) (f x))"
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1775
53677
b51ebeda414d more (co)data docs
blanchet
parents: 53675
diff changeset
  1776
text {* \blankline *}
b51ebeda414d more (co)data docs
blanchet
parents: 53675
diff changeset
  1777
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1778
    primcorec iterate\<^sub>i\<^sub>s :: "('a \<Rightarrow> 'a fset) \<Rightarrow> 'a \<Rightarrow> 'a tree\<^sub>i\<^sub>s" where
54014
21dac9a60f0c base the fset bnf on the new FSet theory
traytel
parents: 53997
diff changeset
  1779
      "iterate\<^sub>i\<^sub>s f x = Node\<^sub>i\<^sub>s x (fimage (iterate\<^sub>i\<^sub>s f) (f x))"
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1780
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1781
text {*
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1782
\noindent
53675
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1783
Deterministic finite automata (DFAs) are usually defined as 5-tuples
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1784
@{text "(Q, \<Sigma>, \<delta>, q\<^sub>0, F)"}, where @{text Q} is a finite set of states,
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1785
@{text \<Sigma>} is a finite alphabet, @{text \<delta>} is a transition function, @{text q\<^sub>0}
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1786
is an initial state, and @{text F} is a set of final states. The following
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1787
function translates a DFA into a @{type state_machine}:
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1788
*}
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1789
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1790
    primcorec (*<*)(in early) (*>*)
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1791
      sm_of_dfa :: "('q \<Rightarrow> 'a \<Rightarrow> 'q) \<Rightarrow> 'q set \<Rightarrow> 'q \<Rightarrow> 'a state_machine"
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1792
    where
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1793
      "sm_of_dfa \<delta> F q = State_Machine (q \<in> F) (sm_of_dfa \<delta> F o \<delta> q)"
53675
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  1794
53751
7a994dc08cea added primcorec examples with lambdas
blanchet
parents: 53750
diff changeset
  1795
text {*
7a994dc08cea added primcorec examples with lambdas
blanchet
parents: 53750
diff changeset
  1796
\noindent
7a994dc08cea added primcorec examples with lambdas
blanchet
parents: 53750
diff changeset
  1797
The map function for the function type (@{text \<Rightarrow>}) is composition
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1798
(@{text "op \<circ>"}). For convenience, corecursion through functions can be
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1799
expressed using @{text \<lambda>}-expressions and function application rather
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1800
than composition. For example:
53751
7a994dc08cea added primcorec examples with lambdas
blanchet
parents: 53750
diff changeset
  1801
*}
7a994dc08cea added primcorec examples with lambdas
blanchet
parents: 53750
diff changeset
  1802
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1803
    primcorec
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1804
      sm_of_dfa :: "('q \<Rightarrow> 'a \<Rightarrow> 'q) \<Rightarrow> 'q set \<Rightarrow> 'q \<Rightarrow> 'a state_machine"
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1805
    where
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1806
      "sm_of_dfa \<delta> F q = State_Machine (q \<in> F) (sm_of_dfa \<delta> F o \<delta> q)"
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1807
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1808
text {* \blankline *}
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1809
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1810
    primcorec empty_sm :: "'a state_machine" where
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1811
      "empty_sm = State_Machine False (\<lambda>_. empty_sm)"
53751
7a994dc08cea added primcorec examples with lambdas
blanchet
parents: 53750
diff changeset
  1812
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1813
text {* \blankline *}
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1814
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1815
    primcorec not_sm :: "'a state_machine \<Rightarrow> 'a state_machine" where
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1816
      "not_sm M = State_Machine (\<not> accept M) (\<lambda>a. not_sm (trans M a))"
53751
7a994dc08cea added primcorec examples with lambdas
blanchet
parents: 53750
diff changeset
  1817
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1818
text {* \blankline *}
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1819
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1820
    primcorec
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1821
      or_sm :: "'a state_machine \<Rightarrow> 'a state_machine \<Rightarrow> 'a state_machine"
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1822
    where
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1823
      "or_sm M N =
53751
7a994dc08cea added primcorec examples with lambdas
blanchet
parents: 53750
diff changeset
  1824
         State_Machine (accept M \<or> accept N)
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1825
           (\<lambda>a. or_sm (trans M a) (trans N a))"
53751
7a994dc08cea added primcorec examples with lambdas
blanchet
parents: 53750
diff changeset
  1826
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1827
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1828
