doc-src/IsarRef/Thy/HOL_Specific.thy
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(* $Id$ *)
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theory HOL_Specific
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imports Main
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begin
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chapter {* Isabelle/HOL \label{ch:hol} *}
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section {* Primitive types \label{sec:hol-typedef} *}
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text {*
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  \begin{matharray}{rcl}
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    @{command_def (HOL) "typedecl"} & : & \isartrans{theory}{theory} \\
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    @{command_def (HOL) "typedef"} & : & \isartrans{theory}{proof(prove)} \\
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  \end{matharray}
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  \begin{rail}
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    'typedecl' typespec infix?
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    ;
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    'typedef' altname? abstype '=' repset
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    ;
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    altname: '(' (name | 'open' | 'open' name) ')'
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    ;
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    abstype: typespec infix?
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    ;
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    repset: term ('morphisms' name name)?
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    ;
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  \end{rail}
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  \begin{descr}
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  \item [@{command (HOL) "typedecl"}~@{text "(\<alpha>\<^sub>1, \<dots>, \<alpha>\<^sub>n)
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  t"}] is similar to the original @{command "typedecl"} of
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  Isabelle/Pure (see \secref{sec:types-pure}), but also declares type
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  arity @{text "t :: (type, \<dots>, type) type"}, making @{text t} an
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  actual HOL type constructor.   %FIXME check, update
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  \item [@{command (HOL) "typedef"}~@{text "(\<alpha>\<^sub>1, \<dots>, \<alpha>\<^sub>n)
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  t = A"}] sets up a goal stating non-emptiness of the set @{text A}.
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  After finishing the proof, the theory will be augmented by a
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  Gordon/HOL-style type definition, which establishes a bijection
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  between the representing set @{text A} and the new type @{text t}.
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  Technically, @{command (HOL) "typedef"} defines both a type @{text
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  t} and a set (term constant) of the same name (an alternative base
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  name may be given in parentheses).  The injection from type to set
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  is called @{text Rep_t}, its inverse @{text Abs_t} (this may be
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  changed via an explicit @{keyword (HOL) "morphisms"} declaration).
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  Theorems @{text Rep_t}, @{text Rep_t_inverse}, and @{text
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  Abs_t_inverse} provide the most basic characterization as a
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  corresponding injection/surjection pair (in both directions).  Rules
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  @{text Rep_t_inject} and @{text Abs_t_inject} provide a slightly
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  more convenient view on the injectivity part, suitable for automated
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  proof tools (e.g.\ in @{attribute simp} or @{attribute iff}
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  declarations).  Rules @{text Rep_t_cases}/@{text Rep_t_induct}, and
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  @{text Abs_t_cases}/@{text Abs_t_induct} provide alternative views
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  on surjectivity; these are already declared as set or type rules for
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  the generic @{method cases} and @{method induct} methods.
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  An alternative name may be specified in parentheses; the default is
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  to use @{text t} as indicated before.  The ``@{text "(open)"}''
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  declaration suppresses a separate constant definition for the
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  representing set.
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  \end{descr}
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  Note that raw type declarations are rarely used in practice; the
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  main application is with experimental (or even axiomatic!) theory
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  fragments.  Instead of primitive HOL type definitions, user-level
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  theories usually refer to higher-level packages such as @{command
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  (HOL) "record"} (see \secref{sec:hol-record}) or @{command (HOL)
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  "datatype"} (see \secref{sec:hol-datatype}).
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*}
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section {* Adhoc tuples *}
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text {*
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  \begin{matharray}{rcl}
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    @{attribute (HOL) split_format}@{text "\<^sup>*"} & : & \isaratt \\
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  \end{matharray}
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  \begin{rail}
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    'split\_format' (((name *) + 'and') | ('(' 'complete' ')'))
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    ;
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  \end{rail}
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  \begin{descr}
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  \item [@{attribute (HOL) split_format}~@{text "p\<^sub>1 \<dots> p\<^sub>m
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  \<AND> \<dots> \<AND> q\<^sub>1 \<dots> q\<^sub>n"}] puts expressions of
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  low-level tuple types into canonical form as specified by the
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  arguments given; the @{text i}-th collection of arguments refers to
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  occurrences in premise @{text i} of the rule.  The ``@{text
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  "(complete)"}'' option causes \emph{all} arguments in function
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  applications to be represented canonically according to their tuple
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  type structure.
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  Note that these operations tend to invent funny names for new local
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  parameters to be introduced.
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  \end{descr}
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*}
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section {* Records \label{sec:hol-record} *}
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text {*
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  In principle, records merely generalize the concept of tuples, where
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  components may be addressed by labels instead of just position.  The
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  logical infrastructure of records in Isabelle/HOL is slightly more
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  advanced, though, supporting truly extensible record schemes.  This
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  admits operations that are polymorphic with respect to record
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  extension, yielding ``object-oriented'' effects like (single)
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  inheritance.  See also \cite{NaraschewskiW-TPHOLs98} for more
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  details on object-oriented verification and record subtyping in HOL.
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*}
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subsection {* Basic concepts *}
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text {*
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  Isabelle/HOL supports both \emph{fixed} and \emph{schematic} records
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  at the level of terms and types.  The notation is as follows:
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  \begin{center}
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  \begin{tabular}{l|l|l}
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    & record terms & record types \\ \hline
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    fixed & @{text "\<lparr>x = a, y = b\<rparr>"} & @{text "\<lparr>x :: A, y :: B\<rparr>"} \\
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    schematic & @{text "\<lparr>x = a, y = b, \<dots> = m\<rparr>"} &
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      @{text "\<lparr>x :: A, y :: B, \<dots> :: M\<rparr>"} \\
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  \end{tabular}
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  \end{center}
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  \noindent The ASCII representation of @{text "\<lparr>x = a\<rparr>"} is @{text
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  "(| x = a |)"}.
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  A fixed record @{text "\<lparr>x = a, y = b\<rparr>"} has field @{text x} of value
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  @{text a} and field @{text y} of value @{text b}.  The corresponding
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  type is @{text "\<lparr>x :: A, y :: B\<rparr>"}, assuming that @{text "a :: A"}
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  and @{text "b :: B"}.
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  A record scheme like @{text "\<lparr>x = a, y = b, \<dots> = m\<rparr>"} contains fields
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  @{text x} and @{text y} as before, but also possibly further fields
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  as indicated by the ``@{text "\<dots>"}'' notation (which is actually part
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  of the syntax).  The improper field ``@{text "\<dots>"}'' of a record
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  scheme is called the \emph{more part}.  Logically it is just a free
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  variable, which is occasionally referred to as ``row variable'' in
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  the literature.  The more part of a record scheme may be
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  instantiated by zero or more further components.  For example, the
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  previous scheme may get instantiated to @{text "\<lparr>x = a, y = b, z =
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  c, \<dots> = m'\<rparr>"}, where @{text m'} refers to a different more part.
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  Fixed records are special instances of record schemes, where
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  ``@{text "\<dots>"}'' is properly terminated by the @{text "() :: unit"}
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  element.  In fact, @{text "\<lparr>x = a, y = b\<rparr>"} is just an abbreviation
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  for @{text "\<lparr>x = a, y = b, \<dots> = ()\<rparr>"}.
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  \medskip Two key observations make extensible records in a simply
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  typed language like HOL work out:
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  \begin{enumerate}
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  \item the more part is internalized, as a free term or type
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  variable,
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  \item field names are externalized, they cannot be accessed within
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  the logic as first-class values.
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  \end{enumerate}
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  \medskip In Isabelle/HOL record types have to be defined explicitly,
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  fixing their field names and types, and their (optional) parent
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  record.  Afterwards, records may be formed using above syntax, while
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  obeying the canonical order of fields as given by their declaration.
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  The record package provides several standard operations like
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  selectors and updates.  The common setup for various generic proof
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  tools enable succinct reasoning patterns.  See also the Isabelle/HOL
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  tutorial \cite{isabelle-hol-book} for further instructions on using
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  records in practice.
