doc-src/IsarRef/Thy/Generic.thy
author wenzelm
Thu May 05 23:23:02 2011 +0200 (2011-05-05)
changeset 42705 528a2ba8fa74
parent 42704 3f19e324ff59
child 42925 c6c4f997ad87
permissions -rw-r--r--
tuned some syntax names;
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theory Generic
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imports Base 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 \label{sec:config} *}
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text {* Isabelle/Pure maintains a record of named configuration
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  options within the theory or proof context, with values of type
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  @{ML_type bool}, @{ML_type int}, @{ML_type real}, or @{ML_type
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  string}.  Tools may declare options in ML, and then refer to these
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  values (relative to the context).  Thus global reference variables
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  are easily avoided.  The user may change the value of a
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  configuration option by means of an associated attribute of the same
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  name.  This form of context declaration works particularly well with
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  commands such as @{command "declare"} or @{command "using"} like
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  this:
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*}
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declare [[show_main_goal = false]]
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notepad
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begin
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  note [[show_main_goal = true]]
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end
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text {* 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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  @{rail "
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    @{syntax name} ('=' ('true' | 'false' | @{syntax int} | @{syntax float} | @{syntax name}))?
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  "}
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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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  @{rail "
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    (@@{method fold} | @@{method unfold} | @@{method insert}) @{syntax thmrefs}
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    ;
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    (@@{method erule} | @@{method drule} | @@{method frule})
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      ('(' @{syntax nat} ')')? @{syntax thmrefs}
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  "}
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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
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  drule}~@{text "a\<^sub>1 \<dots> a\<^sub>n"}, and @{method frule}~@{text
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  "a\<^sub>1 \<dots> a\<^sub>n"} are similar to the basic @{method rule}
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  method (see \secref{sec:pure-meth-att}), but apply rules by
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  elim-resolution, destruct-resolution, and forward-resolution,
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  respectively \cite{isabelle-implementation}.  The optional natural
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  number argument (default 0) specifies additional assumption steps to
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  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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  @{rail "
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    @@{attribute tagged} @{syntax name} @{syntax name}
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    ;
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    @@{attribute untagged} @{syntax name}
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    ;
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    (@@{attribute THEN} | @@{attribute COMP}) ('[' @{syntax nat} ']')? @{syntax thmref}
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    ;
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    (@@{attribute unfolded} | @@{attribute folded}) @{syntax thmrefs}
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    ;
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    @@{attribute rotated} @{syntax int}?
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  "}
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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 "op RS"} and
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  @{ML "op COMP"} in \cite{isabelle-implementation}).
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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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  @{rail "
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    @@{method subst} ('(' 'asm' ')')? \\ ('(' (@{syntax nat}+) ')')? @{syntax thmref}
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    ;
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    @@{method split} ('(' 'asm' ')')? @{syntax thmrefs}
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  "}
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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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  @{rail "
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    (@@{method rule_tac} | @@{method erule_tac} | @@{method drule_tac} |
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      @@{method frule_tac} | @@{method cut_tac} | @@{method thin_tac}) @{syntax goal_spec}? \\
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    ( dynamic_insts @'in' @{syntax thmref} | @{syntax thmrefs} )
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    ;
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    @@{method subgoal_tac} @{syntax goal_spec}? (@{syntax prop} +)
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    ;
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    @@{method rename_tac} @{syntax goal_spec}? (@{syntax name} +)
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    ;
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    @@{method rotate_tac} @{syntax goal_spec}? @{syntax int}?
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    ;
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    (@@{method tactic} | @@{method raw_tactic}) @{syntax text}
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    ;
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    dynamic_insts: ((@{syntax name} '=' @{syntax term}) + @'and')
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  "}
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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{isabelle-implementation})
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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{isabelle-implementation}).
wenzelm@26782
   319
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   320
  \item @{method cut_tac} inserts facts into the proof state as
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   321
  assumption of a subgoal, see also @{ML Tactic.cut_facts_tac} in
wenzelm@30397
   322
  \cite{isabelle-implementation}.  Note that the scope of schematic
wenzelm@26782
   323
  variables is spread over the main goal statement.  Instantiations
wenzelm@28760
   324
  may be given as well, see also ML tactic @{ML cut_inst_tac} in
wenzelm@30397
   325
  \cite{isabelle-implementation}.
wenzelm@26782
   326
wenzelm@28760
   327
  \item @{method thin_tac}~@{text \<phi>} deletes the specified assumption
wenzelm@28760
   328
  from a subgoal; note that @{text \<phi>} may contain schematic variables.
