doc-src/IsarRef/Thy/HOL_Specific.thy

 (* $Id$ *)
 
 theory HOL_Specific
-imports HOL
+imports Main
 begin
 
+chapter {* HOL specific elements \label{ch:logics} *}
+
+section {* Primitive types \label{sec:hol-typedef} *}
+
+text {*
+  \begin{matharray}{rcl}
+    @{command_def (HOL) "typedecl"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "typedef"} & : & \isartrans{theory}{proof(prove)} \\
+  \end{matharray}
+
+  \begin{rail}
+    'typedecl' typespec infix?
+    ;
+    'typedef' altname? abstype '=' repset
+    ;
+
+    altname: '(' (name | 'open' | 'open' name) ')'
+    ;
+    abstype: typespec infix?
+    ;
+    repset: term ('morphisms' name name)?
+    ;
+  \end{rail}
+
+  \begin{descr}
+  
+  \item [@{command (HOL) "typedecl"}~@{text "(\<alpha>\<^sub>1, \<dots>, \<alpha>\<^sub>n)
+  t"}] is similar to the original @{command "typedecl"} of
+  Isabelle/Pure (see \secref{sec:types-pure}), but also declares type
+  arity @{text "t :: (type, \<dots>, type) type"}, making @{text t} an
+  actual HOL type constructor.   %FIXME check, update
+  
+  \item [@{command (HOL) "typedef"}~@{text "(\<alpha>\<^sub>1, \<dots>, \<alpha>\<^sub>n)
+  t = A"}] sets up a goal stating non-emptiness of the set @{text A}.
+  After finishing the proof, the theory will be augmented by a
+  Gordon/HOL-style type definition, which establishes a bijection
+  between the representing set @{text A} and the new type @{text t}.
+  
+  Technically, @{command (HOL) "typedef"} defines both a type @{text
+  t} and a set (term constant) of the same name (an alternative base
+  name may be given in parentheses).  The injection from type to set
+  is called @{text Rep_t}, its inverse @{text Abs_t} (this may be
+  changed via an explicit @{keyword (HOL) "morphisms"} declaration).
+  
+  Theorems @{text Rep_t}, @{text Rep_t_inverse}, and @{text
+  Abs_t_inverse} provide the most basic characterization as a
+  corresponding injection/surjection pair (in both directions).  Rules
+  @{text Rep_t_inject} and @{text Abs_t_inject} provide a slightly
+  more convenient view on the injectivity part, suitable for automated
+  proof tools (e.g.\ in @{method simp} or @{method iff} declarations).
+  Rules @{text Rep_t_cases}/@{text Rep_t_induct}, and @{text
+  Abs_t_cases}/@{text Abs_t_induct} provide alternative views on
+  surjectivity; these are already declared as set or type rules for
+  the generic @{method cases} and @{method induct} methods.
+  
+  An alternative name may be specified in parentheses; the default is
+  to use @{text t} as indicated before.  The ``@{text "(open)"}''
+  declaration suppresses a separate constant definition for the
+  representing set.
+
+  \end{descr}
+
+  Note that raw type declarations are rarely used in practice; the
+  main application is with experimental (or even axiomatic!) theory
+  fragments.  Instead of primitive HOL type definitions, user-level
+  theories usually refer to higher-level packages such as @{command
+  (HOL) "record"} (see \secref{sec:hol-record}) or @{command (HOL)
+  "datatype"} (see \secref{sec:hol-datatype}).
+*}
+
+
+section {* Adhoc tuples *}
+
+text {*
+  \begin{matharray}{rcl}
+    @{attribute (HOL) split_format}@{text "\<^sup>*"} & : & \isaratt \\
+  \end{matharray}
+
+  \begin{rail}
+    'split\_format' (((name *) + 'and') | ('(' 'complete' ')'))
+    ;
+  \end{rail}
+
+  \begin{descr}
+  
+  \item [@{method (HOL) split_format}~@{text "p\<^sub>1 \<dots> p\<^sub>m
+  \<AND> \<dots> \<AND> q\<^sub>1 \<dots> q\<^sub>n"}] puts expressions of
+  low-level tuple types into canonical form as specified by the
+  arguments given; the @{text i}-th collection of arguments refers to
+  occurrences in premise @{text i} of the rule.  The ``@{text
+  "(complete)"}'' option causes \emph{all} arguments in function
+  applications to be represented canonically according to their tuple
+  type structure.
+
+  Note that these operations tend to invent funny names for new local
+  parameters to be introduced.
+
+  \end{descr}
+*}
+
+
+section {* Records \label{sec:hol-record} *}
+
+text {*
+  In principle, records merely generalize the concept of tuples, where
+  components may be addressed by labels instead of just position.  The
+  logical infrastructure of records in Isabelle/HOL is slightly more
+  advanced, though, supporting truly extensible record schemes.  This
+  admits operations that are polymorphic with respect to record
+  extension, yielding ``object-oriented'' effects like (single)
+  inheritance.  See also \cite{NaraschewskiW-TPHOLs98} for more
+  details on object-oriented verification and record subtyping in HOL.
+*}
+
+
+subsection {* Basic concepts *}
+
+text {*
+  Isabelle/HOL supports both \emph{fixed} and \emph{schematic} records
+  at the level of terms and types.  The notation is as follows:
+
+  \begin{center}
+  \begin{tabular}{l|l|l}
+    & record terms & record types \\ \hline
+    fixed & @{text "\<lparr>x = a, y = b\<rparr>"} & @{text "\<lparr>x :: A, y :: B\<rparr>"} \\
+    schematic & @{text "\<lparr>x = a, y = b, \<dots> = m\<rparr>"} &
+      @{text "\<lparr>x :: A, y :: B, \<dots> :: M\<rparr>"} \\
+  \end{tabular}
+  \end{center}
+
+  \noindent The ASCII representation of @{text "\<lparr>x = a\<rparr>"} is @{text
+  "(| x = a |)"}.
+
+  A fixed record @{text "\<lparr>x = a, y = b\<rparr>"} has field @{text x} of value
+  @{text a} and field @{text y} of value @{text b}.  The corresponding
+  type is @{text "\<lparr>x :: A, y :: B\<rparr>"}, assuming that @{text "a :: A"}
+  and @{text "b :: B"}.