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*}
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subsection {* Record specifications *}
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text {*
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  \begin{matharray}{rcl}
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    @{command_def (HOL) "record"} & : & \isartrans{theory}{theory} \\
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  \end{matharray}
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  \begin{rail}
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    'record' typespec '=' (type '+')? (constdecl +)
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    ;
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  \end{rail}
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  \begin{descr}
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  \item [@{command (HOL) "record"}~@{text "(\<alpha>\<^sub>1, \<dots>, \<alpha>\<^sub>m) t
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  = \<tau> + c\<^sub>1 :: \<sigma>\<^sub>1 \<dots> c\<^sub>n :: \<sigma>\<^sub>n"}] defines
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  extensible record type @{text "(\<alpha>\<^sub>1, \<dots>, \<alpha>\<^sub>m) t"},
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  derived from the optional parent record @{text "\<tau>"} by adding new
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  field components @{text "c\<^sub>i :: \<sigma>\<^sub>i"} etc.
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  The type variables of @{text "\<tau>"} and @{text "\<sigma>\<^sub>i"} need to be
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  covered by the (distinct) parameters @{text "\<alpha>\<^sub>1, \<dots>,
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  \<alpha>\<^sub>m"}.  Type constructor @{text t} has to be new, while @{text
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  \<tau>} needs to specify an instance of an existing record type.  At
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  least one new field @{text "c\<^sub>i"} has to be specified.
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  Basically, field names need to belong to a unique record.  This is
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  not a real restriction in practice, since fields are qualified by
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  the record name internally.
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  The parent record specification @{text \<tau>} is optional; if omitted
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  @{text t} becomes a root record.  The hierarchy of all records
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  declared within a theory context forms a forest structure, i.e.\ a
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  set of trees starting with a root record each.  There is no way to
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  merge multiple parent records!
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  For convenience, @{text "(\<alpha>\<^sub>1, \<dots>, \<alpha>\<^sub>m) t"} is made a
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  type abbreviation for the fixed record type @{text "\<lparr>c\<^sub>1 ::
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  \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n\<rparr>"}, likewise is @{text
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  "(\<alpha>\<^sub>1, \<dots>, \<alpha>\<^sub>m, \<zeta>) t_scheme"} made an abbreviation for
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  @{text "\<lparr>c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n, \<dots> ::
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  \<zeta>\<rparr>"}.
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  \end{descr}
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*}
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subsection {* Record operations *}
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text {*
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  Any record definition of the form presented above produces certain
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  standard operations.  Selectors and updates are provided for any
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  field, including the improper one ``@{text more}''.  There are also
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  cumulative record constructor functions.  To simplify the
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  presentation below, we assume for now that @{text "(\<alpha>\<^sub>1, \<dots>,
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  \<alpha>\<^sub>m) t"} is a root record with fields @{text "c\<^sub>1 ::
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  \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n"}.
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  \medskip \textbf{Selectors} and \textbf{updates} are available for
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  any field (including ``@{text more}''):
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  \begin{matharray}{lll}
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    @{text "c\<^sub>i"} & @{text "::"} & @{text "\<lparr>\<^vec>c :: \<^vec>\<sigma>, \<dots> :: \<zeta>\<rparr> \<Rightarrow> \<sigma>\<^sub>i"} \\
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    @{text "c\<^sub>i_update"} & @{text "::"} & @{text "\<sigma>\<^sub>i \<Rightarrow> \<lparr>\<^vec>c :: \<^vec>\<sigma>, \<dots> :: \<zeta>\<rparr> \<Rightarrow> \<lparr>\<^vec>c :: \<^vec>\<sigma>, \<dots> :: \<zeta>\<rparr>"} \\
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  \end{matharray}
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  There is special syntax for application of updates: @{text "r\<lparr>x :=
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  a\<rparr>"} abbreviates term @{text "x_update a r"}.  Further notation for
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  repeated updates is also available: @{text "r\<lparr>x := a\<rparr>\<lparr>y := b\<rparr>\<lparr>z :=
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  c\<rparr>"} may be written @{text "r\<lparr>x := a, y := b, z := c\<rparr>"}.  Note that
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  because of postfix notation the order of fields shown here is
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  reverse than in the actual term.  Since repeated updates are just
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  function applications, fields may be freely permuted in @{text "\<lparr>x
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  := a, y := b, z := c\<rparr>"}, as far as logical equality is concerned.
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  Thus commutativity of independent updates can be proven within the
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  logic for any two fields, but not as a general theorem.
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  \medskip The \textbf{make} operation provides a cumulative record
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  constructor function:
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  \begin{matharray}{lll}
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    @{text "t.make"} & @{text "::"} & @{text "\<sigma>\<^sub>1 \<Rightarrow> \<dots> \<sigma>\<^sub>n \<Rightarrow> \<lparr>\<^vec>c :: \<^vec>\<sigma>\<rparr>"} \\
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  \end{matharray}
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  \medskip We now reconsider the case of non-root records, which are
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  derived of some parent.  In general, the latter may depend on
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  another parent as well, resulting in a list of \emph{ancestor
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  records}.  Appending the lists of fields of all ancestors results in
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  a certain field prefix.  The record package automatically takes care
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  of this by lifting operations over this context of ancestor fields.
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  Assuming that @{text "(\<alpha>\<^sub>1, \<dots>, \<alpha>\<^sub>m) t"} has ancestor
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  fields @{text "b\<^sub>1 :: \<rho>\<^sub>1, \<dots>, b\<^sub>k :: \<rho>\<^sub>k"},
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  the above record operations will get the following types:
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  \medskip
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  \begin{tabular}{lll}
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    @{text "c\<^sub>i"} & @{text "::"} & @{text "\<lparr>\<^vec>b :: \<^vec>\<rho>, \<^vec>c :: \<^vec>\<sigma>, \<dots> :: \<zeta>\<rparr> \<Rightarrow> \<sigma>\<^sub>i"} \\
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    @{text "c\<^sub>i_update"} & @{text "::"} & @{text "\<sigma>\<^sub>i \<Rightarrow> 
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      \<lparr>\<^vec>b :: \<^vec>\<rho>, \<^vec>c :: \<^vec>\<sigma>, \<dots> :: \<zeta>\<rparr> \<Rightarrow>
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      \<lparr>\<^vec>b :: \<^vec>\<rho>, \<^vec>c :: \<^vec>\<sigma>, \<dots> :: \<zeta>\<rparr>"} \\
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    @{text "t.make"} & @{text "::"} & @{text "\<rho>\<^sub>1 \<Rightarrow> \<dots> \<rho>\<^sub>k \<Rightarrow> \<sigma>\<^sub>1 \<Rightarrow> \<dots> \<sigma>\<^sub>n \<Rightarrow>
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      \<lparr>\<^vec>b :: \<^vec>\<rho>, \<^vec>c :: \<^vec>\<sigma>\<rparr>"} \\
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  \end{tabular}
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  \medskip
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  \noindent Some further operations address the extension aspect of a
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  derived record scheme specifically: @{text "t.fields"} produces a
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  record fragment consisting of exactly the new fields introduced here
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  (the result may serve as a more part elsewhere); @{text "t.extend"}
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  takes a fixed record and adds a given more part; @{text
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  "t.truncate"} restricts a record scheme to a fixed record.