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   329
  See also @{ML thin_tac} in \cite{isabelle-implementation}.
wenzelm@28760
   330
wenzelm@28760
   331
  \item @{method subgoal_tac}~@{text \<phi>} adds @{text \<phi>} as an
wenzelm@27239
   332
  assumption to a subgoal.  See also @{ML subgoal_tac} and @{ML
wenzelm@30397
   333
  subgoals_tac} in \cite{isabelle-implementation}.
wenzelm@26782
   334
wenzelm@28760
   335
  \item @{method rename_tac}~@{text "x\<^sub>1 \<dots> x\<^sub>n"} renames parameters of a
wenzelm@28760
   336
  goal according to the list @{text "x\<^sub>1, \<dots>, x\<^sub>n"}, which refers to the
wenzelm@28760
   337
  \emph{suffix} of variables.
wenzelm@26782
   338
wenzelm@28760
   339
  \item @{method rotate_tac}~@{text n} rotates the assumptions of a
wenzelm@26782
   340
  goal by @{text n} positions: from right to left if @{text n} is
wenzelm@26782
   341
  positive, and from left to right if @{text n} is negative; the
wenzelm@26782
   342
  default value is 1.  See also @{ML rotate_tac} in
wenzelm@30397
   343
  \cite{isabelle-implementation}.
wenzelm@26782
   344
wenzelm@28760
   345
  \item @{method tactic}~@{text "text"} produces a proof method from
wenzelm@26782
   346
  any ML text of type @{ML_type tactic}.  Apart from the usual ML
wenzelm@27223
   347
  environment and the current proof context, the ML code may refer to
wenzelm@27223
   348
  the locally bound values @{ML_text facts}, which indicates any
wenzelm@27223
   349
  current facts used for forward-chaining.
wenzelm@26782
   350
wenzelm@28760
   351
  \item @{method raw_tactic} is similar to @{method tactic}, but
wenzelm@27223
   352
  presents the goal state in its raw internal form, where simultaneous
wenzelm@27223
   353
  subgoals appear as conjunction of the logical framework instead of
wenzelm@27223
   354
  the usual split into several subgoals.  While feature this is useful
wenzelm@27223
   355
  for debugging of complex method definitions, it should not never
wenzelm@27223
   356
  appear in production theories.
wenzelm@26782
   357
wenzelm@28760
   358
  \end{description}
wenzelm@26782
   359
*}
wenzelm@26782
   360
wenzelm@26782
   361
wenzelm@27040
   362
section {* The Simplifier \label{sec:simplifier} *}
wenzelm@26782
   363
wenzelm@27040
   364
subsection {* Simplification methods *}
wenzelm@26782
   365
wenzelm@26782
   366
text {*
wenzelm@26782
   367
  \begin{matharray}{rcl}
wenzelm@28761
   368
    @{method_def simp} & : & @{text method} \\
wenzelm@28761
   369
    @{method_def simp_all} & : & @{text method} \\
wenzelm@26782
   370
  \end{matharray}
wenzelm@26782
   371
wenzelm@42596
   372
  @{rail "
wenzelm@42596
   373
    (@@{method simp} | @@{method simp_all}) opt? (@{syntax simpmod} * )
wenzelm@26782
   374
    ;
wenzelm@26782
   375
wenzelm@40255
   376
    opt: '(' ('no_asm' | 'no_asm_simp' | 'no_asm_use' | 'asm_lr' ) ')'
wenzelm@26782
   377
    ;
wenzelm@42596
   378
    @{syntax_def simpmod}: ('add' | 'del' | 'only' | 'cong' (() | 'add' | 'del') |
wenzelm@42596
   379
      'split' (() | 'add' | 'del')) ':' @{syntax thmrefs}
wenzelm@42596
   380
  "}
wenzelm@26782
   381
wenzelm@28760
   382
  \begin{description}
wenzelm@26782
   383
wenzelm@28760
   384
  \item @{method simp} invokes the Simplifier, after declaring
wenzelm@26782
   385
  additional rules according to the arguments given.  Note that the
wenzelm@42596
   386
  @{text only} modifier first removes all other rewrite rules,
wenzelm@26782
   387
  congruences, and looper tactics (including splits), and then behaves
wenzelm@42596
   388
  like @{text add}.