subsubsection {* Nested-as-Mutual Corecursion
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1829
  \label{sssec:primcorec-nested-as-mutual-corecursion} *}
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1830
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1831
text {*
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1832
Just as it is possible to recurse over nested recursive datatypes as if they
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1833
were mutually recursive
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1834
(Section~\ref{sssec:primrec-nested-as-mutual-recursion}), it is possible to
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1835
pretend that nested codatatypes are mutually corecursive. For example:
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1836
*}
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  1837
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1838
    primcorec_notyet
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1839
      iterate\<^sub>i\<^sub>i :: "('a \<Rightarrow> 'a llist) \<Rightarrow> 'a \<Rightarrow> 'a tree\<^sub>i\<^sub>i" and
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1840
      iterates\<^sub>i\<^sub>i :: "('a \<Rightarrow> 'a llist) \<Rightarrow> 'a llist \<Rightarrow> 'a tree\<^sub>i\<^sub>i llist"
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1841
    where
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1842
      "iterate\<^sub>i\<^sub>i f x = Node\<^sub>i\<^sub>i x (iterates\<^sub>i\<^sub>i f (f x))" |
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1843
      "iterates\<^sub>i\<^sub>i f xs =
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1844
         (case xs of
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1845
            LNil \<Rightarrow> LNil
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1846
          | LCons x xs' \<Rightarrow> LCons (iterate\<^sub>i\<^sub>i f x) (iterates\<^sub>i\<^sub>i f xs'))"
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1847
(*<*)
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1848
    end
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1849
(*>*)
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1850
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1851
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1852
subsubsection {* Constructor View
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1853
  \label{ssec:primrec-constructor-view} *}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1854
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1855
(*<*)
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1856
    locale ctr_view = code_view
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1857
    begin
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1858
(*>*)
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1859
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1860
text {*
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1861
The constructor view is similar to the code view, but there is one separate
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1862
conditional equation per constructor rather than a single unconditional
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1863
equation. Examples that rely on a single constructor, such as @{const literate}
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1864
and @{const siterate}, are identical in both styles.
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1865
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1866
Here is an example where there is a difference:
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1867
*}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1868
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1869
    primcorec lappend :: "'a llist \<Rightarrow> 'a llist \<Rightarrow> 'a llist" where
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1870
      "lnull xs \<Longrightarrow> lnull ys \<Longrightarrow> lappend xs ys = LNil" |
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1871
      "_ \<Longrightarrow> lappend xs ys = LCons (lhd (if lnull xs then ys else xs))
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1872
         (if xs = LNil then ltl ys else lappend (ltl xs) ys)"
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1873
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1874
text {*
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1875
\noindent
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1876
With the constructor view, we must distinguish between the @{const LNil} and
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1877
the @{const LCons} case. The condition for @{const LCons} is
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1878
left implicit, as the negation of that for @{const LNil}.
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1879
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1880
For this example, the constructor view is slighlty more involved than the
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1881
code equation. Recall the code view version presented in
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1882
Section~\ref{sssec:primcorec-simple-corecursion}.
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1883
% TODO: \[{thm code_view.lappend.code}\]
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1884
The constructor view requires us to analyze the second argument (@{term ys}).
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1885
The code equation generated from the constructor view also suffers from this.