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  \medskip
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  \begin{tabular}{lll}
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    @{text "t.fields"} & @{text "::"} & @{text "\<sigma>\<^sub>1 \<Rightarrow> \<dots> \<sigma>\<^sub>n \<Rightarrow> \<lparr>\<^vec>c :: \<^vec>\<sigma>\<rparr>"} \\
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    @{text "t.extend"} & @{text "::"} & @{text "\<lparr>\<^vec>b :: \<^vec>\<rho>, \<^vec>c :: \<^vec>\<sigma>\<rparr> \<Rightarrow>
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      \<zeta> \<Rightarrow> \<lparr>\<^vec>b :: \<^vec>\<rho>, \<^vec>c :: \<^vec>\<sigma>, \<dots> :: \<zeta>\<rparr>"} \\
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    @{text "t.truncate"} & @{text "::"} & @{text "\<lparr>\<^vec>b :: \<^vec>\<rho>, \<^vec>c :: \<^vec>\<sigma>, \<dots> :: \<zeta>\<rparr> \<Rightarrow> \<lparr>\<^vec>b :: \<^vec>\<rho>, \<^vec>c :: \<^vec>\<sigma>\<rparr>"} \\
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  \end{tabular}
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  \medskip
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  \noindent Note that @{text "t.make"} and @{text "t.fields"} coincide
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  for root records.
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*}
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subsection {* Derived rules and proof tools *}
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text {*
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  The record package proves several results internally, declaring
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  these facts to appropriate proof tools.  This enables users to
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  reason about record structures quite conveniently.  Assume that
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  @{text t} is a record type as specified above.
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  \begin{enumerate}
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   319
  
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  \item Standard conversions for selectors or updates applied to
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diff changeset
   321
  record constructor terms are made part of the default Simplifier
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diff changeset
   322
  context; thus proofs by reduction of basic operations merely require
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   323
  the @{method simp} method without further arguments.  These rules
df50bc1249d7 converted HOL specific elements;
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   324
  are available as @{text "t.simps"}, too.
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   325
  
df50bc1249d7 converted HOL specific elements;
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diff changeset
   326
  \item Selectors applied to updated records are automatically reduced
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diff changeset
   327
  by an internal simplification procedure, which is also part of the
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   328
  standard Simplifier setup.
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diff changeset
   329
df50bc1249d7 converted HOL specific elements;
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   330
  \item Inject equations of a form analogous to @{prop "(x, y) = (x',
df50bc1249d7 converted HOL specific elements;
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parents: 26840
diff changeset
   331
  y') \<equiv> x = x' \<and> y = y'"} are declared to the Simplifier and Classical
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parents: 26840
diff changeset
   332
  Reasoner as @{attribute iff} rules.  These rules are available as
df50bc1249d7 converted HOL specific elements;
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parents: 26840
diff changeset
   333
  @{text "t.iffs"}.
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diff changeset
   334
df50bc1249d7 converted HOL specific elements;
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diff changeset
   335
  \item The introduction rule for record equality analogous to @{text
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diff changeset
   336
  "x r = x r' \<Longrightarrow> y r = y r' \<dots> \<Longrightarrow> r = r'"} is declared to the Simplifier,
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   337
  and as the basic rule context as ``@{attribute intro}@{text "?"}''.
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diff changeset
   338
  The rule is called @{text "t.equality"}.
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   339
df50bc1249d7 converted HOL specific elements;
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diff changeset
   340
  \item Representations of arbitrary record expressions as canonical
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diff changeset
   341
  constructor terms are provided both in @{method cases} and @{method
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parents: 26840
diff changeset
   342
  induct} format (cf.\ the generic proof methods of the same name,
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parents: 26840
diff changeset
   343
  \secref{sec:cases-induct}).  Several variations are available, for
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parents: 26840
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   344
  fixed records, record schemes, more parts etc.
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   345
  
df50bc1249d7 converted HOL specific elements;
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   346
  The generic proof methods are sufficiently smart to pick the most
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diff changeset
   347
  sensible rule according to the type of the indicated record
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diff changeset
   348
  expression: users just need to apply something like ``@{text "(cases
df50bc1249d7 converted HOL specific elements;
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parents: 26840
diff changeset
   349
  r)"}'' to a certain proof problem.
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   350
df50bc1249d7 converted HOL specific elements;
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   351
  \item The derived record operations @{text "t.make"}, @{text
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diff changeset
   352
  "t.fields"}, @{text "t.extend"}, @{text "t.truncate"} are \emph{not}
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   353
  treated automatically, but usually need to be expanded by hand,
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   354
  using the collective fact @{text "t.defs"}.
df50bc1249d7 converted HOL specific elements;
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   355
df50bc1249d7 converted HOL specific elements;
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   356
  \end{enumerate}
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   357
*}
df50bc1249d7 converted HOL specific elements;
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   358
df50bc1249d7 converted HOL specific elements;
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parents: 26840
diff changeset
   359
df50bc1249d7 converted HOL specific elements;
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diff changeset
   360
section {* Datatypes \label{sec:hol-datatype} *}
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   361
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parents: 26840
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   362
text {*
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parents: 26840
diff changeset
   363
  \begin{matharray}{rcl}
df50bc1249d7 converted HOL specific elements;
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diff changeset
   364
    @{command_def (HOL) "datatype"} & : & \isartrans{theory}{theory} \\
27452
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   365
  @{command_def (HOL) "rep_datatype"} & : & \isartrans{theory}{proof} \\
26849
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diff changeset
   366
  \end{matharray}
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parents: 26840
diff changeset
   367
df50bc1249d7 converted HOL specific elements;
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parents: 26840
diff changeset
   368
  \begin{rail}
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parents: 26840
diff changeset
   369
    'datatype' (dtspec + 'and')
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diff changeset
   370
    ;
27452
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diff changeset
   371
    'rep\_datatype' ('(' (name +) ')')? (term +)
26849
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   372
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
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   373
df50bc1249d7 converted HOL specific elements;
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   374
    dtspec: parname? typespec infix? '=' (cons + '|')
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diff changeset
   375
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   376
    cons: name (type *) mixfix?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   377
  \end{rail}
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parents: 26840
diff changeset
   378
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   379
  \begin{descr}
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parents: 26840
diff changeset
   380
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   381
  \item [@{command (HOL) "datatype"}] defines inductive datatypes in
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   382
  HOL.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   383
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   384
  \item [@{command (HOL) "rep_datatype"}] represents existing types as
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   385
  inductive ones, generating the standard infrastructure of derived
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   386
  concepts (primitive recursion etc.).
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   387
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   388
  \end{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   389
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   390
  The induction and exhaustion theorems generated provide case names
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   391
  according to the constructors involved, while parameters are named
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   392
  after the types (see also \secref{sec:cases-induct}).
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   393
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   394
  See \cite{isabelle-HOL} for more details on datatypes, but beware of
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   395
  the old-style theory syntax being used there!  Apart from proper
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   396
  proof methods for case-analysis and induction, there are also
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   397
  emulations of ML tactics @{method (HOL) case_tac} and @{method (HOL)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   398
  induct_tac} available, see \secref{sec:hol-induct-tac}; these admit
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   399
  to refer directly to the internal structure of subgoals (including
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   400
  internally bound parameters).