wenzelm@26782
   389
wenzelm@42596
   390
  \medskip The @{text cong} modifiers add or delete Simplifier
wenzelm@26782
   391
  congruence rules (see also \cite{isabelle-ref}), the default is to
wenzelm@26782
   392
  add.
wenzelm@26782
   393
wenzelm@42596
   394
  \medskip The @{text split} modifiers add or delete rules for the
wenzelm@26782
   395
  Splitter (see also \cite{isabelle-ref}), the default is to add.
wenzelm@26782
   396
  This works only if the Simplifier method has been properly setup to
wenzelm@26782
   397
  include the Splitter (all major object logics such HOL, HOLCF, FOL,
wenzelm@26782
   398
  ZF do this already).
wenzelm@26782
   399
wenzelm@28760
   400
  \item @{method simp_all} is similar to @{method simp}, but acts on
wenzelm@26782
   401
  all goals (backwards from the last to the first one).
wenzelm@26782
   402
wenzelm@28760
   403
  \end{description}
wenzelm@26782
   404
wenzelm@26782
   405
  By default the Simplifier methods take local assumptions fully into
wenzelm@26782
   406
  account, using equational assumptions in the subsequent
wenzelm@26782
   407
  normalization process, or simplifying assumptions themselves (cf.\
wenzelm@30397
   408
  @{ML asm_full_simp_tac} in \cite{isabelle-ref}).  In structured
wenzelm@30397
   409
  proofs this is usually quite well behaved in practice: just the
wenzelm@30397
   410
  local premises of the actual goal are involved, additional facts may
wenzelm@30397
   411
  be inserted via explicit forward-chaining (via @{command "then"},
wenzelm@35613
   412
  @{command "from"}, @{command "using"} etc.).
wenzelm@26782
   413
wenzelm@26782
   414
  Additional Simplifier options may be specified to tune the behavior
wenzelm@26782
   415
  further (mostly for unstructured scripts with many accidental local
wenzelm@26782
   416
  facts): ``@{text "(no_asm)"}'' means assumptions are ignored
wenzelm@26782
   417
  completely (cf.\ @{ML simp_tac}), ``@{text "(no_asm_simp)"}'' means
wenzelm@26782
   418
  assumptions are used in the simplification of the conclusion but are
wenzelm@26782
   419
  not themselves simplified (cf.\ @{ML asm_simp_tac}), and ``@{text
wenzelm@26782
   420
  "(no_asm_use)"}'' means assumptions are simplified but are not used
wenzelm@26782
   421
  in the simplification of each other or the conclusion (cf.\ @{ML
wenzelm@26782
   422
  full_simp_tac}).  For compatibility reasons, there is also an option
wenzelm@26782
   423
  ``@{text "(asm_lr)"}'', which means that an assumption is only used
wenzelm@26782
   424
  for simplifying assumptions which are to the right of it (cf.\ @{ML
wenzelm@26782
   425
  asm_lr_simp_tac}).
wenzelm@26782
   426
wenzelm@27092
   427
  The configuration option @{text "depth_limit"} limits the number of
wenzelm@26782
   428
  recursive invocations of the simplifier during conditional
wenzelm@26782
   429
  rewriting.
wenzelm@26782
   430
wenzelm@26782
   431
  \medskip The Splitter package is usually configured to work as part
wenzelm@26782
   432
  of the Simplifier.  The effect of repeatedly applying @{ML
wenzelm@26782
   433
  split_tac} can be simulated by ``@{text "(simp only: split:
wenzelm@26782
   434
  a\<^sub>1 \<dots> a\<^sub>n)"}''.  There is also a separate @{text split}
wenzelm@26782
   435
  method available for single-step case splitting.
