doc-src/IsarRef/Thy/Generic.thy
author wenzelm
Thu Nov 13 21:50:30 2008 +0100 (2008-11-13)
changeset 28764 b65194fe4434
parent 28761 9ec4482c9201
child 30168 9a20be5be90b
permissions -rw-r--r--
fixed/tuned syntax for attribute "tagged";
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(* $Id$ *)
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theory Generic
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imports Main
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begin
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chapter {* Generic tools and packages \label{ch:gen-tools} *}
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section {* Configuration options *}
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text {*
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  Isabelle/Pure maintains a record of named configuration options
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  within the theory or proof context, with values of type @{ML_type
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  bool}, @{ML_type int}, or @{ML_type string}.  Tools may declare
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  options in ML, and then refer to these values (relative to the
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  context).  Thus global reference variables are easily avoided.  The
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  user may change the value of a configuration option by means of an
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  associated attribute of the same name.  This form of context
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  declaration works particularly well with commands such as @{command
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  "declare"} or @{command "using"}.
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  For historical reasons, some tools cannot take the full proof
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  context into account and merely refer to the background theory.
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  This is accommodated by configuration options being declared as
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  ``global'', which may not be changed within a local context.
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  \begin{matharray}{rcll}
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    @{command_def "print_configs"} & : & @{text "context \<rightarrow>"} \\
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  \end{matharray}
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  \begin{rail}
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    name ('=' ('true' | 'false' | int | name))?
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  \end{rail}
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  \begin{description}
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  \item @{command "print_configs"} prints the available configuration
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  options, with names, types, and current values.
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  \item @{text "name = value"} as an attribute expression modifies the
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  named option, with the syntax of the value depending on the option's
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  type.  For @{ML_type bool} the default value is @{text true}.  Any
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  attempt to change a global option in a local context is ignored.
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  \end{description}
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*}
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section {* Basic proof tools *}
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subsection {* Miscellaneous methods and attributes \label{sec:misc-meth-att} *}
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text {*
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  \begin{matharray}{rcl}
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    @{method_def unfold} & : & @{text method} \\
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    @{method_def fold} & : & @{text method} \\
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    @{method_def insert} & : & @{text method} \\[0.5ex]
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    @{method_def erule}@{text "\<^sup>*"} & : & @{text method} \\
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    @{method_def drule}@{text "\<^sup>*"} & : & @{text method} \\
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    @{method_def frule}@{text "\<^sup>*"} & : & @{text method} \\
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    @{method_def succeed} & : & @{text method} \\
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    @{method_def fail} & : & @{text method} \\
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  \end{matharray}
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  \begin{rail}
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    ('fold' | 'unfold' | 'insert') thmrefs
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    ;
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    ('erule' | 'drule' | 'frule') ('('nat')')? thmrefs
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    ;
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  \end{rail}
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  \begin{description}
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  \item @{method unfold}~@{text "a\<^sub>1 \<dots> a\<^sub>n"} and @{method fold}~@{text
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  "a\<^sub>1 \<dots> a\<^sub>n"} expand (or fold back) the given definitions throughout
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  all goals; any chained facts provided are inserted into the goal and
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  subject to rewriting as well.
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  \item @{method insert}~@{text "a\<^sub>1 \<dots> a\<^sub>n"} inserts theorems as facts
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  into all goals of the proof state.  Note that current facts
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  indicated for forward chaining are ignored.
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  \item @{method erule}~@{text "a\<^sub>1 \<dots> a\<^sub>n"}, @{method drule}~@{text "a\<^sub>1
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  \<dots> a\<^sub>n"}, and @{method frule}~@{text "a\<^sub>1 \<dots> a\<^sub>n"} are similar to the
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  basic @{method rule} method (see \secref{sec:pure-meth-att}), but
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  apply rules by elim-resolution, destruct-resolution, and
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  forward-resolution, respectively \cite{isabelle-ref}.  The optional
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  natural number argument (default 0) specifies additional assumption
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  steps to be performed here.
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  Note that these methods are improper ones, mainly serving for
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  experimentation and tactic script emulation.  Different modes of
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  basic rule application are usually expressed in Isar at the proof
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  language level, rather than via implicit proof state manipulations.
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  For example, a proper single-step elimination would be done using
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  the plain @{method rule} method, with forward chaining of current
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  facts.
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  \item @{method succeed} yields a single (unchanged) result; it is
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  the identity of the ``@{text ","}'' method combinator (cf.\
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  \secref{sec:proof-meth}).
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  \item @{method fail} yields an empty result sequence; it is the
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  identity of the ``@{text "|"}'' method combinator (cf.\
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  \secref{sec:proof-meth}).
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  \end{description}
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  \begin{matharray}{rcl}
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    @{attribute_def tagged} & : & @{text attribute} \\
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    @{attribute_def untagged} & : & @{text attribute} \\[0.5ex]
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    @{attribute_def THEN} & : & @{text attribute} \\
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    @{attribute_def COMP} & : & @{text attribute} \\[0.5ex]
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    @{attribute_def unfolded} & : & @{text attribute} \\
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    @{attribute_def folded} & : & @{text attribute} \\[0.5ex]
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    @{attribute_def rotated} & : & @{text attribute} \\
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    @{attribute_def (Pure) elim_format} & : & @{text attribute} \\
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    @{attribute_def standard}@{text "\<^sup>*"} & : & @{text attribute} \\
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    @{attribute_def no_vars}@{text "\<^sup>*"} & : & @{text attribute} \\
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  \end{matharray}
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  \begin{rail}
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    'tagged' name name
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    ;
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    'untagged' name
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    ;
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    ('THEN' | 'COMP') ('[' nat ']')? thmref
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    ;
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    ('unfolded' | 'folded') thmrefs
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    ;
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    'rotated' ( int )?
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  \end{rail}
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  \begin{description}
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  \item @{attribute tagged}~@{text "name value"} and @{attribute
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  untagged}~@{text name} add and remove \emph{tags} of some theorem.
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  Tags may be any list of string pairs that serve as formal comment.
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  The first string is considered the tag name, the second its value.
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  Note that @{attribute untagged} removes any tags of the same name.