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1886
% TODO: \[{thm lappend.code}\]
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1887
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1888
In contrast, the next example is arguably more naturally expressed in the
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1889
constructor view:
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1890
*}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1891
53831
80423b9080cf support "of" syntax to disambiguate selector equations
panny
parents: 53829
diff changeset
  1892
    primcorec
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1893
      random_process :: "'a stream \<Rightarrow> (int \<Rightarrow> int) \<Rightarrow> int \<Rightarrow> 'a process"
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1894
    where
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1895
      "n mod 4 = 0 \<Longrightarrow> random_process s f n = Fail" |
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1896
      "n mod 4 = 1 \<Longrightarrow>
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1897
         random_process s f n = Skip (random_process s f (f n))" |
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1898
      "n mod 4 = 2 \<Longrightarrow>
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1899
         random_process s f n = Action (shd s) (random_process (stl s) f (f n))" |
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1900
      "n mod 4 = 3 \<Longrightarrow>
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1901
         random_process s f n = Choice (random_process (every_snd s) f (f n))
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1902
           (random_process (every_snd (stl s)) f (f n))"
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1903
(*<*)
53644
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1904
    end
eb8362530715 more (co)data docs
blanchet
parents: 53643
diff changeset
  1905
(*>*)
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  1906
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1907
text {*
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1908
\noindent
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1909
Since there is no sequentiality, we can apply the equation for @{const Choice}
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1910
without having first to discharge @{term "n mod (4\<Colon>int) \<noteq> 0"},
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1911
@{term "n mod (4\<Colon>int) \<noteq> 1"}, and
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1912
@{term "n mod (4\<Colon>int) \<noteq> 2"}.
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1913
The price to pay for this elegance is that we must discharge exclusivity proof
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1914
obligations, one for each pair of conditions
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1915
@{term "(n mod (4\<Colon>int) = i, n mod (4\<Colon>int) = j)"}
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1916
with @{term "i < j"}. If we prefer not to discharge any obligations, we can
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1917
enable the @{text "sequential"} option. This pushes the problem to the users of
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1918
the generated properties.
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1919
%Here are more examples to conclude:
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1920
*}
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1921
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  1922
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1923
subsubsection {* Destructor View
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1924
  \label{ssec:primrec-destructor-view} *}
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1925
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1926
(*<*)
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1927
    locale dest_view
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1928
    begin
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1929
(*>*)
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1930
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1931
text {*
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1932
The destructor view is in many respects dual to the constructor view. Conditions
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1933
determine which constructor to choose, and these conditions are interpreted
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1934
sequentially or not depending on the @{text "sequential"} option.
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1935
Consider the following examples:
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1936
*}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1937
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1938
    primcorec literate :: "('a \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> 'a llist" where
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1939
      "\<not> lnull (literate _ x)" |
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1940
      "lhd (literate _ x) = x" |
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1941
      "ltl (literate f x) = literate f (f x)"
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1942
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1943
text {* \blankline *}
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1944
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1945
    primcorec siterate :: "('a \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> 'a stream" where
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1946
      "shd (siterate _ x) = x" |
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1947
      "stl (siterate f x) = siterate f (f x)"
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1948
53752
1a883094fbe0 more primcorec docs
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parents: 53751
diff changeset
  1949
text {* \blankline *}
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1950
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1951
    primcorec every_snd :: "'a stream \<Rightarrow> 'a stream" where
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1952
      "shd (every_snd s) = shd s" |
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1953
      "stl (every_snd s) = stl (stl s)"
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1954
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1955
text {*
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1956
\noindent
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1957
The first formula in the @{const literate} specification indicates which
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1958
constructor to choose. For @{const siterate} and @{const every_snd}, no such
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1959
formula is necessary, since the type has only one constructor. The last two
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1960
formulas are equations specifying the value of the result for the relevant
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1961
selectors. Corecursive calls appear directly to the right of the equal sign.
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  1962
Their arguments are unrestricted.