wenzelm@26782
   436
*}
wenzelm@26782
   437
wenzelm@26782
   438
wenzelm@27040
   439
subsection {* Declaring rules *}
wenzelm@26782
   440
wenzelm@26782
   441
text {*
wenzelm@26782
   442
  \begin{matharray}{rcl}
wenzelm@28761
   443
    @{command_def "print_simpset"}@{text "\<^sup>*"} & : & @{text "context \<rightarrow>"} \\
wenzelm@28761
   444
    @{attribute_def simp} & : & @{text attribute} \\
wenzelm@28761
   445
    @{attribute_def cong} & : & @{text attribute} \\
wenzelm@28761
   446
    @{attribute_def split} & : & @{text attribute} \\
wenzelm@26782
   447
  \end{matharray}
wenzelm@26782
   448
wenzelm@42596
   449
  @{rail "
wenzelm@42596
   450
    (@@{attribute simp} | @@{attribute cong} | @@{attribute split}) (() | 'add' | 'del')
wenzelm@42596
   451
  "}
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@42596
   477
  @{rail "
wenzelm@42596
   478
    @@{command simproc_setup} @{syntax name} '(' (@{syntax term} + '|') ')' '='
wenzelm@42596
   479
      @{syntax text} \\ (@'identifier' (@{syntax nameref}+))?
wenzelm@26782
   480
    ;
wenzelm@26782
   481
wenzelm@42596
   482
    @@{attribute simproc} (('add' ':')? | 'del' ':') (@{syntax name}+)
wenzelm@42596
   483
  "}
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@42596
   522
  @{rail "
wenzelm@42596
   523
    @@{attribute simplified} opt? @{syntax thmrefs}?
wenzelm@26782
   524
    ;
wenzelm@26782
   525
wenzelm@40255
   526
    opt: '(' ('no_asm' | 'no_asm_simp' | 'no_asm_use') ')'
wenzelm@42596
   527
  "}
wenzelm@26782
   528
wenzelm@28760
   529
  \begin{description}
wenzelm@26782
   530
  
wenzelm@28760
   531
  \item @{attribute simplified}~@{text "a\<^sub>1 \<dots> a\<^sub>n"} causes a theorem to
wenzelm@28760
   532
  be simplified, either by exactly the specified rules @{text "a\<^sub>1, \<dots>,
wenzelm@28760
   533
  a\<^sub>n"}, or the implicit Simplifier context if no arguments are given.
wenzelm@28760
   534
  The result is fully simplified by default, including assumptions and
wenzelm@28760
   535
  conclusion; the options @{text no_asm} etc.\ tune the Simplifier in
wenzelm@28760
   536
  the same way as the for the @{text simp} method.
wenzelm@26782
   537
wenzelm@26782
   538
  Note that forward simplification restricts the simplifier to its
wenzelm@26782
   539
  most basic operation of term rewriting; solver and looper tactics
wenzelm@26782
   540
  \cite{isabelle-ref} are \emph{not} involved here.  The @{text
wenzelm@26782
   541
  simplified} attribute should be only rarely required under normal
wenzelm@26782
   542
  circumstances.
wenzelm@26782
   543
wenzelm@28760
   544
  \end{description}
wenzelm@26782
   545
*}
wenzelm@26782
   546
wenzelm@26782
   547
wenzelm@27040
   548
section {* The Classical Reasoner \label{sec:classical} *}
wenzelm@26782
   549
wenzelm@27040
   550
subsection {* Basic methods *}
wenzelm@26782
   551
wenzelm@26782
   552
text {*
wenzelm@26782
   553
  \begin{matharray}{rcl}
wenzelm@28761
   554
    @{method_def rule} & : & @{text method} \\
wenzelm@28761
   555
    @{method_def contradiction} & : & @{text method} \\
wenzelm@28761
   556
    @{method_def intro} & : & @{text method} \\
wenzelm@28761
   557
    @{method_def elim} & : & @{text method} \\
wenzelm@26782
   558
  \end{matharray}
wenzelm@26782
   559
wenzelm@42596
   560
  @{rail "
wenzelm@42596
   561
    (@@{method rule} | @@{method intro} | @@{method elim}) @{syntax thmrefs}?
wenzelm@42596
   562
  "}
wenzelm@26782
   563
wenzelm@28760
   564
  \begin{description}
wenzelm@26782
   565
wenzelm@28760
   566
  \item @{method rule} as offered by the Classical Reasoner is a
wenzelm@26782
   567
  refinement over the primitive one (see \secref{sec:pure-meth-att}).
wenzelm@26782
   568
  Both versions essentially work the same, but the classical version
wenzelm@26782
   569
  observes the classical rule context in addition to that of
wenzelm@26782
   570
  Isabelle/Pure.