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  \item @{attribute THEN}~@{text a} and @{attribute COMP}~@{text a}
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  compose rules by resolution.  @{attribute THEN} resolves with the
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  first premise of @{text a} (an alternative position may be also
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  specified); the @{attribute COMP} version skips the automatic
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  lifting process that is normally intended (cf.\ @{ML [source=false]
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  "op RS"} and @{ML [source=false] "op COMP"} in
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  \cite[\S5]{isabelle-ref}).
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  \item @{attribute unfolded}~@{text "a\<^sub>1 \<dots> a\<^sub>n"} and @{attribute
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  folded}~@{text "a\<^sub>1 \<dots> a\<^sub>n"} expand and fold back again the given
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  definitions throughout a rule.
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  \item @{attribute rotated}~@{text n} rotate the premises of a
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  theorem by @{text n} (default 1).
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  \item @{attribute (Pure) elim_format} turns a destruction rule into
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  elimination rule format, by resolving with the rule @{prop "PROP A \<Longrightarrow>
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  (PROP A \<Longrightarrow> PROP B) \<Longrightarrow> PROP B"}.
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  Note that the Classical Reasoner (\secref{sec:classical}) provides
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  its own version of this operation.
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  \item @{attribute standard} puts a theorem into the standard form of
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  object-rules at the outermost theory level.  Note that this
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  operation violates the local proof context (including active
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  locales).
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  \item @{attribute no_vars} replaces schematic variables by free
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  ones; this is mainly for tuning output of pretty printed theorems.
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  \end{description}
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*}
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subsection {* Low-level equational reasoning *}
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text {*
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  \begin{matharray}{rcl}
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    @{method_def subst} & : & @{text method} \\
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    @{method_def hypsubst} & : & @{text method} \\
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    @{method_def split} & : & @{text method} \\
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  \end{matharray}
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  \begin{rail}
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    'subst' ('(' 'asm' ')')? ('(' (nat+) ')')? thmref
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    ;
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    'split' ('(' 'asm' ')')? thmrefs
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    ;
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  \end{rail}
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  These methods provide low-level facilities for equational reasoning
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  that are intended for specialized applications only.  Normally,
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  single step calculations would be performed in a structured text
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  (see also \secref{sec:calculation}), while the Simplifier methods
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  provide the canonical way for automated normalization (see
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  \secref{sec:simplifier}).
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  \begin{description}
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  \item @{method subst}~@{text eq} performs a single substitution step
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  using rule @{text eq}, which may be either a meta or object
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  equality.
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  \item @{method subst}~@{text "(asm) eq"} substitutes in an
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  assumption.
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  \item @{method subst}~@{text "(i \<dots> j) eq"} performs several
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  substitutions in the conclusion. The numbers @{text i} to @{text j}
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  indicate the positions to substitute at.  Positions are ordered from
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  the top of the term tree moving down from left to right. For
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  example, in @{text "(a + b) + (c + d)"} there are three positions
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  where commutativity of @{text "+"} is applicable: 1 refers to @{text
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  "a + b"}, 2 to the whole term, and 3 to @{text "c + d"}.
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  If the positions in the list @{text "(i \<dots> j)"} are non-overlapping
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  (e.g.\ @{text "(2 3)"} in @{text "(a + b) + (c + d)"}) you may
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  assume all substitutions are performed simultaneously.  Otherwise
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  the behaviour of @{text subst} is not specified.
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  \item @{method subst}~@{text "(asm) (i \<dots> j) eq"} performs the
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  substitutions in the assumptions. The positions refer to the
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  assumptions in order from left to right.  For example, given in a
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  goal of the form @{text "P (a + b) \<Longrightarrow> P (c + d) \<Longrightarrow> \<dots>"}, position 1 of
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  commutativity of @{text "+"} is the subterm @{text "a + b"} and
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  position 2 is the subterm @{text "c + d"}.
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  \item @{method hypsubst} performs substitution using some
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  assumption; this only works for equations of the form @{text "x =
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  t"} where @{text x} is a free or bound variable.
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  \item @{method split}~@{text "a\<^sub>1 \<dots> a\<^sub>n"} performs single-step case
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  splitting using the given rules.  By default, splitting is performed
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  in the conclusion of a goal; the @{text "(asm)"} option indicates to
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  operate on assumptions instead.
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  Note that the @{method simp} method already involves repeated
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  application of split rules as declared in the current context.
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  \end{description}
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*}
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subsection {* Further tactic emulations \label{sec:tactics} *}
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text {*
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  The following improper proof methods emulate traditional tactics.
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  These admit direct access to the goal state, which is normally
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  considered harmful!  In particular, this may involve both numbered
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  goal addressing (default 1), and dynamic instantiation within the
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  scope of some subgoal.
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  \begin{warn}
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    Dynamic instantiations refer to universally quantified parameters
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    of a subgoal (the dynamic context) rather than fixed variables and
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    term abbreviations of a (static) Isar context.
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  \end{warn}
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  Tactic emulation methods, unlike their ML counterparts, admit
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  simultaneous instantiation from both dynamic and static contexts.
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  If names occur in both contexts goal parameters hide locally fixed
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  variables.  Likewise, schematic variables refer to term
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  abbreviations, if present in the static context.  Otherwise the
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  schematic variable is interpreted as a schematic variable and left
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  to be solved by unification with certain parts of the subgoal.
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  Note that the tactic emulation proof methods in Isabelle/Isar are
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  consistently named @{text foo_tac}.  Note also that variable names
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  occurring on left hand sides of instantiations must be preceded by a
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  question mark if they coincide with a keyword or contain dots.  This
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  is consistent with the attribute @{attribute "where"} (see
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  \secref{sec:pure-meth-att}).
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  \begin{matharray}{rcl}
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    @{method_def rule_tac}@{text "\<^sup>*"} & : & @{text method} \\
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    @{method_def erule_tac}@{text "\<^sup>*"} & : & @{text method} \\
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    @{method_def drule_tac}@{text "\<^sup>*"} & : & @{text method} \\
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    @{method_def frule_tac}@{text "\<^sup>*"} & : & @{text method} \\
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    @{method_def cut_tac}@{text "\<^sup>*"} & : & @{text method} \\
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    @{method_def thin_tac}@{text "\<^sup>*"} & : & @{text method} \\
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    @{method_def subgoal_tac}@{text "\<^sup>*"} & : & @{text method} \\
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    @{method_def rename_tac}@{text "\<^sup>*"} & : & @{text method} \\
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    @{method_def rotate_tac}@{text "\<^sup>*"} & : & @{text method} \\
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    @{method_def tactic}@{text "\<^sup>*"} & : & @{text method} \\
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    @{method_def raw_tactic}@{text "\<^sup>*"} & : & @{text method} \\
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  \end{matharray}
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  \begin{rail}
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    ( 'rule\_tac' | 'erule\_tac' | 'drule\_tac' | 'frule\_tac' | 'cut\_tac' | 'thin\_tac' ) goalspec?