53750
03c5c2db3a47 more primcorec docs
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parents: 53749
diff changeset
  1963
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1964
The next example shows how to specify functions that rely on more than one
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1965
constructor:
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1966
*}
03c5c2db3a47 more primcorec docs
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parents: 53749
diff changeset
  1967
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1968
    primcorec lappend :: "'a llist \<Rightarrow> 'a llist \<Rightarrow> 'a llist" where
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1969
      "lnull xs \<Longrightarrow> lnull ys \<Longrightarrow> lnull (lappend xs ys)" |
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1970
      "lhd (lappend xs ys) = lhd (if lnull xs then ys else xs)" |
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1971
      "ltl (lappend xs ys) = (if xs = LNil then ltl ys else lappend (ltl xs) ys)"
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1972
03c5c2db3a47 more primcorec docs
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parents: 53749
diff changeset
  1973
text {*
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1974
\noindent
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1975
For a codatatype with $n$ constructors, it is sufficient to specify $n - 1$
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1976
discriminator formulas. The command will then assume that the remaining
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1977
constructor should be taken otherwise. This can be made explicit by adding
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1978
*}
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1979
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1980
(*<*)
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1981
    end
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1982
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  1983
    primcorec lappend :: "'a llist \<Rightarrow> 'a llist \<Rightarrow> 'a llist" where
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1984
      "lnull xs \<Longrightarrow> lnull ys \<Longrightarrow> lnull (lappend xs ys)" |
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1985
(*>*)
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1986
      "_ \<Longrightarrow> \<not> lnull (lappend xs ys)"
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1987
(*<*) |
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1988
      "lhd (lappend xs ys) = lhd (if lnull xs then ys else xs)" |
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1989
      "ltl (lappend xs ys) = (if xs = LNil then ltl ys else lappend (ltl xs) ys)"
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1990
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1991
    context dest_view begin
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1992
(*>*)
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1993
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1994
text {*
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1995
\noindent
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  1996
to the specification. The generated selector theorems are conditional.
1a883094fbe0 more primcorec docs
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parents: 53751
diff changeset
  1997
1a883094fbe0 more primcorec docs
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parents: 53751
diff changeset
  1998
The next example illustrates how to cope with selectors defined for several
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  1999
constructors:
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2000
*}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2001
53831
80423b9080cf support "of" syntax to disambiguate selector equations
panny
parents: 53829
diff changeset
  2002
    primcorec
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  2003
      random_process :: "'a stream \<Rightarrow> (int \<Rightarrow> int) \<Rightarrow> int \<Rightarrow> 'a process"
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  2004
    where
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2005
      "n mod 4 = 0 \<Longrightarrow> is_Fail (random_process s f n)" |
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2006
      "n mod 4 = 1 \<Longrightarrow> is_Skip (random_process s f n)" |
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2007
      "n mod 4 = 2 \<Longrightarrow> is_Action (random_process s f n)" |
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2008
      "n mod 4 = 3 \<Longrightarrow> is_Choice (random_process s f n)" |
53831
80423b9080cf support "of" syntax to disambiguate selector equations
panny
parents: 53829
diff changeset
  2009
      "cont (random_process s f n) = random_process s f (f n)" of Skip |
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2010
      "prefix (random_process s f n) = shd s" |
53831
80423b9080cf support "of" syntax to disambiguate selector equations
panny
parents: 53829
diff changeset
  2011
      "cont (random_process s f n) = random_process (stl s) f (f n)" of Action |
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2012
      "left (random_process s f n) = random_process (every_snd s) f (f n)" |
53831
80423b9080cf support "of" syntax to disambiguate selector equations
panny
parents: 53829
diff changeset
  2013
      "right (random_process s f n) = random_process (every_snd (stl s)) f (f n)"
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2014
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2015
text {*
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  2016
\noindent
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  2017
Using the @{text "of"} keyword, different equations are specified for @{const
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  2018
cont} depending on which constructor is selected.