+
+  A record scheme like @{text "\<lparr>x = a, y = b, \<dots> = m\<rparr>"} contains fields
+  @{text x} and @{text y} as before, but also possibly further fields
+  as indicated by the ``@{text "\<dots>"}'' notation (which is actually part
+  of the syntax).  The improper field ``@{text "\<dots>"}'' of a record
+  scheme is called the \emph{more part}.  Logically it is just a free
+  variable, which is occasionally referred to as ``row variable'' in
+  the literature.  The more part of a record scheme may be
+  instantiated by zero or more further components.  For example, the
+  previous scheme may get instantiated to @{text "\<lparr>x = a, y = b, z =
+  c, \<dots> = m'"}, where @{text m'} refers to a different more part.
+  Fixed records are special instances of record schemes, where
+  ``@{text "\<dots>"}'' is properly terminated by the @{text "() :: unit"}
+  element.  In fact, @{text "\<lparr>x = a, y = b\<rparr>"} is just an abbreviation
+  for @{text "\<lparr>x = a, y = b, \<dots> = ()\<rparr>"}.
+  
+  \medskip Two key observations make extensible records in a simply
+  typed language like HOL work out:
+
+  \begin{enumerate}
+
+  \item the more part is internalized, as a free term or type
+  variable,
+
+  \item field names are externalized, they cannot be accessed within the logic
+  as first-class values.
+
+  \end{enumerate}
+
+  \medskip In Isabelle/HOL record types have to be defined explicitly,
+  fixing their field names and types, and their (optional) parent
+  record.  Afterwards, records may be formed using above syntax, while
+  obeying the canonical order of fields as given by their declaration.
+  The record package provides several standard operations like
+  selectors and updates.  The common setup for various generic proof
+  tools enable succinct reasoning patterns.  See also the Isabelle/HOL
+  tutorial \cite{isabelle-hol-book} for further instructions on using
+  records in practice.
+*}
+
+
+subsection {* Record specifications *}
+
+text {*
+  \begin{matharray}{rcl}
+    @{command_def (HOL) "record"} & : & \isartrans{theory}{theory} \\
+  \end{matharray}
+
+  \begin{rail}
+    'record' typespec '=' (type '+')? (constdecl +)
+    ;
+  \end{rail}
+
+  \begin{descr}
+
+  \item [@{command (HOL) "record"}~@{text "(\<alpha>\<^sub>1, \<dots>, \<alpha>\<^sub>m) t
+  = \<tau> + c\<^sub>1 :: \<sigma>\<^sub>1 \<dots> c\<^sub>n :: \<sigma>\<^sub>n"}] defines
+  extensible record type @{text "(\<alpha>\<^sub>1, \<dots>, \<alpha>\<^sub>m) t"},
+  derived from the optional parent record @{text "\<tau>"} by adding new
+  field components @{text "c\<^sub>i :: \<sigma>\<^sub>i"} etc.
+
+  The type variables of @{text "\<tau>"} and @{text "\<sigma>\<^sub>i"} need to be
+  covered by the (distinct) parameters @{text "\<alpha>\<^sub>1, \<dots>,
+  \<alpha>\<^sub>m"}.  Type constructor @{text t} has to be new, while @{text
+  \<tau>} needs to specify an instance of an existing record type.  At
+  least one new field @{text "c\<^sub>i"} has to be specified.
+  Basically, field names need to belong to a unique record.  This is
+  not a real restriction in practice, since fields are qualified by
+  the record name internally.
+
+  The parent record specification @{text \<tau>} is optional; if omitted
+  @{text t} becomes a root record.  The hierarchy of all records
+  declared within a theory context forms a forest structure, i.e.\ a
+  set of trees starting with a root record each.  There is no way to
+  merge multiple parent records!
+
+  For convenience, @{text "(\<alpha>\<^sub>1, \<dots>, \<alpha>\<^sub>m) t"} is made a
+  type abbreviation for the fixed record type @{text "\<lparr>c\<^sub>1 ::
+  \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n\<rparr>"}, likewise is @{text
+  "(\<alpha>\<^sub>1, \<dots>, \<alpha>\<^sub>m, \<zeta>) t_scheme"} made an abbreviation for
+  @{text "\<lparr>c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n, \<dots> ::
+  \<zeta>\<rparr>"}.
+
+  \end{descr}
+*}
+
+
+subsection {* Record operations *}
+
+text {*
+  Any record definition of the form presented above produces certain
+  standard operations.  Selectors and updates are provided for any
+  field, including the improper one ``@{text more}''.  There are also
+  cumulative record constructor functions.  To simplify the
+  presentation below, we assume for now that @{text "(\<alpha>\<^sub>1, \<dots>,
+  \<alpha>\<^sub>m) t"} is a root record with fields @{text "c\<^sub>1 ::
+  \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n"}.
+
+  \medskip \textbf{Selectors} and \textbf{updates} are available for
+  any field (including ``@{text more}''):
+
+  \begin{matharray}{lll}
+    @{text "c\<^sub>i"} & @{text "::"} & @{text "\<lparr>c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n, \<dots> :: \<zeta>\<rparr> \<Rightarrow> \<sigma>\<^sub>i"} \\
+    @{text "c\<^sub>i_update"} & @{text "::"} & @{text "\<sigma>\<^sub>i \<Rightarrow> \<lparr>c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n, \<dots> :: \<zeta>\<rparr> \<Rightarrow> \<lparr>c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n, \<dots> :: \<zeta>\<rparr>"} \\
+  \end{matharray}
+
+  There is special syntax for application of updates: @{text "r\<lparr>x :=
+  a\<rparr>"} abbreviates term @{text "x_update a r"}.  Further notation for
+  repeated updates is also available: @{text "r\<lparr>x := a\<rparr>\<lparr>y := b\<rparr>\<lparr>z :=
+  c\<rparr>"} may be written @{text "r\<lparr>x := a, y := b, z := c\<rparr>"}.  Note that
+  because of postfix notation the order of fields shown here is
+  reverse than in the actual term.  Since repeated updates are just
+  function applications, fields may be freely permuted in @{text "\<lparr>x
+  := a, y := b, z := c\<rparr>"}, as far as logical equality is concerned.
+  Thus commutativity of independent updates can be proven within the
+  logic for any two fields, but not as a general theorem.