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    ( insts thmref | thmrefs )
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    ;
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    'subgoal\_tac' goalspec? (prop +)
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    ;
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    'rename\_tac' goalspec? (name +)
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    ;
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    'rotate\_tac' goalspec? int?
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    ;
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    ('tactic' | 'raw_tactic') text
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    ;
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    insts: ((name '=' term) + 'and') 'in'
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    ;
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  \end{rail}
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\begin{description}
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  \item @{method rule_tac} etc. do resolution of rules with explicit
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  instantiation.  This works the same way as the ML tactics @{ML
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  res_inst_tac} etc. (see \cite[\S3]{isabelle-ref})
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  Multiple rules may be only given if there is no instantiation; then
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  @{method rule_tac} is the same as @{ML resolve_tac} in ML (see
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  \cite[\S3]{isabelle-ref}).
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  \item @{method cut_tac} inserts facts into the proof state as
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  assumption of a subgoal, see also @{ML Tactic.cut_facts_tac} in
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  \cite[\S3]{isabelle-ref}.  Note that the scope of schematic
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  variables is spread over the main goal statement.  Instantiations
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  may be given as well, see also ML tactic @{ML cut_inst_tac} in
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  \cite[\S3]{isabelle-ref}.
wenzelm@26782
   321
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   322
  \item @{method thin_tac}~@{text \<phi>} deletes the specified assumption
wenzelm@28760
   323
  from a subgoal; note that @{text \<phi>} may contain schematic variables.
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   324
  See also @{ML thin_tac} in \cite[\S3]{isabelle-ref}.
wenzelm@28760
   325
wenzelm@28760
   326
  \item @{method subgoal_tac}~@{text \<phi>} adds @{text \<phi>} as an
wenzelm@27239
   327
  assumption to a subgoal.  See also @{ML subgoal_tac} and @{ML
wenzelm@27239
   328
  subgoals_tac} in \cite[\S3]{isabelle-ref}.
wenzelm@26782
   329
wenzelm@28760
   330
  \item @{method rename_tac}~@{text "x\<^sub>1 \<dots> x\<^sub>n"} renames parameters of a
wenzelm@28760
   331
  goal according to the list @{text "x\<^sub>1, \<dots>, x\<^sub>n"}, which refers to the
wenzelm@28760
   332
  \emph{suffix} of variables.
wenzelm@26782
   333
wenzelm@28760
   334
  \item @{method rotate_tac}~@{text n} rotates the assumptions of a
wenzelm@26782
   335
  goal by @{text n} positions: from right to left if @{text n} is
wenzelm@26782
   336
  positive, and from left to right if @{text n} is negative; the
wenzelm@26782
   337
  default value is 1.  See also @{ML rotate_tac} in
wenzelm@26782
   338
  \cite[\S3]{isabelle-ref}.
wenzelm@26782
   339
wenzelm@28760
   340
  \item @{method tactic}~@{text "text"} produces a proof method from
wenzelm@26782
   341
  any ML text of type @{ML_type tactic}.  Apart from the usual ML
wenzelm@27223
   342
  environment and the current proof context, the ML code may refer to
wenzelm@27223
   343
  the locally bound values @{ML_text facts}, which indicates any
wenzelm@27223
   344
  current facts used for forward-chaining.
wenzelm@26782
   345
wenzelm@28760
   346
  \item @{method raw_tactic} is similar to @{method tactic}, but
wenzelm@27223
   347
  presents the goal state in its raw internal form, where simultaneous
wenzelm@27223
   348
  subgoals appear as conjunction of the logical framework instead of
wenzelm@27223
   349
  the usual split into several subgoals.  While feature this is useful
wenzelm@27223
   350
  for debugging of complex method definitions, it should not never
wenzelm@27223
   351
  appear in production theories.
wenzelm@26782
   352
wenzelm@28760
   353
  \end{description}
wenzelm@26782
   354
*}
wenzelm@26782
   355
wenzelm@26782
   356
wenzelm@27040
   357
section {* The Simplifier \label{sec:simplifier} *}
wenzelm@26782
   358
wenzelm@27040
   359
subsection {* Simplification methods *}
wenzelm@26782
   360
wenzelm@26782
   361
text {*
wenzelm@26782
   362
  \begin{matharray}{rcl}
wenzelm@28761
   363
    @{method_def simp} & : & @{text method} \\
wenzelm@28761
   364
    @{method_def simp_all} & : & @{text method} \\
wenzelm@26782
   365
  \end{matharray}
wenzelm@26782
   366
wenzelm@26782
   367
  \indexouternonterm{simpmod}
wenzelm@26782
   368
  \begin{rail}
wenzelm@26782
   369
    ('simp' | 'simp\_all') ('!' ?) opt? (simpmod *)
wenzelm@26782
   370
    ;
wenzelm@26782
   371
wenzelm@27092
   372
    opt: '(' ('no\_asm' | 'no\_asm\_simp' | 'no\_asm\_use' | 'asm\_lr' ) ')'
wenzelm@26782
   373
    ;
wenzelm@26782
   374
    simpmod: ('add' | 'del' | 'only' | 'cong' (() | 'add' | 'del') |
wenzelm@26782
   375
      'split' (() | 'add' | 'del')) ':' thmrefs
wenzelm@26782
   376
    ;
wenzelm@26782
   377
  \end{rail}
wenzelm@26782
   378
wenzelm@28760
   379
  \begin{description}
wenzelm@26782
   380
wenzelm@28760
   381
  \item @{method simp} invokes the Simplifier, after declaring
wenzelm@26782
   382
  additional rules according to the arguments given.  Note that the
wenzelm@26782
   383
  \railtterm{only} modifier first removes all other rewrite rules,
wenzelm@26782
   384
  congruences, and looper tactics (including splits), and then behaves
wenzelm@26782
   385
  like \railtterm{add}.