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  2019
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  2020
Here are more examples to conclude:
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2021
*}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2022
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  2023
    primcorec
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2024
      even_infty :: even_enat and
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2025
      odd_infty :: odd_enat
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2026
    where
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2027
      "\<not> is_Even_EZero even_infty" |
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2028
      "un_Even_ESuc even_infty = odd_infty" |
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2029
      "un_Odd_ESuc odd_infty = even_infty"
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2030
53752
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  2031
text {* \blankline *}
1a883094fbe0 more primcorec docs
blanchet
parents: 53751
diff changeset
  2032
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  2033
    primcorec iterate\<^sub>i\<^sub>i :: "('a \<Rightarrow> 'a llist) \<Rightarrow> 'a \<Rightarrow> 'a tree\<^sub>i\<^sub>i" where
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2034
      "lbl\<^sub>i\<^sub>i (iterate\<^sub>i\<^sub>i f x) = x" |
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2035
      "sub\<^sub>i\<^sub>i (iterate\<^sub>i\<^sub>i f x) = lmap (iterate\<^sub>i\<^sub>i f) (f x)"
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2036
(*<*)
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2037
    end
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2038
(*>*)
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2039
53750
03c5c2db3a47 more primcorec docs
blanchet
parents: 53749
diff changeset
  2040
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2041
subsection {* Command Syntax
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2042
  \label{ssec:primcorec-command-syntax} *}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2043
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2044
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  2045
subsubsection {* \keyw{primcorec} and \keyw{primcorecursive}
53753
ae7f50e70c09 renamed "primcorec" to "primcorecursive", to open the door to a 'theory -> theory' command called "primcorec" (cf. "fun" vs. "function")
blanchet
parents: 53752
diff changeset
  2046
  \label{sssec:primcorecursive-and-primcorec} *}
52840
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  2047
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  2048
text {*
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2049
\begin{matharray}{rcl}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2050
  @{command_def "primcorec"} & : & @{text "local_theory \<rightarrow> local_theory"} \\
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2051
  @{command_def "primcorecursive"} & : & @{text "local_theory \<rightarrow> proof(prove)"}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2052
\end{matharray}
52840
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  2053
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  2054
@{rail "
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2055
  (@@{command primcorec} | @@{command primcorecursive}) target? \\ @{syntax pcr_option}? fixes @'where'
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2056
    (@{syntax pcr_formula} + '|')
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2057
  ;
53828
408c9a3617e3 improved rail diagram
blanchet
parents: 53826
diff changeset
  2058
  @{syntax_def pcr_option}: '(' ('sequential' | 'exhaustive') ')'
52840
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  2059
  ;
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2060
  @{syntax_def pcr_formula}: thmdecl? prop (@'of' (term * ))?
52840
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  2061
"}
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2062
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2063
The optional target is optionally followed by a corecursion-specific option:
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2064
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2065
\begin{itemize}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2066
\setlength{\itemsep}{0pt}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2067
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2068
\item
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2069
The @{text "sequential"} option indicates that the conditions in specifications
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2070
expressed using the constructor or destructor view are to be interpreted
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2071
sequentially.
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  2072
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  2073
\item
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  2074
The @{text "exhaustive"} option indicates that the conditions in specifications
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  2075
expressed using the constructor or destructor view cover all possible cases.
53749
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2076
\end{itemize}
b37db925b663 adapted primcorec documentation to reflect the three views
blanchet
parents: 53748
diff changeset
  2077
53826
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  2078
\noindent
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  2079
The @{command primcorec} command is an abbreviation for @{command primcorecursive} with
92a8ae172242 use "primcorec" in doc
blanchet
parents: 53822
diff changeset
  2080
@{text "by auto?"} to discharge any emerging proof obligations.