wenzelm@26782
   571
wenzelm@26782
   572
  Common object logics (HOL, ZF, etc.) declare a rich collection of
wenzelm@26782
   573
  classical rules (even if these would qualify as intuitionistic
wenzelm@26782
   574
  ones), but only few declarations to the rule context of
wenzelm@26782
   575
  Isabelle/Pure (\secref{sec:pure-meth-att}).
wenzelm@26782
   576
wenzelm@28760
   577
  \item @{method contradiction} solves some goal by contradiction,
wenzelm@26782
   578
  deriving any result from both @{text "\<not> A"} and @{text A}.  Chained
wenzelm@26782
   579
  facts, which are guaranteed to participate, may appear in either
wenzelm@26782
   580
  order.
wenzelm@26782
   581
wenzelm@28760
   582
  \item @{method intro} and @{method elim} repeatedly refine some goal
wenzelm@28760
   583
  by intro- or elim-resolution, after having inserted any chained
wenzelm@26901
   584
  facts.  Exactly the rules given as arguments are taken into account;
wenzelm@26901
   585
  this allows fine-tuned decomposition of a proof problem, in contrast
wenzelm@26901
   586
  to common automated tools.
wenzelm@26782
   587
wenzelm@28760
   588
  \end{description}
wenzelm@26782
   589
*}
wenzelm@26782
   590
wenzelm@26782
   591
wenzelm@27040
   592
subsection {* Automated methods *}
wenzelm@26782
   593
wenzelm@26782
   594
text {*
wenzelm@26782
   595
  \begin{matharray}{rcl}
wenzelm@28761
   596
    @{method_def blast} & : & @{text method} \\
wenzelm@28761
   597
    @{method_def fast} & : & @{text method} \\
wenzelm@28761
   598
    @{method_def slow} & : & @{text method} \\
wenzelm@28761
   599
    @{method_def best} & : & @{text method} \\
wenzelm@28761
   600
    @{method_def safe} & : & @{text method} \\
wenzelm@28761
   601
    @{method_def clarify} & : & @{text method} \\
wenzelm@26782
   602
  \end{matharray}
wenzelm@26782
   603
wenzelm@42596
   604
  @{rail "
wenzelm@42596
   605
    @@{method blast} @{syntax nat}? (@{syntax clamod} * )
wenzelm@26782
   606
    ;
wenzelm@42596
   607
    (@@{method fast} | @@{method slow} | @@{method best} | @@{method safe} | @@{method clarify})
wenzelm@42596
   608
      (@{syntax clamod} * )
wenzelm@26782
   609
    ;
wenzelm@26782
   610
wenzelm@42596
   611
    @{syntax_def clamod}:
wenzelm@42596
   612
      (('intro' | 'elim' | 'dest') ('!' | () | '?') | 'del') ':' @{syntax thmrefs}
wenzelm@42596
   613
  "}
wenzelm@26782
   614
wenzelm@28760
   615
  \begin{description}
wenzelm@26782
   616
wenzelm@28760
   617
  \item @{method blast} refers to the classical tableau prover (see
wenzelm@30397
   618
  @{ML blast_tac} in \cite{isabelle-ref}).  The optional argument
wenzelm@30397
   619
  specifies a user-supplied search bound (default 20).
wenzelm@26782
   620
wenzelm@28760
   621
  \item @{method fast}, @{method slow}, @{method best}, @{method
wenzelm@28760
   622
  safe}, and @{method clarify} refer to the generic classical
wenzelm@26782
   623
  reasoner.  See @{ML fast_tac}, @{ML slow_tac}, @{ML best_tac}, @{ML
wenzelm@30397
   624
  safe_tac}, and @{ML clarify_tac} in \cite{isabelle-ref} for more
wenzelm@30397
   625
  information.
wenzelm@26782
   626
wenzelm@28760
   627
  \end{description}
wenzelm@26782
   628
wenzelm@26782
   629
  Any of the above methods support additional modifiers of the context
wenzelm@26782
   630
  of classical rules.  Their semantics is analogous to the attributes
wenzelm@26782
   631
  given before.  Facts provided by forward chaining are inserted into
wenzelm@35613
   632
  the goal before commencing proof search.