wenzelm@26782
   386
wenzelm@26782
   387
  \medskip The \railtterm{cong} modifiers add or delete Simplifier
wenzelm@26782
   388
  congruence rules (see also \cite{isabelle-ref}), the default is to
wenzelm@26782
   389
  add.
wenzelm@26782
   390
wenzelm@26782
   391
  \medskip The \railtterm{split} modifiers add or delete rules for the
wenzelm@26782
   392
  Splitter (see also \cite{isabelle-ref}), the default is to add.
wenzelm@26782
   393
  This works only if the Simplifier method has been properly setup to
wenzelm@26782
   394
  include the Splitter (all major object logics such HOL, HOLCF, FOL,
wenzelm@26782
   395
  ZF do this already).
wenzelm@26782
   396
wenzelm@28760
   397
  \item @{method simp_all} is similar to @{method simp}, but acts on
wenzelm@26782
   398
  all goals (backwards from the last to the first one).
wenzelm@26782
   399
wenzelm@28760
   400
  \end{description}
wenzelm@26782
   401
wenzelm@26782
   402
  By default the Simplifier methods take local assumptions fully into
wenzelm@26782
   403
  account, using equational assumptions in the subsequent
wenzelm@26782
   404
  normalization process, or simplifying assumptions themselves (cf.\
wenzelm@26782
   405
  @{ML asm_full_simp_tac} in \cite[\S10]{isabelle-ref}).  In
wenzelm@26782
   406
  structured proofs this is usually quite well behaved in practice:
wenzelm@26782
   407
  just the local premises of the actual goal are involved, additional
wenzelm@26782
   408
  facts may be inserted via explicit forward-chaining (via @{command
wenzelm@26782
   409
  "then"}, @{command "from"}, @{command "using"} etc.).  The full
wenzelm@26782
   410
  context of premises is only included if the ``@{text "!"}'' (bang)
wenzelm@26782
   411
  argument is given, which should be used with some care, though.
wenzelm@26782
   412
wenzelm@26782
   413
  Additional Simplifier options may be specified to tune the behavior
wenzelm@26782
   414
  further (mostly for unstructured scripts with many accidental local
wenzelm@26782
   415
  facts): ``@{text "(no_asm)"}'' means assumptions are ignored
wenzelm@26782
   416
  completely (cf.\ @{ML simp_tac}), ``@{text "(no_asm_simp)"}'' means
wenzelm@26782
   417
  assumptions are used in the simplification of the conclusion but are
wenzelm@26782
   418
  not themselves simplified (cf.\ @{ML asm_simp_tac}), and ``@{text
wenzelm@26782
   419
  "(no_asm_use)"}'' means assumptions are simplified but are not used
wenzelm@26782
   420
  in the simplification of each other or the conclusion (cf.\ @{ML
wenzelm@26782
   421
  full_simp_tac}).  For compatibility reasons, there is also an option
wenzelm@26782
   422
  ``@{text "(asm_lr)"}'', which means that an assumption is only used
wenzelm@26782
   423
  for simplifying assumptions which are to the right of it (cf.\ @{ML
wenzelm@26782
   424
  asm_lr_simp_tac}).
wenzelm@26782
   425
wenzelm@27092
   426
  The configuration option @{text "depth_limit"} limits the number of
wenzelm@26782
   427
  recursive invocations of the simplifier during conditional
wenzelm@26782
   428
  rewriting.
wenzelm@26782
   429
wenzelm@26782
   430
  \medskip The Splitter package is usually configured to work as part
wenzelm@26782
   431
  of the Simplifier.  The effect of repeatedly applying @{ML
wenzelm@26782
   432
  split_tac} can be simulated by ``@{text "(simp only: split:
wenzelm@26782
   433
  a\<^sub>1 \<dots> a\<^sub>n)"}''.  There is also a separate @{text split}
wenzelm@26782
   434
  method available for single-step case splitting.
wenzelm@26782
   435
*}
wenzelm@26782
   436
wenzelm@26782
   437
wenzelm@27040
   438
subsection {* Declaring rules *}
wenzelm@26782
   439
wenzelm@26782
   440
text {*
wenzelm@26782
   441
  \begin{matharray}{rcl}
wenzelm@28761
   442
    @{command_def "print_simpset"}@{text "\<^sup>*"} & : & @{text "context \<rightarrow>"} \\
wenzelm@28761
   443
    @{attribute_def simp} & : & @{text attribute} \\
wenzelm@28761
   444
    @{attribute_def cong} & : & @{text attribute} \\
wenzelm@28761
   445
    @{attribute_def split} & : & @{text attribute} \\
wenzelm@26782
   446
  \end{matharray}
wenzelm@26782
   447
wenzelm@26782
   448
  \begin{rail}
wenzelm@26782
   449
    ('simp' | 'cong' | 'split') (() | 'add' | 'del')
wenzelm@26782
   450
    ;
wenzelm@26782
   451
  \end{rail}
wenzelm@26782
   452
wenzelm@28760
   453
  \begin{description}
wenzelm@26782
   454
wenzelm@28760
   455
  \item @{command "print_simpset"} prints the collection of rules
wenzelm@26782
   456
  declared to the Simplifier, which is also known as ``simpset''
wenzelm@26782
   457
  internally \cite{isabelle-ref}.
wenzelm@26782
   458
wenzelm@28760
   459
  \item @{attribute simp} declares simplification rules.
wenzelm@26782
   460
wenzelm@28760
   461
  \item @{attribute cong} declares congruence rules.
wenzelm@26782
   462
wenzelm@28760
   463
  \item @{attribute split} declares case split rules.
wenzelm@26782
   464
wenzelm@28760
   465
  \end{description}
wenzelm@26782
   466
*}
wenzelm@26782
   467
wenzelm@26782
   468
wenzelm@27040
   469
subsection {* Simplification procedures *}
wenzelm@26782
   470
wenzelm@26782
   471
text {*
wenzelm@26782
   472
  \begin{matharray}{rcl}
wenzelm@28761
   473
    @{command_def "simproc_setup"} & : & @{text "local_theory \<rightarrow> local_theory"} \\
wenzelm@28761
   474
    simproc & : & @{text attribute} \\
wenzelm@26782
   475
  \end{matharray}
wenzelm@26782
   476
wenzelm@26782
   477
  \begin{rail}
wenzelm@26782
   478
    'simproc\_setup' name '(' (term + '|') ')' '=' text \\ ('identifier' (nameref+))?