52840
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  2081
*}
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2082
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  2083
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  2084
(*
52840
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  2085
subsection {* Generated Theorems
a0da63cec918 more (co)datatype documentation
blanchet
parents: 52829
diff changeset
  2086
  \label{ssec:primcorec-generated-theorems} *}
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  2087
*)
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2088
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2089
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2090
(*
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2091
subsection {* Recursive Default Values for Selectors
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2092
  \label{ssec:primcorec-recursive-default-values-for-selectors} *}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2093
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2094
text {*
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2095
partial_function to the rescue
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2096
*}
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2097
*)
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2098
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2099
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  2100
section {* Registering Bounded Natural Functors
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2101
  \label{sec:registering-bounded-natural-functors} *}
52792
3e651be14fcd sketched documentation for new (co)datatype package
blanchet
parents:
diff changeset
  2102
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2103
text {*
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  2104
The (co)datatype package can be set up to allow nested recursion through
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  2105
arbitrary type constructors, as long as they adhere to the BNF requirements and
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  2106
are registered as BNFs.
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2107
*}
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2108
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  2109
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  2110
(*
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2111
subsection {* Introductory Example
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2112
  \label{ssec:bnf-introductory-example} *}
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2113
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2114
text {*
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2115
More examples in \verb|~~/src/HOL/BNF/Basic_BNFs.thy| and
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2116
\verb|~~/src/HOL/BNF/More_BNFs.thy|.
52806
146ce45c3619 more work on (co)datatype docs
blanchet
parents: 52805
diff changeset
  2117
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2118
%Mention distinction between live and dead type arguments;
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2119
%  * and existence of map, set for those
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2120
%mention =>.
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2121
*}
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  2122
*)
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2123
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  2124
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2125
subsection {* Command Syntax
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2126
  \label{ssec:bnf-command-syntax} *}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2127
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2128
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  2129
subsubsection {* \keyw{bnf}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  2130
  \label{sssec:bnf} *}
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2131
53028
a1e64c804c35 more (co)datatype documentation
blanchet
parents: 53025
diff changeset
  2132
text {*
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2133
\begin{matharray}{rcl}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2134
  @{command_def "bnf"} & : & @{text "local_theory \<rightarrow> proof(prove)"}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2135
\end{matharray}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2136
53028
a1e64c804c35 more (co)datatype documentation
blanchet
parents: 53025
diff changeset
  2137
@{rail "
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2138
  @@{command bnf} target? (name ':')? term \\
53534
de2027f9aff3 more (co)datatype documentation
blanchet
parents: 53491
diff changeset
  2139
    term_list term term_list term?
53028
a1e64c804c35 more (co)datatype documentation
blanchet
parents: 53025
diff changeset
  2140
  ;
53534
de2027f9aff3 more (co)datatype documentation
blanchet
parents: 53491
diff changeset
  2141
  X_list: '[' (X + ',') ']'
53028
a1e64c804c35 more (co)datatype documentation
blanchet
parents: 53025
diff changeset
  2142
"}
a1e64c804c35 more (co)datatype documentation
blanchet
parents: 53025
diff changeset
  2143
*}
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2144
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2145
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  2146
subsubsection {* \keyw{print\_bnfs}
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  2147
  \label{sssec:print-bnfs} *}
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2148
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2149
text {*
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2150
\begin{matharray}{rcl}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2151
  @{command_def "print_bnfs"} & : & @{text "local_theory \<rightarrow>"}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2152
\end{matharray}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2153
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  2154
@{rail "
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2155
  @@{command print_bnfs}
53647
e78ebb290dd6 more (co)data docs
blanchet
parents: 53646
diff changeset
  2156
"}
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2157
*}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2158
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2159
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2160
section {* Deriving Destructors and Theorems for Free Constructors
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2161
  \label{sec:deriving-destructors-and-theorems-for-free-constructors} *}
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2162
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2163
text {*
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2164
The derivation of convenience theorems for types equipped with free constructors,
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2165
as performed internally by @{command datatype_new} and @{command codatatype},
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2166
is available as a stand-alone command called @{command wrap_free_constructors}.