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   401
*}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   402
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   403
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   404
section {* Recursive functions \label{sec:recursion} *}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   405
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   406
text {*
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   407
  \begin{matharray}{rcl}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   408
    @{command_def (HOL) "primrec"} & : & \isarkeep{local{\dsh}theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   409
    @{command_def (HOL) "fun"} & : & \isarkeep{local{\dsh}theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   410
    @{command_def (HOL) "function"} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   411
    @{command_def (HOL) "termination"} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   412
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   413
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   414
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   415
    'primrec' target? fixes 'where' equations
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   416
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   417
    equations: (thmdecl? prop + '|')
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   418
    ;
26985
51c5acd57b75 function: uniform treatment of target, not as config;
wenzelm
parents: 26894
diff changeset
   419
    ('fun' | 'function') target? functionopts? fixes 'where' clauses
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   420
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   421
    clauses: (thmdecl? prop ('(' 'otherwise' ')')? + '|')
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   422
    ;
26985
51c5acd57b75 function: uniform treatment of target, not as config;
wenzelm
parents: 26894
diff changeset
   423
    functionopts: '(' (('sequential' | 'domintros' | 'tailrec' | 'default' term) + ',') ')'
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   424
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   425
    'termination' ( term )?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   426
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   427
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   428
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   429
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   430
  \item [@{command (HOL) "primrec"}] defines primitive recursive
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   431
  functions over datatypes, see also \cite{isabelle-HOL}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   432
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   433
  \item [@{command (HOL) "function"}] defines functions by general
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   434
  wellfounded recursion. A detailed description with examples can be
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   435
  found in \cite{isabelle-function}. The function is specified by a
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   436
  set of (possibly conditional) recursive equations with arbitrary
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   437
  pattern matching. The command generates proof obligations for the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   438
  completeness and the compatibility of patterns.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   439
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   440
  The defined function is considered partial, and the resulting
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   441
  simplification rules (named @{text "f.psimps"}) and induction rule
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   442
  (named @{text "f.pinduct"}) are guarded by a generated domain
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   443
  predicate @{text "f_dom"}. The @{command (HOL) "termination"}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   444
  command can then be used to establish that the function is total.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   445
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   446
  \item [@{command (HOL) "fun"}] is a shorthand notation for
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   447
  ``@{command (HOL) "function"}~@{text "(sequential)"}, followed by
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   448
  automated proof attempts regarding pattern matching and termination.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   449
  See \cite{isabelle-function} for further details.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   450
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   451
  \item [@{command (HOL) "termination"}~@{text f}] commences a
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   452
  termination proof for the previously defined function @{text f}.  If
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   453
  this is omitted, the command refers to the most recent function
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   454
  definition.  After the proof is closed, the recursive equations and
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   455
  the induction principle is established.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   456
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   457
  \end{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   458
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   459
  %FIXME check
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   460
27452
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27123
diff changeset
   461
  Recursive definitions introduced by the @{command (HOL) "function"}
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27123
diff changeset
   462
  command accommodate
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   463
  reasoning by induction (cf.\ \secref{sec:cases-induct}): rule @{text
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   464
  "c.induct"} (where @{text c} is the name of the function definition)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   465
  refers to a specific induction rule, with parameters named according
27452
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27123
diff changeset
   466
  to the user-specified equations.
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27123
diff changeset
   467
  For the @{command (HOL) "primrec"} the induction principle coincides
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27123
diff changeset
   468
  with structural recursion on the datatype the recursion is carried
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27123
diff changeset
   469
  out.
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27123
diff changeset
   470
  Case names of @{command (HOL)
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   471
  "primrec"} are that of the datatypes involved, while those of
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   472
  @{command (HOL) "function"} are numbered (starting from 1).
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   473
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   474
  The equations provided by these packages may be referred later as
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   475
  theorem list @{text "f.simps"}, where @{text f} is the (collective)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   476
  name of the functions defined.  Individual equations may be named
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   477
  explicitly as well.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   478
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   479
  The @{command (HOL) "function"} command accepts the following
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   480
  options.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   481
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   482
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   483
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   484
  \item [@{text sequential}] enables a preprocessor which
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   485
  disambiguates overlapping patterns by making them mutually disjoint.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   486
  Earlier equations take precedence over later ones.  This allows to
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   487
  give the specification in a format very similar to functional
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   488
  programming.  Note that the resulting simplification and induction
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   489
  rules correspond to the transformed specification, not the one given
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   490
  originally. This usually means that each equation given by the user
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   491
  may result in several theroems.  Also note that this automatic
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   492
  transformation only works for ML-style datatype patterns.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   493
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   494
  \item [@{text domintros}] enables the automated generation of
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   495
  introduction rules for the domain predicate. While mostly not
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   496
  needed, they can be helpful in some proofs about partial functions.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   497
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   498
  \item [@{text tailrec}] generates the unconstrained recursive
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   499
  equations even without a termination proof, provided that the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   500
  function is tail-recursive. This currently only works
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   501
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   502
  \item [@{text "default d"}] allows to specify a default value for a
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   503
  (partial) function, which will ensure that @{text "f x = d x"}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   504
  whenever @{text "x \<notin> f_dom"}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   505
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   506
  \end{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   507
*}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   508
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   509
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   510
subsection {* Proof methods related to recursive definitions *}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   511
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   512
text {*
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   513
  \begin{matharray}{rcl}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   514
    @{method_def (HOL) pat_completeness} & : & \isarmeth \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   515
    @{method_def (HOL) relation} & : & \isarmeth \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   516
    @{method_def (HOL) lexicographic_order} & : & \isarmeth \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   517
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   518
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   519
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   520
    'relation' term
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   521
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   522
    'lexicographic\_order' (clasimpmod *)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   523
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   524
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   525
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   526
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   527
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   528
  \item [@{method (HOL) pat_completeness}] is a specialized method to
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   529
  solve goals regarding the completeness of pattern matching, as
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   530
  required by the @{command (HOL) "function"} package (cf.\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   531
  \cite{isabelle-function}).
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   532
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   533
  \item [@{method (HOL) relation}~@{text R}] introduces a termination
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   534
  proof using the relation @{text R}.  The resulting proof state will
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   535
  contain goals expressing that @{text R} is wellfounded, and that the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   536
  arguments of recursive calls decrease with respect to @{text R}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   537
  Usually, this method is used as the initial proof step of manual
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   538
  termination proofs.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   539
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   540
  \item [@{method (HOL) "lexicographic_order"}] attempts a fully
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   541
  automated termination proof by searching for a lexicographic
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   542
  combination of size measures on the arguments of the function. The
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   543
  method accepts the same arguments as the @{method auto} method,
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   544
  which it uses internally to prove local descents.  The same context
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   545
  modifiers as for @{method auto} are accepted, see
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   546
  \secref{sec:clasimp}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   547
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   548
  In case of failure, extensive information is printed, which can help
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   549
  to analyse the situation (cf.\ \cite{isabelle-function}).
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   550
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   551
  \end{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   552
*}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   553
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   554
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   555
subsection {* Old-style recursive function definitions (TFL) *}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   556
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   557
text {*
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   558
  The old TFL commands @{command (HOL) "recdef"} and @{command (HOL)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   559
  "recdef_tc"} for defining recursive are mostly obsolete; @{command
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   560
  (HOL) "function"} or @{command (HOL) "fun"} should be used instead.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   561
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   562
  \begin{matharray}{rcl}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   563
    @{command_def (HOL) "recdef"} & : & \isartrans{theory}{theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   564
    @{command_def (HOL) "recdef_tc"}@{text "\<^sup>*"} & : & \isartrans{theory}{proof(prove)} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   565
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   566
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   567
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   568
    'recdef' ('(' 'permissive' ')')? \\ name term (prop +) hints?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   569
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   570
    recdeftc thmdecl? tc
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   571
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   572
    hints: '(' 'hints' (recdefmod *) ')'
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   573
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   574
    recdefmod: (('recdef\_simp' | 'recdef\_cong' | 'recdef\_wf') (() | 'add' | 'del') ':' thmrefs) | clasimpmod
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   575
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   576
    tc: nameref ('(' nat ')')?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   577
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   578
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   579
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   580
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   581
  
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   582
  \item [@{command (HOL) "recdef"}] defines general well-founded
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   583
  recursive functions (using the TFL package), see also
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   584
  \cite{isabelle-HOL}.  The ``@{text "(permissive)"}'' option tells
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   585
  TFL to recover from failed proof attempts, returning unfinished
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   586
  results.  The @{text recdef_simp}, @{text recdef_cong}, and @{text
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   587
  recdef_wf} hints refer to auxiliary rules to be used in the internal
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   588
  automated proof process of TFL.  Additional @{syntax clasimpmod}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   589
  declarations (cf.\ \secref{sec:clasimp}) may be given to tune the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   590
  context of the Simplifier (cf.\ \secref{sec:simplifier}) and
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   591
  Classical reasoner (cf.\ \secref{sec:classical}).