wenzelm@26782
   479
    ;
wenzelm@26782
   480
wenzelm@26782
   481
    'simproc' (('add' ':')? | 'del' ':') (name+)
wenzelm@26782
   482
    ;
wenzelm@26782
   483
  \end{rail}
wenzelm@26782
   484
wenzelm@28760
   485
  \begin{description}
wenzelm@26782
   486
wenzelm@28760
   487
  \item @{command "simproc_setup"} defines a named simplification
wenzelm@26782
   488
  procedure that is invoked by the Simplifier whenever any of the
wenzelm@26782
   489
  given term patterns match the current redex.  The implementation,
wenzelm@26782
   490
  which is provided as ML source text, needs to be of type @{ML_type
wenzelm@26782
   491
  "morphism -> simpset -> cterm -> thm option"}, where the @{ML_type
wenzelm@26782
   492
  cterm} represents the current redex @{text r} and the result is
wenzelm@26782
   493
  supposed to be some proven rewrite rule @{text "r \<equiv> r'"} (or a
wenzelm@26782
   494
  generalized version), or @{ML NONE} to indicate failure.  The
wenzelm@26782
   495
  @{ML_type simpset} argument holds the full context of the current
wenzelm@26782
   496
  Simplifier invocation, including the actual Isar proof context.  The
wenzelm@26782
   497
  @{ML_type morphism} informs about the difference of the original
wenzelm@26782
   498
  compilation context wrt.\ the one of the actual application later
wenzelm@26782
   499
  on.  The optional @{keyword "identifier"} specifies theorems that
wenzelm@26782
   500
  represent the logical content of the abstract theory of this
wenzelm@26782
   501
  simproc.
wenzelm@26782
   502
wenzelm@26782
   503
  Morphisms and identifiers are only relevant for simprocs that are
wenzelm@26782
   504
  defined within a local target context, e.g.\ in a locale.
wenzelm@26782
   505
wenzelm@28760
   506
  \item @{text "simproc add: name"} and @{text "simproc del: name"}
wenzelm@26782
   507
  add or delete named simprocs to the current Simplifier context.  The
wenzelm@26782
   508
  default is to add a simproc.  Note that @{command "simproc_setup"}
wenzelm@26782
   509
  already adds the new simproc to the subsequent context.
wenzelm@26782
   510
wenzelm@28760
   511
  \end{description}
wenzelm@26782
   512
*}
wenzelm@26782
   513
wenzelm@26782
   514
wenzelm@27040
   515
subsection {* Forward simplification *}
wenzelm@26782
   516
wenzelm@26782
   517
text {*
wenzelm@26782
   518
  \begin{matharray}{rcl}
wenzelm@28761
   519
    @{attribute_def simplified} & : & @{text attribute} \\
wenzelm@26782
   520
  \end{matharray}
wenzelm@26782
   521
wenzelm@26782
   522
  \begin{rail}
wenzelm@26782
   523
    'simplified' opt? thmrefs?
wenzelm@26782
   524
    ;
wenzelm@26782
   525
wenzelm@26789
   526
    opt: '(' ('no\_asm' | 'no\_asm\_simp' | 'no\_asm\_use') ')'
wenzelm@26782
   527
    ;
wenzelm@26782
   528
  \end{rail}
wenzelm@26782
   529
wenzelm@28760
   530
  \begin{description}
wenzelm@26782
   531
  
wenzelm@28760
   532
  \item @{attribute simplified}~@{text "a\<^sub>1 \<dots> a\<^sub>n"} causes a theorem to
wenzelm@28760
   533
  be simplified, either by exactly the specified rules @{text "a\<^sub>1, \<dots>,
wenzelm@28760
   534
  a\<^sub>n"}, or the implicit Simplifier context if no arguments are given.
wenzelm@28760
   535
  The result is fully simplified by default, including assumptions and
wenzelm@28760
   536
  conclusion; the options @{text no_asm} etc.\ tune the Simplifier in
wenzelm@28760
   537
  the same way as the for the @{text simp} method.
wenzelm@26782
   538
wenzelm@26782
   539
  Note that forward simplification restricts the simplifier to its
wenzelm@26782
   540
  most basic operation of term rewriting; solver and looper tactics
wenzelm@26782
   541
  \cite{isabelle-ref} are \emph{not} involved here.  The @{text
wenzelm@26782
   542
  simplified} attribute should be only rarely required under normal
wenzelm@26782
   543
  circumstances.
wenzelm@26782
   544
wenzelm@28760
   545
  \end{description}
wenzelm@26782
   546
*}
wenzelm@26782
   547
wenzelm@26782
   548
wenzelm@27040
   549
section {* The Classical Reasoner \label{sec:classical} *}
wenzelm@26782
   550
wenzelm@27040
   551
subsection {* Basic methods *}
wenzelm@26782
   552
wenzelm@26782
   553
text {*
wenzelm@26782
   554
  \begin{matharray}{rcl}
wenzelm@28761
   555
    @{method_def rule} & : & @{text method} \\
wenzelm@28761
   556
    @{method_def contradiction} & : & @{text method} \\
wenzelm@28761
   557
    @{method_def intro} & : & @{text method} \\
wenzelm@28761
   558
    @{method_def elim} & : & @{text method} \\
wenzelm@26782
   559
  \end{matharray}
wenzelm@26782
   560
wenzelm@26782
   561
  \begin{rail}
wenzelm@26782
   562
    ('rule' | 'intro' | 'elim') thmrefs?
wenzelm@26782
   563
    ;
wenzelm@26782
   564
  \end{rail}
wenzelm@26782
   565
wenzelm@28760
   566
  \begin{description}
wenzelm@26782
   567
wenzelm@28760
   568
  \item @{method rule} as offered by the Classical Reasoner is a
wenzelm@26782
   569
  refinement over the primitive one (see \secref{sec:pure-meth-att}).