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2167
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2168
%  * need for this is rare but may arise if you want e.g. to add destructors to
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2169
%    a type not introduced by ...
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2170
%
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2171
%  * also useful for compatibility with old package, e.g. add destructors to
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2172
%    old \keyw{datatype}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2173
%
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2174
%  * @{command wrap_free_constructors}
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2175
%    * @{text "no_discs_sels"}, @{text "rep_compat"}
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2176
%    * hack to have both co and nonco view via locale (cf. ext nats)
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2177
*}
52792
3e651be14fcd sketched documentation for new (co)datatype package
blanchet
parents:
diff changeset
  2178
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  2179
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  2180
(*
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2181
subsection {* Introductory Example
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2182
  \label{ssec:ctors-introductory-example} *}
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  2183
*)
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2184
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  2185
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2186
subsection {* Command Syntax
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2187
  \label{ssec:ctors-command-syntax} *}
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2188
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2189
53621
9c3a80af72ff more (co)data doc
blanchet
parents: 53619
diff changeset
  2190
subsubsection {* \keyw{wrap\_free\_constructors}
53675
d4a4b32038eb more (co)data docs
blanchet
parents: 53654
diff changeset
  2191
  \label{sssec:wrap-free-constructors} *}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  2192
53018
11ebef554439 added rail diagram
blanchet
parents: 52969
diff changeset
  2193
text {*
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2194
\begin{matharray}{rcl}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2195
  @{command_def "wrap_free_constructors"} & : & @{text "local_theory \<rightarrow> proof(prove)"}
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2196
\end{matharray}
53018
11ebef554439 added rail diagram
blanchet
parents: 52969
diff changeset
  2197
11ebef554439 added rail diagram
blanchet
parents: 52969
diff changeset
  2198
@{rail "
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2199
  @@{command wrap_free_constructors} target? @{syntax dt_options} \\
53863
c7364dca96f2 textual improvements following Christian Sternagel's feedback
blanchet
parents: 53857
diff changeset
  2200
    term_list name @{syntax wfc_discs_sels}?
53018
11ebef554439 added rail diagram
blanchet
parents: 52969
diff changeset
  2201
  ;
53863
c7364dca96f2 textual improvements following Christian Sternagel's feedback
blanchet
parents: 53857
diff changeset
  2202
  @{syntax_def wfc_discs_sels}: name_list (name_list_list name_term_list_list? )?
53018
11ebef554439 added rail diagram
blanchet
parents: 52969
diff changeset
  2203
  ;
53534
de2027f9aff3 more (co)datatype documentation
blanchet
parents: 53491
diff changeset
  2204
  @{syntax_def name_term}: (name ':' term)
53018
11ebef554439 added rail diagram
blanchet
parents: 52969
diff changeset
  2205
"}
11ebef554439 added rail diagram
blanchet
parents: 52969
diff changeset
  2206
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2207
% options: no_discs_sels rep_compat
53028
a1e64c804c35 more (co)datatype documentation
blanchet
parents: 53025
diff changeset
  2208
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2209
% X_list is as for BNF
53028
a1e64c804c35 more (co)datatype documentation
blanchet
parents: 53025
diff changeset
  2210
53829
92e71eb22ebe more (co)data docs
blanchet
parents: 53828
diff changeset
  2211
\noindent
53542
14000a283ce0 more (co)data docs
blanchet
parents: 53535
diff changeset
  2212
Section~\ref{ssec:datatype-generated-theorems} lists the generated theorems.
53018
11ebef554439 added rail diagram
blanchet
parents: 52969
diff changeset
  2213
*}
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  2214
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2215
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2216
(*
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  2217
section {* Standard ML Interface
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2218
  \label{sec:standard-ml-interface} *}
52792
3e651be14fcd sketched documentation for new (co)datatype package
blanchet
parents:
diff changeset
  2219
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2220
text {*
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2221
The package's programmatic interface.