+
+  \medskip The \textbf{make} operation provides a cumulative record
+  constructor function:
+
+  \begin{matharray}{lll}
+    @{text "t.make"} & @{text "::"} & @{text "\<sigma>\<^sub>1 \<Rightarrow> \<dots> \<sigma>\<^sub>n \<Rightarrow> \<lparr>c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n\<rparr>"} \\
+  \end{matharray}
+
+  \medskip We now reconsider the case of non-root records, which are
+  derived of some parent.  In general, the latter may depend on
+  another parent as well, resulting in a list of \emph{ancestor
+  records}.  Appending the lists of fields of all ancestors results in
+  a certain field prefix.  The record package automatically takes care
+  of this by lifting operations over this context of ancestor fields.
+  Assuming that @{text "(\<alpha>\<^sub>1, \<dots>, \<alpha>\<^sub>m) t"} has ancestor
+  fields @{text "b\<^sub>1 :: \<rho>\<^sub>1, \<dots>, b\<^sub>k :: \<rho>\<^sub>k"},
+  the above record operations will get the following types:
+
+  \begin{matharray}{lll}
+    @{text "c\<^sub>i"} & @{text "::"} & @{text "\<lparr>b\<^sub>1 :: \<rho>\<^sub>1, \<dots>, b\<^sub>k :: \<rho>\<^sub>k, c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n, \<dots> :: \<zeta>\<rparr> \<Rightarrow> \<sigma>\<^sub>i"} \\
+    @{text "c\<^sub>i_update"} & @{text "::"} & @{text "\<sigma>\<^sub>i \<Rightarrow> 
+      \<lparr>b\<^sub>1 :: \<rho>\<^sub>1, \<dots>, b\<^sub>k :: \<rho>\<^sub>k, c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n, \<dots> :: \<zeta>\<rparr> \<Rightarrow>
+      \<lparr>b\<^sub>1 :: \<rho>\<^sub>1, \<dots>, b\<^sub>k :: \<rho>\<^sub>k, c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n, \<dots> :: \<zeta>\<rparr>"} \\
+    @{text "t.make"} & @{text "::"} & @{text "\<rho>\<^sub>1 \<Rightarrow> \<dots> \<rho>\<^sub>k \<Rightarrow> \<sigma>\<^sub>1 \<Rightarrow> \<dots> \<sigma>\<^sub>n \<Rightarrow> 
+      \<lparr>b\<^sub>1 :: \<rho>\<^sub>1, \<dots>, b\<^sub>k :: \<rho>\<^sub>k, c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n"} \\
+  \end{matharray}
+  \noindent
+
+  \medskip Some further operations address the extension aspect of a
+  derived record scheme specifically: @{text "t.fields"} produces a
+  record fragment consisting of exactly the new fields introduced here
+  (the result may serve as a more part elsewhere); @{text "t.extend"}
+  takes a fixed record and adds a given more part; @{text
+  "t.truncate"} restricts a record scheme to a fixed record.
+
+  \begin{matharray}{lll}
+    @{text "t.fields"} & @{text "::"} & @{text "\<sigma>\<^sub>1 \<Rightarrow> \<dots> \<sigma>\<^sub>n \<Rightarrow> \<lparr>c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n"} \\
+    @{text "t.extend"} & @{text "::"} & @{text "\<lparr>b\<^sub>1 :: \<rho>\<^sub>1, \<dots>, b\<^sub>k :: \<rho>\<^sub>k, c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n\<rparr> \<Rightarrow>
+      \<zeta> \<Rightarrow> \<lparr>b\<^sub>1 :: \<rho>\<^sub>1, \<dots>, b\<^sub>k :: \<rho>\<^sub>k, c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n, \<dots> :: \<zeta>\<rparr>"} \\
+    @{text "t.truncate"} & @{text "::"} & @{text "\<lparr>b\<^sub>1 :: \<rho>\<^sub>1, \<dots>, b\<^sub>k :: \<rho>\<^sub>k, c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n, \<dots> :: \<zeta>\<rparr> \<Rightarrow> \<lparr>b\<^sub>1 :: \<rho>\<^sub>1, \<dots>, b\<^sub>k :: \<rho>\<^sub>k, c\<^sub>1 :: \<sigma>\<^sub>1, \<dots>, c\<^sub>n :: \<sigma>\<^sub>n\<rparr>"} \\
+  \end{matharray}
+
+  \noindent Note that @{text "t.make"} and @{text "t.fields"} coincide
+  for root records.
+*}
+
+
+subsection {* Derived rules and proof tools *}
+
+text {*
+  The record package proves several results internally, declaring
+  these facts to appropriate proof tools.  This enables users to
+  reason about record structures quite conveniently.  Assume that
+  @{text t} is a record type as specified above.
+
+  \begin{enumerate}
+  
+  \item Standard conversions for selectors or updates applied to
+  record constructor terms are made part of the default Simplifier
+  context; thus proofs by reduction of basic operations merely require
+  the @{method simp} method without further arguments.  These rules
+  are available as @{text "t.simps"}, too.
+  
+  \item Selectors applied to updated records are automatically reduced
+  by an internal simplification procedure, which is also part of the
+  standard Simplifier setup.
+
+  \item Inject equations of a form analogous to @{prop "(x, y) = (x',
+  y') \<equiv> x = x' \<and> y = y'"} are declared to the Simplifier and Classical
+  Reasoner as @{attribute iff} rules.  These rules are available as
+  @{text "t.iffs"}.
+
+  \item The introduction rule for record equality analogous to @{text
+  "x r = x r' \<Longrightarrow> y r = y r' \<dots> \<Longrightarrow> r = r'"} is declared to the Simplifier,
+  and as the basic rule context as ``@{attribute intro}@{text "?"}''.
+  The rule is called @{text "t.equality"}.
+
+  \item Representations of arbitrary record expressions as canonical
+  constructor terms are provided both in @{method cases} and @{method
+  induct} format (cf.\ the generic proof methods of the same name,
+  \secref{sec:cases-induct}).  Several variations are available, for
+  fixed records, record schemes, more parts etc.
+  
+  The generic proof methods are sufficiently smart to pick the most
+  sensible rule according to the type of the indicated record
+  expression: users just need to apply something like ``@{text "(cases
+  r)"}'' to a certain proof problem.
+
+  \item The derived record operations @{text "t.make"}, @{text
+  "t.fields"}, @{text "t.extend"}, @{text "t.truncate"} are \emph{not}
+  treated automatically, but usually need to be expanded by hand,
+  using the collective fact @{text "t.defs"}.