wenzelm@26782
   570
  Both versions essentially work the same, but the classical version
wenzelm@26782
   571
  observes the classical rule context in addition to that of
wenzelm@26782
   572
  Isabelle/Pure.
wenzelm@26782
   573
wenzelm@26782
   574
  Common object logics (HOL, ZF, etc.) declare a rich collection of
wenzelm@26782
   575
  classical rules (even if these would qualify as intuitionistic
wenzelm@26782
   576
  ones), but only few declarations to the rule context of
wenzelm@26782
   577
  Isabelle/Pure (\secref{sec:pure-meth-att}).
wenzelm@26782
   578
wenzelm@28760
   579
  \item @{method contradiction} solves some goal by contradiction,
wenzelm@26782
   580
  deriving any result from both @{text "\<not> A"} and @{text A}.  Chained
wenzelm@26782
   581
  facts, which are guaranteed to participate, may appear in either
wenzelm@26782
   582
  order.
wenzelm@26782
   583
wenzelm@28760
   584
  \item @{method intro} and @{method elim} repeatedly refine some goal
wenzelm@28760
   585
  by intro- or elim-resolution, after having inserted any chained
wenzelm@26901
   586
  facts.  Exactly the rules given as arguments are taken into account;
wenzelm@26901
   587
  this allows fine-tuned decomposition of a proof problem, in contrast
wenzelm@26901
   588
  to common automated tools.
wenzelm@26782
   589
wenzelm@28760
   590
  \end{description}
wenzelm@26782
   591
*}
wenzelm@26782
   592
wenzelm@26782
   593
wenzelm@27040
   594
subsection {* Automated methods *}
wenzelm@26782
   595
wenzelm@26782
   596
text {*
wenzelm@26782
   597
  \begin{matharray}{rcl}
wenzelm@28761
   598
    @{method_def blast} & : & @{text method} \\
wenzelm@28761
   599
    @{method_def fast} & : & @{text method} \\
wenzelm@28761
   600
    @{method_def slow} & : & @{text method} \\
wenzelm@28761
   601
    @{method_def best} & : & @{text method} \\
wenzelm@28761
   602
    @{method_def safe} & : & @{text method} \\
wenzelm@28761
   603
    @{method_def clarify} & : & @{text method} \\
wenzelm@26782
   604
  \end{matharray}
wenzelm@26782
   605
wenzelm@26782
   606
  \indexouternonterm{clamod}
wenzelm@26782
   607
  \begin{rail}
wenzelm@26782
   608
    'blast' ('!' ?) nat? (clamod *)
wenzelm@26782
   609
    ;
wenzelm@26782
   610
    ('fast' | 'slow' | 'best' | 'safe' | 'clarify') ('!' ?) (clamod *)
wenzelm@26782
   611
    ;
wenzelm@26782
   612
wenzelm@26782
   613
    clamod: (('intro' | 'elim' | 'dest') ('!' | () | '?') | 'del') ':' thmrefs
wenzelm@26782
   614
    ;
wenzelm@26782
   615
  \end{rail}
wenzelm@26782
   616
wenzelm@28760
   617
  \begin{description}
wenzelm@26782
   618
wenzelm@28760
   619
  \item @{method blast} refers to the classical tableau prover (see
wenzelm@26782
   620
  @{ML blast_tac} in \cite[\S11]{isabelle-ref}).  The optional
wenzelm@26782
   621
  argument specifies a user-supplied search bound (default 20).
wenzelm@26782
   622
wenzelm@28760
   623
  \item @{method fast}, @{method slow}, @{method best}, @{method
wenzelm@28760
   624
  safe}, and @{method clarify} refer to the generic classical
wenzelm@26782
   625
  reasoner.  See @{ML fast_tac}, @{ML slow_tac}, @{ML best_tac}, @{ML
wenzelm@26782
   626
  safe_tac}, and @{ML clarify_tac} in \cite[\S11]{isabelle-ref} for
wenzelm@26782
   627
  more information.
wenzelm@26782
   628
wenzelm@28760
   629
  \end{description}
wenzelm@26782
   630
wenzelm@26782
   631
  Any of the above methods support additional modifiers of the context
wenzelm@26782
   632
  of classical rules.  Their semantics is analogous to the attributes
wenzelm@26782
   633
  given before.  Facts provided by forward chaining are inserted into
wenzelm@26782
   634
  the goal before commencing proof search.  The ``@{text
wenzelm@26782
   635
  "!"}''~argument causes the full context of assumptions to be
wenzelm@26782
   636
  included as well.
wenzelm@26782
   637
*}
wenzelm@26782
   638
wenzelm@26782
   639
wenzelm@27040
   640
subsection {* Combined automated methods \label{sec:clasimp} *}
wenzelm@26782
   641
wenzelm@26782
   642
text {*
wenzelm@26782
   643
  \begin{matharray}{rcl}
wenzelm@28761
   644
    @{method_def auto} & : & @{text method} \\
wenzelm@28761
   645
    @{method_def force} & : & @{text method} \\
wenzelm@28761
   646
    @{method_def clarsimp} & : & @{text method} \\
wenzelm@28761
   647
    @{method_def fastsimp} & : & @{text method} \\
wenzelm@28761
   648
    @{method_def slowsimp} & : & @{text method} \\
wenzelm@28761
   649
    @{method_def bestsimp} & : & @{text method} \\
wenzelm@26782
   650
  \end{matharray}
wenzelm@26782
   651
wenzelm@26782
   652
  \indexouternonterm{clasimpmod}
wenzelm@26782
   653
  \begin{rail}
wenzelm@26782
   654
    'auto' '!'? (nat nat)? (clasimpmod *)
wenzelm@26782
   655
    ;
wenzelm@26782
   656
    ('force' | 'clarsimp' | 'fastsimp' | 'slowsimp' | 'bestsimp') '!'? (clasimpmod *)
wenzelm@26782
   657
    ;
wenzelm@26782
   658
wenzelm@26782
   659
    clasimpmod: ('simp' (() | 'add' | 'del' | 'only') |
wenzelm@26782
   660
      ('cong' | 'split') (() | 'add' | 'del') |
wenzelm@26782
   661
      'iff' (((() | 'add') '?'?) | 'del') |
wenzelm@26782
   662
      (('intro' | 'elim' | 'dest') ('!' | () | '?') | 'del')) ':' thmrefs
wenzelm@26782
   663
  \end{rail}
wenzelm@26782
   664
wenzelm@28760
   665
  \begin{description}
wenzelm@26782
   666
wenzelm@28760
   667
  \item @{method auto}, @{method force}, @{method clarsimp}, @{method
wenzelm@28760
   668
  fastsimp}, @{method slowsimp}, and @{method bestsimp} provide access
wenzelm@28760
   669
  to Isabelle's combined simplification and classical reasoning
wenzelm@26782
   670
  tactics.  These correspond to @{ML auto_tac}, @{ML force_tac}, @{ML
wenzelm@26782
   671
  clarsimp_tac}, and Classical Reasoner tactics with the Simplifier
wenzelm@26782
   672
  added as wrapper, see \cite[\S11]{isabelle-ref} for more
wenzelm@26782
   673
  information.  The modifier arguments correspond to those given in
wenzelm@26782
   674
  \secref{sec:simplifier} and \secref{sec:classical}.  Just note that
wenzelm@26782
   675
  the ones related to the Simplifier are prefixed by \railtterm{simp}
wenzelm@26782
   676
  here.