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   592
  
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   593
  \item [@{command (HOL) "recdef_tc"}~@{text "c (i)"}] recommences the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   594
  proof for leftover termination condition number @{text i} (default
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   595
  1) as generated by a @{command (HOL) "recdef"} definition of
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   596
  constant @{text c}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   597
  
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   598
  Note that in most cases, @{command (HOL) "recdef"} is able to finish
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   599
  its internal proofs without manual intervention.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   600
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   601
  \end{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   602
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   603
  \medskip Hints for @{command (HOL) "recdef"} may be also declared
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   604
  globally, using the following attributes.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   605
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   606
  \begin{matharray}{rcl}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   607
    @{attribute_def (HOL) recdef_simp} & : & \isaratt \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   608
    @{attribute_def (HOL) recdef_cong} & : & \isaratt \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   609
    @{attribute_def (HOL) recdef_wf} & : & \isaratt \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   610
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   611
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   612
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   613
    ('recdef\_simp' | 'recdef\_cong' | 'recdef\_wf') (() | 'add' | 'del')
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   614
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   615
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   616
*}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   617
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   618
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   619
section {* Inductive and coinductive definitions \label{sec:hol-inductive} *}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   620
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   621
text {*
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   622
  An \textbf{inductive definition} specifies the least predicate (or
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   623
  set) @{text R} closed under given rules: applying a rule to elements
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   624
  of @{text R} yields a result within @{text R}.  For example, a
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   625
  structural operational semantics is an inductive definition of an
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   626
  evaluation relation.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   627
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   628
  Dually, a \textbf{coinductive definition} specifies the greatest
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   629
  predicate~/ set @{text R} that is consistent with given rules: every
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   630
  element of @{text R} can be seen as arising by applying a rule to
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   631
  elements of @{text R}.  An important example is using bisimulation
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   632
  relations to formalise equivalence of processes and infinite data
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   633
  structures.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   634
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   635
  \medskip The HOL package is related to the ZF one, which is
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   636
  described in a separate paper,\footnote{It appeared in CADE
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   637
  \cite{paulson-CADE}; a longer version is distributed with Isabelle.}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   638
  which you should refer to in case of difficulties.  The package is
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   639
  simpler than that of ZF thanks to implicit type-checking in HOL.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   640
  The types of the (co)inductive predicates (or sets) determine the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   641
  domain of the fixedpoint definition, and the package does not have
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   642
  to use inference rules for type-checking.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   643
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   644
  \begin{matharray}{rcl}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   645
    @{command_def (HOL) "inductive"} & : & \isarkeep{local{\dsh}theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   646
    @{command_def (HOL) "inductive_set"} & : & \isarkeep{local{\dsh}theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   647
    @{command_def (HOL) "coinductive"} & : & \isarkeep{local{\dsh}theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   648
    @{command_def (HOL) "coinductive_set"} & : & \isarkeep{local{\dsh}theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   649
    @{attribute_def (HOL) mono} & : & \isaratt \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   650
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   651
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   652
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   653
    ('inductive' | 'inductive\_set' | 'coinductive' | 'coinductive\_set') target? fixes ('for' fixes)? \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   654
    ('where' clauses)? ('monos' thmrefs)?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   655
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   656
    clauses: (thmdecl? prop + '|')
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   657
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   658
    'mono' (() | 'add' | 'del')
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   659
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   660
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   661
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   662
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   663
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   664
  \item [@{command (HOL) "inductive"} and @{command (HOL)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   665
  "coinductive"}] define (co)inductive predicates from the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   666
  introduction rules given in the @{keyword "where"} part.  The
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   667
  optional @{keyword "for"} part contains a list of parameters of the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   668
  (co)inductive predicates that remain fixed throughout the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   669
  definition.  The optional @{keyword "monos"} section contains
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   670
  \emph{monotonicity theorems}, which are required for each operator
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   671
  applied to a recursive set in the introduction rules.  There
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   672
  \emph{must} be a theorem of the form @{text "A \<le> B \<Longrightarrow> M A \<le> M B"},
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   673
  for each premise @{text "M R\<^sub>i t"} in an introduction rule!
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   674
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   675
  \item [@{command (HOL) "inductive_set"} and @{command (HOL)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   676
  "coinductive_set"}] are wrappers for to the previous commands,
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   677
  allowing the definition of (co)inductive sets.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   678
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   679
  \item [@{attribute (HOL) mono}] declares monotonicity rules.  These
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   680
  rule are involved in the automated monotonicity proof of @{command
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   681
  (HOL) "inductive"}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   682
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   683
  \end{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   684
*}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   685
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   686
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   687
subsection {* Derived rules *}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   688
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   689
text {*
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   690
  Each (co)inductive definition @{text R} adds definitions to the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   691
  theory and also proves some theorems:
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   692
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   693
  \begin{description}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   694
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   695
  \item [@{text R.intros}] is the list of introduction rules as proven
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   696
  theorems, for the recursive predicates (or sets).  The rules are
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   697
  also available individually, using the names given them in the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   698
  theory file;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   699
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   700
  \item [@{text R.cases}] is the case analysis (or elimination) rule;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   701
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   702
  \item [@{text R.induct} or @{text R.coinduct}] is the (co)induction
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   703
  rule.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   704
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   705
  \end{description}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   706
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   707
  When several predicates @{text "R\<^sub>1, \<dots>, R\<^sub>n"} are
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   708
  defined simultaneously, the list of introduction rules is called
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   709
  @{text "R\<^sub>1_\<dots>_R\<^sub>n.intros"}, the case analysis rules are
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   710
  called @{text "R\<^sub>1.cases, \<dots>, R\<^sub>n.cases"}, and the list
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   711
  of mutual induction rules is called @{text
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   712
  "R\<^sub>1_\<dots>_R\<^sub>n.inducts"}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   713
*}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   714
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   715
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   716
subsection {* Monotonicity theorems *}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   717
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   718
text {*
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   719
  Each theory contains a default set of theorems that are used in
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   720
  monotonicity proofs.  New rules can be added to this set via the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   721
  @{attribute (HOL) mono} attribute.  The HOL theory @{text Inductive}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   722
  shows how this is done.  In general, the following monotonicity
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   723
  theorems may be added:
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   724
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   725
  \begin{itemize}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   726
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   727
  \item Theorems of the form @{text "A \<le> B \<Longrightarrow> M A \<le> M B"}, for proving
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   728
  monotonicity of inductive definitions whose introduction rules have
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   729
  premises involving terms such as @{text "M R\<^sub>i t"}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   730
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   731
  \item Monotonicity theorems for logical operators, which are of the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   732
  general form @{text "(\<dots> \<longrightarrow> \<dots>) \<Longrightarrow> \<dots> (\<dots> \<longrightarrow> \<dots>) \<Longrightarrow> \<dots> \<longrightarrow> \<dots>"}.  For example, in
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   733
  the case of the operator @{text "\<or>"}, the corresponding theorem is
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   734
  \[
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   735
  \infer{@{text "P\<^sub>1 \<or> P\<^sub>2 \<longrightarrow> Q\<^sub>1 \<or> Q\<^sub>2"}}{@{text "P\<^sub>1 \<longrightarrow> Q\<^sub>1"} & @{text "P\<^sub>2 \<longrightarrow> Q\<^sub>2"}}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   736
  \]
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   737
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   738
  \item De Morgan style equations for reasoning about the ``polarity''
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   739
  of expressions, e.g.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   740
  \[
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   741
  @{prop "\<not> \<not> P \<longleftrightarrow> P"} \qquad\qquad
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   742
  @{prop "\<not> (P \<and> Q) \<longleftrightarrow> \<not> P \<or> \<not> Q"}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   743