+
+  \end{enumerate}
+*}
+
+
+section {* Datatypes \label{sec:hol-datatype} *}
+
+text {*
+  \begin{matharray}{rcl}
+    @{command_def (HOL) "datatype"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "rep_datatype"} & : & \isartrans{theory}{theory} \\
+  \end{matharray}
+
+  \begin{rail}
+    'datatype' (dtspec + 'and')
+    ;
+    'rep\_datatype' (name *) dtrules
+    ;
+
+    dtspec: parname? typespec infix? '=' (cons + '|')
+    ;
+    cons: name (type *) mixfix?
+    ;
+    dtrules: 'distinct' thmrefs 'inject' thmrefs 'induction' thmrefs
+  \end{rail}
+
+  \begin{descr}
+
+  \item [@{command (HOL) "datatype"}] defines inductive datatypes in
+  HOL.
+
+  \item [@{command (HOL) "rep_datatype"}] represents existing types as
+  inductive ones, generating the standard infrastructure of derived
+  concepts (primitive recursion etc.).
+
+  \end{descr}
+
+  The induction and exhaustion theorems generated provide case names
+  according to the constructors involved, while parameters are named
+  after the types (see also \secref{sec:cases-induct}).
+
+  See \cite{isabelle-HOL} for more details on datatypes, but beware of
+  the old-style theory syntax being used there!  Apart from proper
+  proof methods for case-analysis and induction, there are also
+  emulations of ML tactics @{method (HOL) case_tac} and @{method (HOL)
+  induct_tac} available, see \secref{sec:hol-induct-tac}; these admit
+  to refer directly to the internal structure of subgoals (including
+  internally bound parameters).
+*}
+
+
+section {* Recursive functions \label{sec:recursion} *}
+
+text {*
+  \begin{matharray}{rcl}
+    @{command_def (HOL) "primrec"} & : & \isarkeep{local{\dsh}theory} \\
+    @{command_def (HOL) "fun"} & : & \isarkeep{local{\dsh}theory} \\
+    @{command_def (HOL) "function"} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
+    @{command_def (HOL) "termination"} & : & \isartrans{local{\dsh}theory}{proof(prove)} \\
+  \end{matharray}
+
+  \railalias{funopts}{function\_opts}  %FIXME ??
+
+  \begin{rail}
+    'primrec' target? fixes 'where' equations
+    ;
+    equations: (thmdecl? prop + '|')
+    ;
+    ('fun' | 'function') (funopts)? fixes 'where' clauses
+    ;
+    clauses: (thmdecl? prop ('(' 'otherwise' ')')? + '|')
+    ;
+    funopts: '(' (('sequential' | 'in' name | 'domintros' | 'tailrec' |
+    'default' term) + ',') ')'
+    ;
+    'termination' ( term )?
+  \end{rail}
+
+  \begin{descr}
+
+  \item [@{command (HOL) "primrec"}] defines primitive recursive
+  functions over datatypes, see also \cite{isabelle-HOL}.
+
+  \item [@{command (HOL) "function"}] defines functions by general
+  wellfounded recursion. A detailed description with examples can be
+  found in \cite{isabelle-function}. The function is specified by a
+  set of (possibly conditional) recursive equations with arbitrary
+  pattern matching. The command generates proof obligations for the
+  completeness and the compatibility of patterns.
+
+  The defined function is considered partial, and the resulting
+  simplification rules (named @{text "f.psimps"}) and induction rule
+  (named @{text "f.pinduct"}) are guarded by a generated domain
+  predicate @{text "f_dom"}. The @{command (HOL) "termination"}
+  command can then be used to establish that the function is total.
+
+  \item [@{command (HOL) "fun"}] is a shorthand notation for
+  ``@{command (HOL) "function"}~@{text "(sequential)"}, followed by
+  automated proof attempts regarding pattern matching and termination.
+  See \cite{isabelle-function} for further details.
+
+  \item [@{command (HOL) "termination"}~@{text f}] commences a
+  termination proof for the previously defined function @{text f}.  If
+  this is omitted, the command refers to the most recent function
+  definition.  After the proof is closed, the recursive equations and
+  the induction principle is established.
+
+  \end{descr}
+
+  %FIXME check
+
+  Recursive definitions introduced by both the @{command (HOL)
+  "primrec"} and the @{command (HOL) "function"} command accommodate
+  reasoning by induction (cf.\ \secref{sec:cases-induct}): rule @{text
+  "c.induct"} (where @{text c} is the name of the function definition)
+  refers to a specific induction rule, with parameters named according
+  to the user-specified equations.  Case names of @{command (HOL)
+  "primrec"} are that of the datatypes involved, while those of
+  @{command (HOL) "function"} are numbered (starting from 1).
+
+  The equations provided by these packages may be referred later as
+  theorem list @{text "f.simps"}, where @{text f} is the (collective)
+  name of the functions defined.  Individual equations may be named
+  explicitly as well.
+
+  The @{command (HOL) "function"} command accepts the following
+  options.
+
+  \begin{descr}
+
+  \item [@{text sequential}] enables a preprocessor which
+  disambiguates overlapping patterns by making them mutually disjoint.
+  Earlier equations take precedence over later ones.  This allows to
+  give the specification in a format very similar to functional
+  programming.  Note that the resulting simplification and induction
+  rules correspond to the transformed specification, not the one given
+  originally. This usually means that each equation given by the user
+  may result in several theroems.  Also note that this automatic
+  transformation only works for ML-style datatype patterns.
+
+  \item [@{text "\<IN> name"}] gives the target for the definition.
+  %FIXME ?!?
+
+  \item [@{text domintros}] enables the automated generation of
+  introduction rules for the domain predicate. While mostly not
+  needed, they can be helpful in some proofs about partial functions.
+
+  \item [@{text tailrec}] generates the unconstrained recursive
+  equations even without a termination proof, provided that the
+  function is tail-recursive. This currently only works
+
+  \item [@{text "default d"}] allows to specify a default value for a
+  (partial) function, which will ensure that @{text "f x = d x"}
+  whenever @{text "x \<notin> f_dom"}.