wenzelm@26782
   677
wenzelm@26782
   678
  Facts provided by forward chaining are inserted into the goal before
wenzelm@26782
   679
  doing the search.  The ``@{text "!"}'' argument causes the full
wenzelm@26782
   680
  context of assumptions to be included as well.
wenzelm@26782
   681
wenzelm@28760
   682
  \end{description}
wenzelm@26782
   683
*}
wenzelm@26782
   684
wenzelm@26782
   685
wenzelm@27040
   686
subsection {* Declaring rules *}
wenzelm@26782
   687
wenzelm@26782
   688
text {*
wenzelm@26782
   689
  \begin{matharray}{rcl}
wenzelm@28761
   690
    @{command_def "print_claset"}@{text "\<^sup>*"} & : & @{text "context \<rightarrow>"} \\
wenzelm@28761
   691
    @{attribute_def intro} & : & @{text attribute} \\
wenzelm@28761
   692
    @{attribute_def elim} & : & @{text attribute} \\
wenzelm@28761
   693
    @{attribute_def dest} & : & @{text attribute} \\
wenzelm@28761
   694
    @{attribute_def rule} & : & @{text attribute} \\
wenzelm@28761
   695
    @{attribute_def iff} & : & @{text attribute} \\
wenzelm@26782
   696
  \end{matharray}
wenzelm@26782
   697
wenzelm@26782
   698
  \begin{rail}
wenzelm@26782
   699
    ('intro' | 'elim' | 'dest') ('!' | () | '?') nat?
wenzelm@26782
   700
    ;
wenzelm@26782
   701
    'rule' 'del'
wenzelm@26782
   702
    ;
wenzelm@26782
   703
    'iff' (((() | 'add') '?'?) | 'del')
wenzelm@26782
   704
    ;
wenzelm@26782
   705
  \end{rail}
wenzelm@26782
   706
wenzelm@28760
   707
  \begin{description}
wenzelm@26782
   708
wenzelm@28760
   709
  \item @{command "print_claset"} prints the collection of rules
wenzelm@26782
   710
  declared to the Classical Reasoner, which is also known as
wenzelm@26782
   711
  ``claset'' internally \cite{isabelle-ref}.
wenzelm@26782
   712
  
wenzelm@28760
   713
  \item @{attribute intro}, @{attribute elim}, and @{attribute dest}
wenzelm@26782
   714
  declare introduction, elimination, and destruction rules,
wenzelm@26782
   715
  respectively.  By default, rules are considered as \emph{unsafe}
wenzelm@26782
   716
  (i.e.\ not applied blindly without backtracking), while ``@{text
wenzelm@26782
   717
  "!"}'' classifies as \emph{safe}.  Rule declarations marked by
wenzelm@26782
   718
  ``@{text "?"}'' coincide with those of Isabelle/Pure, cf.\
wenzelm@26782
   719
  \secref{sec:pure-meth-att} (i.e.\ are only applied in single steps
wenzelm@26782
   720
  of the @{method rule} method).  The optional natural number
wenzelm@26782
   721
  specifies an explicit weight argument, which is ignored by automated
wenzelm@26782
   722
  tools, but determines the search order of single rule steps.
wenzelm@26782
   723
wenzelm@28760
   724
  \item @{attribute rule}~@{text del} deletes introduction,
wenzelm@26782
   725
  elimination, or destruction rules from the context.
wenzelm@26782
   726
wenzelm@28760
   727
  \item @{attribute iff} declares logical equivalences to the
wenzelm@26782
   728
  Simplifier and the Classical reasoner at the same time.
wenzelm@26782
   729
  Non-conditional rules result in a ``safe'' introduction and
wenzelm@26782
   730
  elimination pair; conditional ones are considered ``unsafe''.  Rules
wenzelm@26782
   731
  with negative conclusion are automatically inverted (using @{text
wenzelm@26789
   732
  "\<not>"}-elimination internally).
wenzelm@26782
   733
wenzelm@26782
   734
  The ``@{text "?"}'' version of @{attribute iff} declares rules to
wenzelm@26782
   735
  the Isabelle/Pure context only, and omits the Simplifier
wenzelm@26782
   736
  declaration.
wenzelm@26782
   737
wenzelm@28760
   738
  \end{description}
wenzelm@26782
   739
*}
wenzelm@26782
   740
wenzelm@26782
   741
wenzelm@27040
   742
subsection {* Classical operations *}
wenzelm@26782
   743
wenzelm@26782
   744
text {*
wenzelm@26782
   745
  \begin{matharray}{rcl}
wenzelm@28761
   746
    @{attribute_def swapped} & : & @{text attribute} \\
wenzelm@26782
   747
  \end{matharray}
wenzelm@26782
   748
wenzelm@28760
   749
  \begin{description}
wenzelm@26782
   750
wenzelm@28760
   751
  \item @{attribute swapped} turns an introduction rule into an
wenzelm@26782
   752
  elimination, by resolving with the classical swap principle @{text
wenzelm@26782
   753
  "(\<not> B \<Longrightarrow> A) \<Longrightarrow> (\<not> A \<Longrightarrow> B)"}.