  \]
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   744
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   745
  \item Equations for reducing complex operators to more primitive
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   746
  ones whose monotonicity can easily be proved, e.g.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   747
  \[
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   748
  @{prop "(P \<longrightarrow> Q) \<longleftrightarrow> \<not> P \<or> Q"} \qquad\qquad
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   749
  @{prop "Ball A P \<equiv> \<forall>x. x \<in> A \<longrightarrow> P x"}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   750
  \]
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   751
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   752
  \end{itemize}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   753
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   754
  %FIXME: Example of an inductive definition
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   755
*}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   756
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   757
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   758
section {* Arithmetic proof support *}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   759
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   760
text {*
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   761
  \begin{matharray}{rcl}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   762
    @{method_def (HOL) arith} & : & \isarmeth \\
26894
1120f6cc10b0 proper checking of various Isar elements;
wenzelm
parents: 26860
diff changeset
   763
    @{attribute_def (HOL) arith_split} & : & \isaratt \\
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   764
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   765
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   766
  The @{method (HOL) arith} method decides linear arithmetic problems
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   767
  (on types @{text nat}, @{text int}, @{text real}).  Any current
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   768
  facts are inserted into the goal before running the procedure.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   769
26894
1120f6cc10b0 proper checking of various Isar elements;
wenzelm
parents: 26860
diff changeset
   770
  The @{attribute (HOL) arith_split} attribute declares case split
1120f6cc10b0 proper checking of various Isar elements;
wenzelm
parents: 26860
diff changeset
   771
  rules to be expanded before the arithmetic procedure is invoked.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   772
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   773
  Note that a simpler (but faster) version of arithmetic reasoning is
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   774
  already performed by the Simplifier.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   775
*}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   776
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   777
28603
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   778
section {* Invoking automated reasoning tools -- The Sledgehammer *}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   779
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   780
text {*
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   781
  Isabelle/HOL includes a generic \emph{ATP manager} that allows
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   782
  external automated reasoning tools to crunch a pending goal.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   783
  Supported provers include E\footnote{\url{http://www.eprover.org}},
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   784
  SPASS\footnote{\url{http://www.spass-prover.org/}}, and Vampire.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   785
  There is also a wrapper to invoke provers remotely via the
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   786
  SystemOnTPTP\footnote{\url{http://www.cs.miami.edu/~tptp/cgi-bin/SystemOnTPTP}}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   787
  web service.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   788
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   789
  The problem passed to external provers consists of the goal together
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   790
  with a smart selection of lemmas from the current theory context.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   791
  The result of a successful proof search is some source text that
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   792
  usually reconstructs the proof within Isabelle, without requiring
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   793
  external provers again.  The Metis
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   794
  prover\footnote{\url{http://www.gilith.com/software/metis/}} that is
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   795
  integrated into Isabelle/HOL is being used here.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   796
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   797
  In this mode of operation, heavy means of automated reasoning are
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   798
  used as a strong relevance filter, while the main proof checking
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   799
  works via explicit inferences going through the Isabelle kernel.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   800
  Moreover, rechecking Isabelle proof texts with already specified
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   801
  auxiliary facts is much faster than performing fully automated
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   802
  search over and over again.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   803
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   804
  \begin{matharray}{rcl}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   805
    @{command_def (HOL) "sledgehammer"}@{text "\<^sup>*"} & : & \isarkeep{proof} \\
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   806
    @{command_def (HOL) "print_atps"}@{text "\<^sup>*"} & : & \isarkeep{theory~|~proof} \\
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   807
    @{command_def (HOL) "atp_info"}@{text "\<^sup>*"} & : & \isarkeep{\cdot} \\
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   808
    @{command_def (HOL) "atp_kill"}@{text "\<^sup>*"} & : & \isarkeep{\cdot} \\
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   809
    @{method_def (HOL) metis} & : & \isarmeth \\
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   810
  \end{matharray}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   811
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   812
  \begin{rail}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   813
  'sledgehammer' (nameref *)
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   814
  ;
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   815
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   816
  'metis' thmrefs
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   817
  ;
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   818
  \end{rail}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   819
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   820
  \begin{descr}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   821
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   822
  \item [@{command (HOL) sledgehammer}~@{text "prover\<^sub>1 \<dots>
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   823
  prover\<^sub>n"}] invokes the specified automated theorem provers on
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   824
  the first subgoal.  Provers are run in parallel, the first
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   825
  successful result is displayed, and the other attempts are
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   826
  terminated.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   827
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   828
  Provers are defined in the theory context, see also @{command (HOL)
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   829
  print_atps}.  If no provers are given as arguments to @{command
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   830
  (HOL) sledgehammer}, the system refers to the default defined as
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   831
  ``ATP provers'' preference by the user interface.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   832
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   833
  There are additional preferences for timeout (default: 60 seconds),
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   834
  and the maximum number of independent prover processes (default: 5);
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   835
  excessive provers are automatically terminated.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   836
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   837
  \item [@{command (HOL) print_atps}] prints the list of automated
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   838
  theorem provers available to the @{command (HOL) sledgehammer}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   839
  command.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   840
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   841
  \item [@{command (HOL) atp_info}] prints information about presently
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   842
  running provers, including elapsed runtime, and the remaining time
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   843
  until timeout.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   844
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   845
  \item [@{command (HOL) atp_kill}] terminates all presently running
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   846
  provers.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   847
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   848
  \item [@{method (HOL) metis}~@{text "facts"}] invokes the Metis
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   849
  prover with the given facts.  Metis is an automated proof tool of
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   850
  medium strength, but is fully integrated into Isabelle/HOL, with
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   851
  explicit inferences going through the kernel.  Thus its results are
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   852
  guaranteed to be ``correct by construction''.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   853
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   854
  Note that all facts used with Metis need to be specified as explicit
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   855
  arguments.  There are no rule declarations as for other Isabelle
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   856
  provers, like @{method blast} or @{method fast}.
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   857
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   858
  \end{descr}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   859
*}
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   860
b40800eef8a7 added sledgehammer etc.;
wenzelm
parents: 28562
diff changeset
   861
27123
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   862
section {* Unstructured cases analysis and induction \label{sec:hol-induct-tac} *}
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   863
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   864
text {*
27123
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   865
  The following tools of Isabelle/HOL support cases analysis and
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   866
  induction in unstructured tactic scripts; see also
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   867
  \secref{sec:cases-induct} for proper Isar versions of similar ideas.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   868
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   869
  \begin{matharray}{rcl}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   870
    @{method_def (HOL) case_tac}@{text "\<^sup>*"} & : & \isarmeth \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   871
    @{method_def (HOL) induct_tac}@{text "\<^sup>*"} & : & \isarmeth \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   872
    @{method_def (HOL) ind_cases}@{text "\<^sup>*"} & : & \isarmeth \\
27123
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   873
    @{command_def (HOL) "inductive_cases"}@{text "\<^sup>*"} & : & \isartrans{theory}{theory} \\
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   874
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   875
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   876
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   877
    'case\_tac' goalspec? term rule?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   878
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   879
    'induct\_tac' goalspec? (insts * 'and') rule?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   880
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   881
    'ind\_cases' (prop +) ('for' (name +)) ?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   882
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   883
    'inductive\_cases' (thmdecl? (prop +) + 'and')
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   884
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   885
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   886
    rule: ('rule' ':' thmref)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   887
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   888
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   889
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   890
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   891
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   892
  \item [@{method (HOL) case_tac} and @{method (HOL) induct_tac}]
27123
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   893
  admit to reason about inductive types.  Rules are selected according
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   894
  to the declarations by the @{attribute cases} and @{attribute
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   895
  induct} attributes, cf.\ \secref{sec:cases-induct}.  The @{command
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   896
  (HOL) datatype} package already takes care of this.