+
+  \end{descr}
+*}
+
+
+subsection {* Proof methods related to recursive definitions *}
+
+text {*
+  \begin{matharray}{rcl}
+    @{method_def (HOL) pat_completeness} & : & \isarmeth \\
+    @{method_def (HOL) relation} & : & \isarmeth \\
+    @{method_def (HOL) lexicographic_order} & : & \isarmeth \\
+  \end{matharray}
+
+  \begin{rail}
+    'relation' term
+    ;
+    'lexicographic\_order' (clasimpmod *)
+    ;
+  \end{rail}
+
+  \begin{descr}
+
+  \item [@{method (HOL) pat_completeness}] is a specialized method to
+  solve goals regarding the completeness of pattern matching, as
+  required by the @{command (HOL) "function"} package (cf.\
+  \cite{isabelle-function}).
+
+  \item [@{method (HOL) relation}~@{text R}] introduces a termination
+  proof using the relation @{text R}.  The resulting proof state will
+  contain goals expressing that @{text R} is wellfounded, and that the
+  arguments of recursive calls decrease with respect to @{text R}.
+  Usually, this method is used as the initial proof step of manual
+  termination proofs.
+
+  \item [@{method (HOL) "lexicographic_order"}] attempts a fully
+  automated termination proof by searching for a lexicographic
+  combination of size measures on the arguments of the function. The
+  method accepts the same arguments as the @{method auto} method,
+  which it uses internally to prove local descents.  The same context
+  modifiers as for @{method auto} are accepted, see
+  \secref{sec:clasimp}.
+
+  In case of failure, extensive information is printed, which can help
+  to analyse the situation (cf.\ \cite{isabelle-function}).
+
+  \end{descr}
+*}
+
+
+subsection {* Old-style recursive function definitions (TFL) *}
+
+text {*
+  The old TFL commands @{command (HOL) "recdef"} and @{command (HOL)
+  "recdef_tc"} for defining recursive are mostly obsolete; @{command
+  (HOL) "function"} or @{command (HOL) "fun"} should be used instead.
+
+  \begin{matharray}{rcl}
+    @{command_def (HOL) "recdef"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "recdef_tc"}@{text "\<^sup>*"} & : & \isartrans{theory}{proof(prove)} \\
+  \end{matharray}
+
+  \begin{rail}
+    'recdef' ('(' 'permissive' ')')? \\ name term (prop +) hints?
+    ;
+    recdeftc thmdecl? tc
+    ;
+    hints: '(' 'hints' (recdefmod *) ')'
+    ;
+    recdefmod: (('recdef\_simp' | 'recdef\_cong' | 'recdef\_wf') (() | 'add' | 'del') ':' thmrefs) | clasimpmod
+    ;
+    tc: nameref ('(' nat ')')?
+    ;
+  \end{rail}
+
+  \begin{descr}
+  
+  \item [@{command (HOL) "recdef"}] defines general well-founded
+  recursive functions (using the TFL package), see also
+  \cite{isabelle-HOL}.  The ``@{text "(permissive)"}'' option tells
+  TFL to recover from failed proof attempts, returning unfinished
+  results.  The @{text recdef_simp}, @{text recdef_cong}, and @{text
+  recdef_wf} hints refer to auxiliary rules to be used in the internal
+  automated proof process of TFL.  Additional @{syntax clasimpmod}
+  declarations (cf.\ \secref{sec:clasimp}) may be given to tune the
+  context of the Simplifier (cf.\ \secref{sec:simplifier}) and
+  Classical reasoner (cf.\ \secref{sec:classical}).
+  
+  \item [@{command (HOL) "recdef_tc"}~@{text "c (i)"}] recommences the
+  proof for leftover termination condition number @{text i} (default
+  1) as generated by a @{command (HOL) "recdef"} definition of
+  constant @{text c}.
+  
+  Note that in most cases, @{command (HOL) "recdef"} is able to finish
+  its internal proofs without manual intervention.
+
+  \end{descr}
+
+  \medskip Hints for @{command (HOL) "recdef"} may be also declared
+  globally, using the following attributes.
+
+  \begin{matharray}{rcl}
+    @{attribute_def (HOL) recdef_simp} & : & \isaratt \\
+    @{attribute_def (HOL) recdef_cong} & : & \isaratt \\
+    @{attribute_def (HOL) recdef_wf} & : & \isaratt \\
+  \end{matharray}
+
+  \begin{rail}
+    ('recdef\_simp' | 'recdef\_cong' | 'recdef\_wf') (() | 'add' | 'del')
+    ;
+  \end{rail}
+*}
+
+
+section {* Definition by specification \label{sec:hol-specification} *}
+
+text {*
+  \begin{matharray}{rcl}
+    @{command_def (HOL) "specification"} & : & \isartrans{theory}{proof(prove)} \\
+    @{command_def (HOL) "ax_specification"} & : & \isartrans{theory}{proof(prove)} \\
+  \end{matharray}
+
+  \begin{rail}
+  ('specification' | 'ax\_specification') '(' (decl +) ')' \\ (thmdecl? prop +)
+  ;
+  decl: ((name ':')? term '(' 'overloaded' ')'?)
+  \end{rail}
+
+  \begin{descr}
+
+  \item [@{command (HOL) "specification"}~@{text "decls \<phi>"}] sets up a
+  goal stating the existence of terms with the properties specified to
+  hold for the constants given in @{text decls}.  After finishing the
+  proof, the theory will be augmented with definitions for the given
+  constants, as well as with theorems stating the properties for these
+  constants.
+
+  \item [@{command (HOL) "ax_specification"}~@{text "decls \<phi>"}] sets
+  up a goal stating the existence of terms with the properties
+  specified to hold for the constants given in @{text decls}.  After
+  finishing the proof, the theory will be augmented with axioms
+  expressing the properties given in the first place.
+
+  \item [@{text decl}] declares a constant to be defined by the
+  specification given.  The definition for the constant @{text c} is
+  bound to the name @{text c_def} unless a theorem name is given in
+  the declaration.  Overloaded constants should be declared as such.
+
+  \end{descr}
+
+  Whether to use @{command (HOL) "specification"} or @{command (HOL)
+  "ax_specification"} is to some extent a matter of style.  @{command
+  (HOL) "specification"} introduces no new axioms, and so by
+  construction cannot introduce inconsistencies, whereas @{command
+  (HOL) "ax_specification"} does introduce axioms, but only after the
+  user has explicitly proven it to be safe.  A practical issue must be
+  considered, though: After introducing two constants with the same
+  properties using @{command (HOL) "specification"}, one can prove
+  that the two constants are, in fact, equal.  If this might be a
+  problem, one should use @{command (HOL) "ax_specification"}.