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2222
*}
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2223
*)
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2224
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2225
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2226
(*
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  2227
section {* Interoperability
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2228
  \label{sec:interoperability} *}
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2229
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2230
text {*
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2231
The package's interaction with other Isabelle packages and tools, such as the
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2232
code generator and the counterexample generators.
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2233
*}
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2234
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  2235
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  2236
subsection {* Transfer and Lifting
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  2237
  \label{ssec:transfer-and-lifting} *}
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2238
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  2239
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  2240
subsection {* Code Generator
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  2241
  \label{ssec:code-generator} *}
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2242
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  2243
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  2244
subsection {* Quickcheck
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  2245
  \label{ssec:quickcheck} *}
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2246
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  2247
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  2248
subsection {* Nitpick
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  2249
  \label{ssec:nitpick} *}
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2250
52824
b7a83845bc93 more (co)datatype documentation
blanchet
parents: 52822
diff changeset
  2251
52828
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  2252
subsection {* Nominal Isabelle
e1c6fa322d96 more (co)datatype docs
blanchet
parents: 52827
diff changeset
  2253
  \label{ssec:nominal-isabelle} *}
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2254
*)
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2255
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2256
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2257
(*
52827
395d3df496ed more (co)datatype documentation
blanchet
parents: 52824
diff changeset
  2258
section {* Known Bugs and Limitations
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2259
  \label{sec:known-bugs-and-limitations} *}
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2260
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2261
text {*
53623
501e2091182b more (co)data docs
blanchet
parents: 53621
diff changeset
  2262
Known open issues of the package.
52805
7f2f42046361 more (co)datatype documentation
blanchet
parents: 52795
diff changeset
  2263
*}
52794
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2264
aae782070611 more (co)datatype documentation
blanchet
parents: 52792
diff changeset
  2265
text {*
53753
ae7f50e70c09 renamed "primcorec" to "primcorecursive", to open the door to a 'theory -> theory' command called "primcorec" (cf. "fun" vs. "function")
blanchet
parents: 53752
diff changeset
  2266
%* primcorecursive and primcorec is unfinished
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2267
%
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2268
%* slow n-ary mutual (co)datatype, avoid as much as possible (e.g. using nesting)
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2269
%
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2270
%* issues with HOL-Proofs?
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2271
%
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2272
%* partial documentation
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2273
%
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2274
%* no way to register "sum" and "prod" as (co)datatypes to enable N2M reduction for them
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2275
%  (for @{command datatype_new_compat} and prim(co)rec)
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2276
%
53619
27d2c98d9d9f more (co)data docs
blanchet
parents: 53617
diff changeset
  2277
%    * a fortiori, no way to register same type as both data- and codatatype
53617
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2278
%
da5e1887d7a7 more (co)data doc
blanchet
parents: 53565
diff changeset
  2279
%* no recursion through unused arguments (unlike with the old package)
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  2280
%
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  2281
%* in a locale, cannot use locally fixed types (because of limitation in typedef)?
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  2282
%
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  2283
% *names of variables suboptimal
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  2284
*}
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  2285
*)
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  2286
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  2287
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  2288
text {*
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  2289
\section*{Acknowledgment}
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  2290
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b37db925b663 adapted primcorec documentation to reflect the three views
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  2291
Tobias Nipkow and Makarius Wenzel encouraged us to implement the new
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  2292
(co)datatype package. Andreas Lochbihler provided lots of comments on earlier
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  2293
versions of the package, especially for the coinductive part. Brian Huffman
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  2294
suggested major simplifications to the internal constructions, much of which has
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  2295
yet to be implemented. Florian Haftmann and Christian Urban provided general
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  2296
advice on Isabelle and package writing. Stefan Milius and Lutz Schr\"oder
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  2297
found an elegant proof to eliminate one of the BNF assumptions. Christian
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  2298
Sternagel suggested many textual improvements to this tutorial.
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*}
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  2300
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  2301
end