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   897
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   898
  These unstructured tactics feature both goal addressing and dynamic
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   899
  instantiation.  Note that named rule cases are \emph{not} provided
27123
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   900
  as would be by the proper @{method cases} and @{method induct} proof
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   901
  methods (see \secref{sec:cases-induct}).  Unlike the @{method
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   902
  induct} method, @{method induct_tac} does not handle structured rule
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   903
  statements, only the compact object-logic conclusion of the subgoal
11fcdd5897dd case_tac/induct_tac: use same declarations as cases/induct;
wenzelm
parents: 27103
diff changeset
   904
  being addressed.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   905
  
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   906
  \item [@{method (HOL) ind_cases} and @{command (HOL)
26860
7c749112261c replaced some latex macros by antiquotations;
wenzelm
parents: 26852
diff changeset
   907
  "inductive_cases"}] provide an interface to the internal @{ML_text
7c749112261c replaced some latex macros by antiquotations;
wenzelm
parents: 26852
diff changeset
   908
  mk_cases} operation.  Rules are simplified in an unrestricted
7c749112261c replaced some latex macros by antiquotations;
wenzelm
parents: 26852
diff changeset
   909
  forward manner.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   910
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   911
  While @{method (HOL) ind_cases} is a proof method to apply the
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   912
  result immediately as elimination rules, @{command (HOL)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   913
  "inductive_cases"} provides case split theorems at the theory level
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   914
  for later use.  The @{keyword "for"} argument of the @{method (HOL)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   915
  ind_cases} method allows to specify a list of variables that should
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   916
  be generalized before applying the resulting rule.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   917
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   918
  \end{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   919
*}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   920
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   921
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   922
section {* Executable code *}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   923
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   924
text {*
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   925
  Isabelle/Pure provides two generic frameworks to support code
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   926
  generation from executable specifications.  Isabelle/HOL
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   927
  instantiates these mechanisms in a way that is amenable to end-user
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   928
  applications.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   929
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   930
  One framework generates code from both functional and relational
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   931
  programs to SML.  See \cite{isabelle-HOL} for further information
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   932
  (this actually covers the new-style theory format as well).
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   933
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   934
  \begin{matharray}{rcl}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   935
    @{command_def (HOL) "value"}@{text "\<^sup>*"} & : & \isarkeep{theory~|~proof} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   936
    @{command_def (HOL) "code_module"} & : & \isartrans{theory}{theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   937
    @{command_def (HOL) "code_library"} & : & \isartrans{theory}{theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   938
    @{command_def (HOL) "consts_code"} & : & \isartrans{theory}{theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   939
    @{command_def (HOL) "types_code"} & : & \isartrans{theory}{theory} \\  
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   940
    @{attribute_def (HOL) code} & : & \isaratt \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   941
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   942
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   943
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   944
  'value' term
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   945
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   946
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   947
  ( 'code\_module' | 'code\_library' ) modespec ? name ? \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   948
    ( 'file' name ) ? ( 'imports' ( name + ) ) ? \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   949
    'contains' ( ( name '=' term ) + | term + )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   950
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   951
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   952
  modespec: '(' ( name * ) ')'
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   953
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   954
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   955
  'consts\_code' (codespec +)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   956
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   957
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   958
  codespec: const template attachment ?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   959
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   960
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   961
  'types\_code' (tycodespec +)
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   962
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   963
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   964
  tycodespec: name template attachment ?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   965
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   966
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   967
  const: term
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   968
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   969
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   970
  template: '(' string ')'
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   971
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   972
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   973
  attachment: 'attach' modespec ? verblbrace text verbrbrace
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   974
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   975
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   976
  'code' (name)?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   977
  ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   978
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   979
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   980
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   981
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   982
  \item [@{command (HOL) "value"}~@{text t}] evaluates and prints a
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   983
  term using the code generator.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   984
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   985
  \end{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   986
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   987
  \medskip The other framework generates code from functional programs
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   988
  (including overloading using type classes) to SML \cite{SML}, OCaml
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   989
  \cite{OCaml} and Haskell \cite{haskell-revised-report}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   990
  Conceptually, code generation is split up in three steps:
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   991
  \emph{selection} of code theorems, \emph{translation} into an
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   992
  abstract executable view and \emph{serialization} to a specific
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   993
  \emph{target language}.  See \cite{isabelle-codegen} for an
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   994
  introduction on how to use it.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   995
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   996
  \begin{matharray}{rcl}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   997
    @{command_def (HOL) "export_code"}@{text "\<^sup>*"} & : & \isarkeep{theory~|~proof} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   998
    @{command_def (HOL) "code_thms"}@{text "\<^sup>*"} & : & \isarkeep{theory~|~proof} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
   999
    @{command_def (HOL) "code_deps"}@{text "\<^sup>*"} & : & \isarkeep{theory~|~proof} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1000
    @{command_def (HOL) "code_datatype"} & : & \isartrans{theory}{theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1001
    @{command_def (HOL) "code_const"} & : & \isartrans{theory}{theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1002
    @{command_def (HOL) "code_type"} & : & \isartrans{theory}{theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1003
    @{command_def (HOL) "code_class"} & : & \isartrans{theory}{theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1004
    @{command_def (HOL) "code_instance"} & : & \isartrans{theory}{theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1005
    @{command_def (HOL) "code_monad"} & : & \isartrans{theory}{theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1006
    @{command_def (HOL) "code_reserved"} & : & \isartrans{theory}{theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1007
    @{command_def (HOL) "code_include"} & : & \isartrans{theory}{theory} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1008
    @{command_def (HOL) "code_modulename"} & : & \isartrans{theory}{theory} \\
27103
d8549f4d900b major refactorings in code generator modules
haftmann
parents: 27045
diff changeset
  1009
    @{command_def (HOL) "code_abort"} & : & \isartrans{theory}{theory} \\
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1010
    @{command_def (HOL) "print_codesetup"}@{text "\<^sup>*"} & : & \isarkeep{theory~|~proof} \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1011
    @{attribute_def (HOL) code} & : & \isaratt \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1012
  \end{matharray}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1013
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1014
  \begin{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1015
    'export\_code' ( constexpr + ) ? \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1016
      ( ( 'in' target ( 'module\_name' string ) ? \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1017
        ( 'file' ( string | '-' ) ) ? ( '(' args ')' ) ?) + ) ?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1018
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1019
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1020
    'code\_thms' ( constexpr + ) ?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1021
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1022
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1023
    'code\_deps' ( constexpr + ) ?
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1024
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1025
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1026
    const: term
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1027
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1028
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1029
    constexpr: ( const | 'name.*' | '*' )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1030
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1031
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1032
    typeconstructor: nameref
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1033
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1034
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1035
    class: nameref
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1036
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1037
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1038
    target: 'OCaml' | 'SML' | 'Haskell'
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1039
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1040
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1041
    'code\_datatype' const +
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1042
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1043
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1044
    'code\_const' (const + 'and') \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1045
      ( ( '(' target ( syntax ? + 'and' ) ')' ) + )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1046
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1047
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1048
    'code\_type' (typeconstructor + 'and') \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1049
      ( ( '(' target ( syntax ? + 'and' ) ')' ) + )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1050
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1051
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1052
    'code\_class' (class + 'and') \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1053
      ( ( '(' target \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1054
        ( ( string ('where' \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1055
          ( const ( '==' | equiv ) string ) + ) ? ) ? + 'and' ) ')' ) + )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1056
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1057
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1058
    'code\_instance' (( typeconstructor '::' class ) + 'and') \\
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1059
      ( ( '(' target ( '-' ? + 'and' ) ')' ) + )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1060
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1061
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1062
    'code\_monad' const const target
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1063
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1064
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1065
    'code\_reserved' target ( string + )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1066
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1067
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1068
    'code\_include' target ( string ( string | '-') )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1069
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1070
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1071
    'code\_modulename' target ( ( string string ) + )
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1072
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1073
27452
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27123
diff changeset
  1074
    'code\_abort' ( const + )
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1075
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1076
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1077
    syntax: string | ( 'infix' | 'infixl' | 'infixr' ) nat string
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1078
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1079
28562
4e74209f113e `code func` now just `code`
haftmann
parents: 27706
diff changeset
  1080
    'code' ( 'inline' ) ? ( 'del' ) ?