+*}
+
+
+section {* Inductive and coinductive definitions \label{sec:hol-inductive} *}
+
+text {*
+  An \textbf{inductive definition} specifies the least predicate (or
+  set) @{text R} closed under given rules: applying a rule to elements
+  of @{text R} yields a result within @{text R}.  For example, a
+  structural operational semantics is an inductive definition of an
+  evaluation relation.
+
+  Dually, a \textbf{coinductive definition} specifies the greatest
+  predicate~/ set @{text R} that is consistent with given rules: every
+  element of @{text R} can be seen as arising by applying a rule to
+  elements of @{text R}.  An important example is using bisimulation
+  relations to formalise equivalence of processes and infinite data
+  structures.
+
+  \medskip The HOL package is related to the ZF one, which is
+  described in a separate paper,\footnote{It appeared in CADE
+  \cite{paulson-CADE}; a longer version is distributed with Isabelle.}
+  which you should refer to in case of difficulties.  The package is
+  simpler than that of ZF thanks to implicit type-checking in HOL.
+  The types of the (co)inductive predicates (or sets) determine the
+  domain of the fixedpoint definition, and the package does not have
+  to use inference rules for type-checking.
+
+  \begin{matharray}{rcl}
+    @{command_def (HOL) "inductive"} & : & \isarkeep{local{\dsh}theory} \\
+    @{command_def (HOL) "inductive_set"} & : & \isarkeep{local{\dsh}theory} \\
+    @{command_def (HOL) "coinductive"} & : & \isarkeep{local{\dsh}theory} \\
+    @{command_def (HOL) "coinductive_set"} & : & \isarkeep{local{\dsh}theory} \\
+    @{attribute_def (HOL) mono} & : & \isaratt \\
+  \end{matharray}
+
+  \begin{rail}
+    ('inductive' | 'inductive\_set' | 'coinductive' | 'coinductive\_set') target? fixes ('for' fixes)? \\
+    ('where' clauses)? ('monos' thmrefs)?
+    ;
+    clauses: (thmdecl? prop + '|')
+    ;
+    'mono' (() | 'add' | 'del')
+    ;
+  \end{rail}
+
+  \begin{descr}
+
+  \item [@{command (HOL) "inductive"} and @{command (HOL)
+  "coinductive"}] define (co)inductive predicates from the
+  introduction rules given in the @{keyword "where"} part.  The
+  optional @{keyword "for"} part contains a list of parameters of the
+  (co)inductive predicates that remain fixed throughout the
+  definition.  The optional @{keyword "monos"} section contains
+  \emph{monotonicity theorems}, which are required for each operator
+  applied to a recursive set in the introduction rules.  There
+  \emph{must} be a theorem of the form @{text "A \<le> B \<Longrightarrow> M A \<le> M B"},
+  for each premise @{text "M R\<^sub>i t"} in an introduction rule!
+
+  \item [@{command (HOL) "inductive_set"} and @{command (HOL)
+  "coinductive_set"}] are wrappers for to the previous commands,
+  allowing the definition of (co)inductive sets.
+
+  \item [@{attribute (HOL) mono}] declares monotonicity rules.  These
+  rule are involved in the automated monotonicity proof of @{command
+  (HOL) "inductive"}.
+
+  \end{descr}
+*}
+
+
+subsection {* Derived rules *}
+
+text {*
+  Each (co)inductive definition @{text R} adds definitions to the
+  theory and also proves some theorems:
+
+  \begin{description}
+
+  \item [@{text R.intros}] is the list of introduction rules as proven
+  theorems, for the recursive predicates (or sets).  The rules are
+  also available individually, using the names given them in the
+  theory file;
+
+  \item [@{text R.cases}] is the case analysis (or elimination) rule;
+
+  \item [@{text R.induct} or @{text R.coinduct}] is the (co)induction
+  rule.
+
+  \end{description}
+
+  When several predicates @{text "R\<^sub>1, \<dots>, R\<^sub>n"} are
+  defined simultaneously, the list of introduction rules is called
+  @{text "R\<^sub>1_\<dots>_R\<^sub>n.intros"}, the case analysis rules are
+  called @{text "R\<^sub>1.cases, \<dots>, R\<^sub>n.cases"}, and the list
+  of mutual induction rules is called @{text
+  "R\<^sub>1_\<dots>_R\<^sub>n.inducts"}.
+*}
+
+
+subsection {* Monotonicity theorems *}
+
+text {*
+  Each theory contains a default set of theorems that are used in
+  monotonicity proofs.  New rules can be added to this set via the
+  @{attribute (HOL) mono} attribute.  The HOL theory @{text Inductive}
+  shows how this is done.  In general, the following monotonicity
+  theorems may be added:
+
+  \begin{itemize}
+
+  \item Theorems of the form @{text "A \<le> B \<Longrightarrow> M A \<le> M B"}, for proving
+  monotonicity of inductive definitions whose introduction rules have
+  premises involving terms such as @{text "M R\<^sub>i t"}.
+
+  \item Monotonicity theorems for logical operators, which are of the
+  general form @{text "(\<dots> \<longrightarrow> \<dots>) \<Longrightarrow> \<dots> (\<dots> \<longrightarrow> \<dots>) \<Longrightarrow> \<dots> \<longrightarrow> \<dots>"}.  For example, in
+  the case of the operator @{text "\<or>"}, the corresponding theorem is
+  \[
+  \infer{@{text "P\<^sub>1 \<or> P\<^sub>2 \<longrightarrow> Q\<^sub>1 \<or> Q\<^sub>2"}}{@{text "P\<^sub>1 \<longrightarrow> Q\<^sub>1"} & @{text "P\<^sub>2 \<longrightarrow> Q\<^sub>2"}}
+  \]
+
+  \item De Morgan style equations for reasoning about the ``polarity''
+  of expressions, e.g.
+  \[
+  @{prop "\<not> \<not> P \<longleftrightarrow> P"} \qquad\qquad
+  @{prop "\<not> (P \<and> Q) \<longleftrightarrow> \<not> P \<or> \<not> Q"}
+  \]
+
+  \item Equations for reducing complex operators to more primitive
+  ones whose monotonicity can easily be proved, e.g.