wenzelm@26782
   754
wenzelm@28760
   755
  \end{description}
wenzelm@26782
   756
*}
wenzelm@26782
   757
wenzelm@26782
   758
wenzelm@27044
   759
section {* Object-logic setup \label{sec:object-logic} *}
wenzelm@26790
   760
wenzelm@26790
   761
text {*
wenzelm@26790
   762
  \begin{matharray}{rcl}
wenzelm@28761
   763
    @{command_def "judgment"} & : & @{text "theory \<rightarrow> theory"} \\
wenzelm@28761
   764
    @{method_def atomize} & : & @{text method} \\
wenzelm@28761
   765
    @{attribute_def atomize} & : & @{text attribute} \\
wenzelm@28761
   766
    @{attribute_def rule_format} & : & @{text attribute} \\
wenzelm@28761
   767
    @{attribute_def rulify} & : & @{text attribute} \\
wenzelm@26790
   768
  \end{matharray}
wenzelm@26790
   769
wenzelm@26790
   770
  The very starting point for any Isabelle object-logic is a ``truth
wenzelm@26790
   771
  judgment'' that links object-level statements to the meta-logic
wenzelm@26790
   772
  (with its minimal language of @{text prop} that covers universal
wenzelm@26790
   773
  quantification @{text "\<And>"} and implication @{text "\<Longrightarrow>"}).
wenzelm@26790
   774
wenzelm@26790
   775
  Common object-logics are sufficiently expressive to internalize rule
wenzelm@26790
   776
  statements over @{text "\<And>"} and @{text "\<Longrightarrow>"} within their own
wenzelm@26790
   777
  language.  This is useful in certain situations where a rule needs
wenzelm@26790
   778
  to be viewed as an atomic statement from the meta-level perspective,
wenzelm@26790
   779
  e.g.\ @{text "\<And>x. x \<in> A \<Longrightarrow> P x"} versus @{text "\<forall>x \<in> A. P x"}.
wenzelm@26790
   780
wenzelm@26790
   781
  From the following language elements, only the @{method atomize}
wenzelm@26790
   782
  method and @{attribute rule_format} attribute are occasionally
wenzelm@26790
   783
  required by end-users, the rest is for those who need to setup their
wenzelm@26790
   784
  own object-logic.  In the latter case existing formulations of
wenzelm@26790
   785
  Isabelle/FOL or Isabelle/HOL may be taken as realistic examples.
wenzelm@26790
   786
wenzelm@26790
   787
  Generic tools may refer to the information provided by object-logic
wenzelm@26790
   788
  declarations internally.
wenzelm@26790
   789
wenzelm@26790
   790
  \begin{rail}
wenzelm@26790
   791
    'judgment' constdecl
wenzelm@26790
   792
    ;
wenzelm@26790
   793
    'atomize' ('(' 'full' ')')?
wenzelm@26790
   794
    ;
wenzelm@26790
   795
    'rule\_format' ('(' 'noasm' ')')?
wenzelm@26790
   796
    ;
wenzelm@26790
   797
  \end{rail}
wenzelm@26790
   798
wenzelm@28760
   799
  \begin{description}
wenzelm@26790
   800
  
wenzelm@28760
   801
  \item @{command "judgment"}~@{text "c :: \<sigma> (mx)"} declares constant
wenzelm@28760
   802
  @{text c} as the truth judgment of the current object-logic.  Its
wenzelm@28760
   803
  type @{text \<sigma>} should specify a coercion of the category of
wenzelm@28760
   804
  object-level propositions to @{text prop} of the Pure meta-logic;
wenzelm@28760
   805
  the mixfix annotation @{text "(mx)"} would typically just link the
wenzelm@28760
   806
  object language (internally of syntactic category @{text logic})
wenzelm@28760
   807
  with that of @{text prop}.  Only one @{command "judgment"}
wenzelm@28760
   808
  declaration may be given in any theory development.
wenzelm@26790
   809
  
wenzelm@28760
   810
  \item @{method atomize} (as a method) rewrites any non-atomic
wenzelm@26790
   811
  premises of a sub-goal, using the meta-level equations declared via
wenzelm@26790
   812
  @{attribute atomize} (as an attribute) beforehand.  As a result,
wenzelm@26790
   813
  heavily nested goals become amenable to fundamental operations such
wenzelm@26790
   814
  as resolution (cf.\ the @{method rule} method).  Giving the ``@{text
wenzelm@26790
   815
  "(full)"}'' option here means to turn the whole subgoal into an
wenzelm@26790
   816
  object-statement (if possible), including the outermost parameters
wenzelm@26790
   817
  and assumptions as well.
wenzelm@26790
   818
wenzelm@26790
   819
  A typical collection of @{attribute atomize} rules for a particular
wenzelm@26790
   820
  object-logic would provide an internalization for each of the
wenzelm@26790
   821
  connectives of @{text "\<And>"}, @{text "\<Longrightarrow>"}, and @{text "\<equiv>"}.
wenzelm@26790
   822
  Meta-level conjunction should be covered as well (this is
wenzelm@26790
   823
  particularly important for locales, see \secref{sec:locale}).
wenzelm@26790
   824
wenzelm@28760
   825
  \item @{attribute rule_format} rewrites a theorem by the equalities
wenzelm@28760
   826
  declared as @{attribute rulify} rules in the current object-logic.
wenzelm@28760
   827
  By default, the result is fully normalized, including assumptions
wenzelm@28760
   828
  and conclusions at any depth.  The @{text "(no_asm)"} option
wenzelm@28760
   829
  restricts the transformation to the conclusion of a rule.
wenzelm@26790
   830
wenzelm@26790
   831
  In common object-logics (HOL, FOL, ZF), the effect of @{attribute
wenzelm@26790
   832
  rule_format} is to replace (bounded) universal quantification
wenzelm@26790
   833
  (@{text "\<forall>"}) and implication (@{text "\<longrightarrow>"}) by the corresponding
wenzelm@26790
   834
  rule statements over @{text "\<And>"} and @{text "\<Longrightarrow>"}.
wenzelm@26790
   835
wenzelm@28760
   836
  \end{description}
wenzelm@26790
   837
*}
wenzelm@26790
   838
wenzelm@26782
   839
end