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1081
    ;
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1082
  \end{rail}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1083
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1084
  \begin{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1085
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1086
  \item [@{command (HOL) "export_code"}] is the canonical interface
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1087
  for generating and serializing code: for a given list of constants,
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1088
  code is generated for the specified target languages.  Abstract code
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1089
  is cached incrementally.  If no constant is given, the currently
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1090
  cached code is serialized.  If no serialization instruction is
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1091
  given, only abstract code is cached.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1092
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1093
  Constants may be specified by giving them literally, referring to
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1094
  all executable contants within a certain theory by giving @{text
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1095
  "name.*"}, or referring to \emph{all} executable constants currently
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1096
  available by giving @{text "*"}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1097
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1098
  By default, for each involved theory one corresponding name space
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1099
  module is generated.  Alternativly, a module name may be specified
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1100
  after the @{keyword "module_name"} keyword; then \emph{all} code is
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1101
  placed in this module.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1102
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1103
  For \emph{SML} and \emph{OCaml}, the file specification refers to a
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1104
  single file; for \emph{Haskell}, it refers to a whole directory,
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1105
  where code is generated in multiple files reflecting the module
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1106
  hierarchy.  The file specification ``@{text "-"}'' denotes standard
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1107
  output.  For \emph{SML}, omitting the file specification compiles
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1108
  code internally in the context of the current ML session.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1109
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1110
  Serializers take an optional list of arguments in parentheses.  For
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1111
  \emph{Haskell} a module name prefix may be given using the ``@{text
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1112
  "root:"}'' argument; ``@{text string_classes}'' adds a ``@{verbatim
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1113
  "deriving (Read, Show)"}'' clause to each appropriate datatype
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1114
  declaration.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1115
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1116
  \item [@{command (HOL) "code_thms"}] prints a list of theorems
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1117
  representing the corresponding program containing all given
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1118
  constants; if no constants are given, the currently cached code
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1119
  theorems are printed.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1120
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1121
  \item [@{command (HOL) "code_deps"}] visualizes dependencies of
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1122
  theorems representing the corresponding program containing all given
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1123
  constants; if no constants are given, the currently cached code
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1124
  theorems are visualized.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1125
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1126
  \item [@{command (HOL) "code_datatype"}] specifies a constructor set
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1127
  for a logical type.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1128
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1129
  \item [@{command (HOL) "code_const"}] associates a list of constants
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1130
  with target-specific serializations; omitting a serialization
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1131
  deletes an existing serialization.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1132
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1133
  \item [@{command (HOL) "code_type"}] associates a list of type
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1134
  constructors with target-specific serializations; omitting a
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1135
  serialization deletes an existing serialization.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1136
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1137
  \item [@{command (HOL) "code_class"}] associates a list of classes
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1138
  with target-specific class names; in addition, constants associated
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1139
  with this class may be given target-specific names used for instance
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1140
  declarations; omitting a serialization deletes an existing
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1141
  serialization.  This applies only to \emph{Haskell}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1142
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1143
  \item [@{command (HOL) "code_instance"}] declares a list of type
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1144
  constructor / class instance relations as ``already present'' for a
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1145
  given target.  Omitting a ``@{text "-"}'' deletes an existing
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1146
  ``already present'' declaration.  This applies only to
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1147
  \emph{Haskell}.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1148
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1149
  \item [@{command (HOL) "code_monad"}] provides an auxiliary
27706
10a6ede68bc8 clarified
haftmann
parents: 27452
diff changeset
  1150
  mechanism to generate monadic code for Haskell.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1151
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1152
  \item [@{command (HOL) "code_reserved"}] declares a list of names as
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1153
  reserved for a given target, preventing it to be shadowed by any
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1154
  generated code.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1155
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1156
  \item [@{command (HOL) "code_include"}] adds arbitrary named content
27706
10a6ede68bc8 clarified
haftmann
parents: 27452
diff changeset
  1157
  (``include'') to generated code.  A ``@{text "-"}'' as last argument
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1158
  will remove an already added ``include''.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1159
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1160
  \item [@{command (HOL) "code_modulename"}] declares aliasings from
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1161
  one module name onto another.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1162
27103
d8549f4d900b major refactorings in code generator modules
haftmann
parents: 27045
diff changeset
  1163
  \item [@{command (HOL) "code_abort"}] declares constants which
27452
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27123
diff changeset
  1164
  are not required to have a definition by means of defining equations;
27103
d8549f4d900b major refactorings in code generator modules
haftmann
parents: 27045
diff changeset
  1165
  if needed these are implemented by program abort instead.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1166
28562
4e74209f113e `code func` now just `code`
haftmann
parents: 27706
diff changeset
  1167
  \item [@{attribute (HOL) code}] explicitly selects (or
4e74209f113e `code func` now just `code`
haftmann
parents: 27706
diff changeset
  1168
  with option ``@{text "del"}'' deselects) a defining equation for
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1169
  code generation.  Usually packages introducing defining equations
27452
5c1fb7d262bf adjusted rep_datatype
haftmann
parents: 27123
diff changeset
  1170
  provide a reasonable default setup for selection.
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1171
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1172
  \item [@{attribute (HOL) code}@{text inline}] declares (or with
28562
4e74209f113e `code func` now just `code`
haftmann
parents: 27706
diff changeset
  1173
  option ``@{text "del"}'' removes) inlining theorems which are
26849
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1174
  applied as rewrite rules to any defining equation during
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1175
  preprocessing.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1176
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1177
  \item [@{command (HOL) "print_codesetup"}] gives an overview on
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1178
  selected defining equations, code generator datatypes and
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1179
  preprocessor setup.
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1180
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1181
  \end{descr}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1182
*}
df50bc1249d7 converted HOL specific elements;
wenzelm
parents: 26840
diff changeset
  1183
27045
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1184
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1185
section {* Definition by specification \label{sec:hol-specification} *}
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1186
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1187
text {*
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1188
  \begin{matharray}{rcl}
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1189
    @{command_def (HOL) "specification"} & : & \isartrans{theory}{proof(prove)} \\
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1190
    @{command_def (HOL) "ax_specification"} & : & \isartrans{theory}{proof(prove)} \\
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1191
  \end{matharray}
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1192
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1193
  \begin{rail}
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1194
  ('specification' | 'ax\_specification') '(' (decl +) ')' \\ (thmdecl? prop +)
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1195
  ;
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1196
  decl: ((name ':')? term '(' 'overloaded' ')'?)
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1197
  \end{rail}
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1198
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1199
  \begin{descr}
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1200
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1201
  \item [@{command (HOL) "specification"}~@{text "decls \<phi>"}] sets up a
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1202
  goal stating the existence of terms with the properties specified to
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1203
  hold for the constants given in @{text decls}.  After finishing the
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1204
  proof, the theory will be augmented with definitions for the given
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1205
  constants, as well as with theorems stating the properties for these
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1206
  constants.
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1207
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1208
  \item [@{command (HOL) "ax_specification"}~@{text "decls \<phi>"}] sets
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1209
  up a goal stating the existence of terms with the properties
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1210
  specified to hold for the constants given in @{text decls}.  After
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1211
  finishing the proof, the theory will be augmented with axioms
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1212
  expressing the properties given in the first place.
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1213
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1214
  \item [@{text decl}] declares a constant to be defined by the
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1215
  specification given.  The definition for the constant @{text c} is
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1216
  bound to the name @{text c_def} unless a theorem name is given in
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1217
  the declaration.  Overloaded constants should be declared as such.
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1218
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1219
  \end{descr}
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1220
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1221
  Whether to use @{command (HOL) "specification"} or @{command (HOL)
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1222
  "ax_specification"} is to some extent a matter of style.  @{command
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1223
  (HOL) "specification"} introduces no new axioms, and so by
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1224
  construction cannot introduce inconsistencies, whereas @{command
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1225
  (HOL) "ax_specification"} does introduce axioms, but only after the
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1226
  user has explicitly proven it to be safe.  A practical issue must be
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1227
  considered, though: After introducing two constants with the same
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1228
  properties using @{command (HOL) "specification"}, one can prove
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1229
  that the two constants are, in fact, equal.  If this might be a
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1230
  problem, one should use @{command (HOL) "ax_specification"}.
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1231
*}
4e7ecec1b685 moved (ax_)specification to end;
wenzelm
parents: 27041
diff changeset
  1232
26840
ec46381f149d added logic-specific sessions;
wenzelm
parents:
diff changeset
  1233
end