+  \[
+  @{prop "(P \<longrightarrow> Q) \<longleftrightarrow> \<not> P \<or> Q"} \qquad\qquad
+  @{prop "Ball A P \<equiv> \<forall>x. x \<in> A \<longrightarrow> P x"}
+  \]
+
+  \end{itemize}
+
+  %FIXME: Example of an inductive definition
+*}
+
+
+section {* Arithmetic proof support *}
+
+text {*
+  \begin{matharray}{rcl}
+    @{method_def (HOL) arith} & : & \isarmeth \\
+    @{method_def (HOL) arith_split} & : & \isaratt \\
+  \end{matharray}
+
+  The @{method (HOL) arith} method decides linear arithmetic problems
+  (on types @{text nat}, @{text int}, @{text real}).  Any current
+  facts are inserted into the goal before running the procedure.
+
+  The @{method (HOL) arith_split} attribute declares case split rules
+  to be expanded before the arithmetic procedure is invoked.
+
+  Note that a simpler (but faster) version of arithmetic reasoning is
+  already performed by the Simplifier.
+*}
+
+
+section {* Cases and induction: emulating tactic scripts \label{sec:hol-induct-tac} *}
+
+text {*
+  The following important tactical tools of Isabelle/HOL have been
+  ported to Isar.  These should be never used in proper proof texts!
+
+  \begin{matharray}{rcl}
+    @{method_def (HOL) case_tac}@{text "\<^sup>*"} & : & \isarmeth \\
+    @{method_def (HOL) induct_tac}@{text "\<^sup>*"} & : & \isarmeth \\
+    @{method_def (HOL) ind_cases}@{text "\<^sup>*"} & : & \isarmeth \\
+    @{command_def (HOL) "inductive_cases"} & : & \isartrans{theory}{theory} \\
+  \end{matharray}
+
+  \begin{rail}
+    'case\_tac' goalspec? term rule?
+    ;
+    'induct\_tac' goalspec? (insts * 'and') rule?
+    ;
+    'ind\_cases' (prop +) ('for' (name +)) ?
+    ;
+    'inductive\_cases' (thmdecl? (prop +) + 'and')
+    ;
+
+    rule: ('rule' ':' thmref)
+    ;
+  \end{rail}
+
+  \begin{descr}
+
+  \item [@{method (HOL) case_tac} and @{method (HOL) induct_tac}]
+  admit to reason about inductive datatypes only (unless an
+  alternative rule is given explicitly).  Furthermore, @{method (HOL)
+  case_tac} does a classical case split on booleans; @{method (HOL)
+  induct_tac} allows only variables to be given as instantiation.
+  These tactic emulations feature both goal addressing and dynamic
+  instantiation.  Note that named rule cases are \emph{not} provided
+  as would be by the proper @{method induct} and @{method cases} proof
+  methods (see \secref{sec:cases-induct}).
+  
+  \item [@{method (HOL) ind_cases} and @{command (HOL)
+  "inductive_cases"}] provide an interface to the internal
+  \texttt{mk_cases} operation.  Rules are simplified in an
+  unrestricted forward manner.
+
+  While @{method (HOL) ind_cases} is a proof method to apply the
+  result immediately as elimination rules, @{command (HOL)
+  "inductive_cases"} provides case split theorems at the theory level
+  for later use.  The @{keyword "for"} argument of the @{method (HOL)
+  ind_cases} method allows to specify a list of variables that should
+  be generalized before applying the resulting rule.
+
+  \end{descr}
+*}
+
+
+section {* Executable code *}
+
+text {*
+  Isabelle/Pure provides two generic frameworks to support code
+  generation from executable specifications.  Isabelle/HOL
+  instantiates these mechanisms in a way that is amenable to end-user
+  applications.
+
+  One framework generates code from both functional and relational
+  programs to SML.  See \cite{isabelle-HOL} for further information
+  (this actually covers the new-style theory format as well).
+
+  \begin{matharray}{rcl}
+    @{command_def (HOL) "value"}@{text "\<^sup>*"} & : & \isarkeep{theory~|~proof} \\
+    @{command_def (HOL) "code_module"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "code_library"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "consts_code"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "types_code"} & : & \isartrans{theory}{theory} \\  
+    @{attribute_def (HOL) code} & : & \isaratt \\
+  \end{matharray}
+
+  \begin{rail}
+  'value' term
+  ;
+
+  ( 'code\_module' | 'code\_library' ) modespec ? name ? \\
+    ( 'file' name ) ? ( 'imports' ( name + ) ) ? \\
+    'contains' ( ( name '=' term ) + | term + )
+  ;
+
+  modespec: '(' ( name * ) ')'
+  ;
+
+  'consts\_code' (codespec +)
+  ;
+
+  codespec: const template attachment ?
+  ;
+
+  'types\_code' (tycodespec +)
+  ;
+
+  tycodespec: name template attachment ?
+  ;
+
+  const: term
+  ;
+
+  template: '(' string ')'
+  ;
+
+  attachment: 'attach' modespec ? verblbrace text verbrbrace
+  ;
+
+  'code' (name)?
+  ;
+  \end{rail}
+
+  \begin{descr}
+
+  \item [@{command (HOL) "value"}~@{text t}] evaluates and prints a
+  term using the code generator.
+
+  \end{descr}
+
+  \medskip The other framework generates code from functional programs
+  (including overloading using type classes) to SML \cite{SML}, OCaml
+  \cite{OCaml} and Haskell \cite{haskell-revised-report}.
+  Conceptually, code generation is split up in three steps:
+  \emph{selection} of code theorems, \emph{translation} into an
+  abstract executable view and \emph{serialization} to a specific
+  \emph{target language}.  See \cite{isabelle-codegen} for an
+  introduction on how to use it.
+
+  \begin{matharray}{rcl}
+    @{command_def (HOL) "export_code"}@{text "\<^sup>*"} & : & \isarkeep{theory~|~proof} \\
+    @{command_def (HOL) "code_thms"}@{text "\<^sup>*"} & : & \isarkeep{theory~|~proof} \\
+    @{command_def (HOL) "code_deps"}@{text "\<^sup>*"} & : & \isarkeep{theory~|~proof} \\
+    @{command_def (HOL) "code_datatype"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "code_const"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "code_type"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "code_class"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "code_instance"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "code_monad"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "code_reserved"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "code_include"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "code_modulename"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "code_exception"} & : & \isartrans{theory}{theory} \\
+    @{command_def (HOL) "print_codesetup"}@{text "\<^sup>*"} & : & \isarkeep{theory~|~proof} \\
+    @{attribute_def (HOL) code} & : & \isaratt \\
+  \end{matharray}
+
+  \begin{rail}
+    'export\_code' ( constexpr + ) ? \\
+      ( ( 'in' target ( 'module\_name' string ) ? \\
+        ( 'file' ( string | '-' ) ) ? ( '(' args ')' ) ?) + ) ?
+    ;
+
+    'code\_thms' ( constexpr + ) ?
+    ;
+
+    'code\_deps' ( constexpr + ) ?
+    ;
+
+    const: term
+    ;
+
+    constexpr: ( const | 'name.*' | '*' )
+    ;
+
+    typeconstructor: nameref
+    ;
+
+    class: nameref
+    ;
+
+    target: 'OCaml' | 'SML' | 'Haskell'
+    ;
+
+    'code\_datatype' const +
+    ;
+
+    'code\_const' (const + 'and') \\
+      ( ( '(' target ( syntax ? + 'and' ) ')' ) + )
+    ;
+
+    'code\_type' (typeconstructor + 'and') \\
+      ( ( '(' target ( syntax ? + 'and' ) ')' ) + )
+    ;
+
+    'code\_class' (class + 'and') \\
+      ( ( '(' target \\
+        ( ( string ('where' \\
+          ( const ( '==' | equiv ) string ) + ) ? ) ? + 'and' ) ')' ) + )
+    ;
+
+    'code\_instance' (( typeconstructor '::' class ) + 'and') \\
+      ( ( '(' target ( '-' ? + 'and' ) ')' ) + )
+    ;
+
+    'code\_monad' const const target
+    ;
+
+    'code\_reserved' target ( string + )
+    ;
+
+    'code\_include' target ( string ( string | '-') )
+    ;
+
+    'code\_modulename' target ( ( string string ) + )
+    ;
+
+    'code\_exception' ( const + )
+    ;
+
+    syntax: string | ( 'infix' | 'infixl' | 'infixr' ) nat string
+    ;
+
+    'code' ('func' | 'inline') ( 'del' )?
+    ;
+  \end{rail}
+
+  \begin{descr}
+
+  \item [@{command (HOL) "export_code"}] is the canonical interface
+  for generating and serializing code: for a given list of constants,
+  code is generated for the specified target languages.  Abstract code
+  is cached incrementally.  If no constant is given, the currently
+  cached code is serialized.  If no serialization instruction is
+  given, only abstract code is cached.
+
+  Constants may be specified by giving them literally, referring to
+  all executable contants within a certain theory by giving @{text
+  "name.*"}, or referring to \emph{all} executable constants currently
+  available by giving @{text "*"}.
+
+  By default, for each involved theory one corresponding name space
+  module is generated.  Alternativly, a module name may be specified
+  after the @{keyword "module_name"} keyword; then \emph{all} code is
+  placed in this module.
+
+  For \emph{SML} and \emph{OCaml}, the file specification refers to a
+  single file; for \emph{Haskell}, it refers to a whole directory,
+  where code is generated in multiple files reflecting the module
+  hierarchy.  The file specification ``@{text "-"}'' denotes standard
+  output.  For \emph{SML}, omitting the file specification compiles
+  code internally in the context of the current ML session.
+
+  Serializers take an optional list of arguments in parentheses.  For
+  \emph{Haskell} a module name prefix may be given using the ``@{text
+  "root:"}'' argument; ``@{text string_classes}'' adds a ``@{verbatim
+  "deriving (Read, Show)"}'' clause to each appropriate datatype
+  declaration.
+
+  \item [@{command (HOL) "code_thms"}] prints a list of theorems
+  representing the corresponding program containing all given
+  constants; if no constants are given, the currently cached code
+  theorems are printed.
+
+  \item [@{command (HOL) "code_deps"}] visualizes dependencies of
+  theorems representing the corresponding program containing all given
+  constants; if no constants are given, the currently cached code
+  theorems are visualized.
+
+  \item [@{command (HOL) "code_datatype"}] specifies a constructor set
+  for a logical type.
+
+  \item [@{command (HOL) "code_const"}] associates a list of constants
+  with target-specific serializations; omitting a serialization
+  deletes an existing serialization.
+
+  \item [@{command (HOL) "code_type"}] associates a list of type
+  constructors with target-specific serializations; omitting a
+  serialization deletes an existing serialization.
+
+  \item [@{command (HOL) "code_class"}] associates a list of classes
+  with target-specific class names; in addition, constants associated
+  with this class may be given target-specific names used for instance
+  declarations; omitting a serialization deletes an existing
+  serialization.  This applies only to \emph{Haskell}.
+
+  \item [@{command (HOL) "code_instance"}] declares a list of type
+  constructor / class instance relations as ``already present'' for a
+  given target.  Omitting a ``@{text "-"}'' deletes an existing
+  ``already present'' declaration.  This applies only to
+  \emph{Haskell}.
+
+  \item [@{command (HOL) "code_monad"}] provides an auxiliary
+  mechanism to generate monadic code.
+
+  \item [@{command (HOL) "code_reserved"}] declares a list of names as
+  reserved for a given target, preventing it to be shadowed by any
+  generated code.
+
+  \item [@{command (HOL) "code_include"}] adds arbitrary named content
+  (``include'') to generated code.  A as last argument ``@{text "-"}''
+  will remove an already added ``include''.
+
+  \item [@{command (HOL) "code_modulename"}] declares aliasings from
+  one module name onto another.
+
+  \item [@{command (HOL) "code_exception"}] declares constants which
+  are not required to have a definition by a defining equations; these
+  are mapped on exceptions instead.
+
+  \item [@{attribute (HOL) code}~@{text func}] explicitly selects (or
+  with option ``@{text "del:"}'' deselects) a defining equation for
+  code generation.  Usually packages introducing defining equations
+  provide a resonable default setup for selection.
+
+  \item [@{attribute (HOL) code}@{text inline}] declares (or with
+  option ``@{text "del:"}'' removes) inlining theorems which are
+  applied as rewrite rules to any defining equation during
+  preprocessing.
+
+  \item [@{command (HOL) "print_codesetup"}] gives an overview on
+  selected defining equations, code generator datatypes and
+  preprocessor setup.
+
+  \end{descr}
+*}
+
 end
+