wenzelm@26782
   633
*}
wenzelm@26782
   634
wenzelm@26782
   635
wenzelm@27040
   636
subsection {* Combined automated methods \label{sec:clasimp} *}
wenzelm@26782
   637
wenzelm@26782
   638
text {*
wenzelm@26782
   639
  \begin{matharray}{rcl}
wenzelm@28761
   640
    @{method_def auto} & : & @{text method} \\
wenzelm@28761
   641
    @{method_def force} & : & @{text method} \\
wenzelm@28761
   642
    @{method_def clarsimp} & : & @{text method} \\
wenzelm@28761
   643
    @{method_def fastsimp} & : & @{text method} \\
wenzelm@28761
   644
    @{method_def slowsimp} & : & @{text method} \\
wenzelm@28761
   645
    @{method_def bestsimp} & : & @{text method} \\
wenzelm@26782
   646
  \end{matharray}
wenzelm@26782
   647
wenzelm@42596
   648
  @{rail "
wenzelm@42596
   649
    @@{method auto} (@{syntax nat} @{syntax nat})? (@{syntax clasimpmod} * )
wenzelm@26782
   650
    ;
wenzelm@42596
   651
    (@@{method force} | @@{method clarsimp} | @@{method fastsimp} | @@{method slowsimp} |
wenzelm@42596
   652
      @@{method bestsimp}) (@{syntax clasimpmod} * )
wenzelm@26782
   653
    ;
wenzelm@26782
   654
wenzelm@42596
   655
    @{syntax_def clasimpmod}: ('simp' (() | 'add' | 'del' | 'only') |
wenzelm@26782
   656
      ('cong' | 'split') (() | 'add' | 'del') |
wenzelm@26782
   657
      'iff' (((() | 'add') '?'?) | 'del') |
wenzelm@42596
   658
      (('intro' | 'elim' | 'dest') ('!' | () | '?') | 'del')) ':' @{syntax thmrefs}
wenzelm@42596
   659
  "}
wenzelm@26782
   660
wenzelm@28760
   661
  \begin{description}
wenzelm@26782
   662
wenzelm@28760
   663
  \item @{method auto}, @{method force}, @{method clarsimp}, @{method
wenzelm@28760
   664
  fastsimp}, @{method slowsimp}, and @{method bestsimp} provide access
wenzelm@28760
   665
  to Isabelle's combined simplification and classical reasoning
wenzelm@26782
   666
  tactics.  These correspond to @{ML auto_tac}, @{ML force_tac}, @{ML
wenzelm@26782
   667
  clarsimp_tac}, and Classical Reasoner tactics with the Simplifier
wenzelm@30397
   668
  added as wrapper, see \cite{isabelle-ref} for more information.  The
wenzelm@30397
   669
  modifier arguments correspond to those given in
wenzelm@26782
   670
  \secref{sec:simplifier} and \secref{sec:classical}.  Just note that
wenzelm@42596
   671
  the ones related to the Simplifier are prefixed by @{text simp}
wenzelm@26782
   672
  here.
wenzelm@26782
   673
wenzelm@26782
   674
  Facts provided by forward chaining are inserted into the goal before
wenzelm@35613
   675
  doing the search.
wenzelm@26782
   676
wenzelm@28760
   677
  \end{description}
wenzelm@26782
   678
*}
wenzelm@26782
   679
wenzelm@26782
   680
wenzelm@27040
   681
subsection {* Declaring rules *}
wenzelm@26782
   682
wenzelm@26782
   683
text {*
wenzelm@26782
   684
  \begin{matharray}{rcl}
wenzelm@28761
   685
    @{command_def "print_claset"}@{text "\<^sup>*"} & : & @{text "context \<rightarrow>"} \\
wenzelm@28761
   686
    @{attribute_def intro} & : & @{text attribute} \\
wenzelm@28761
   687
    @{attribute_def elim} & : & @{text attribute} \\
wenzelm@28761
   688
    @{attribute_def dest} & : & @{text attribute} \\
wenzelm@28761
   689
    @{attribute_def rule} & : & @{text attribute} \\
wenzelm@28761
   690
    @{attribute_def iff} & : & @{text attribute} \\
wenzelm@26782
   691
  \end{matharray}
wenzelm@26782
   692
wenzelm@42596
   693
  @{rail "
wenzelm@42596
   694
    (@@{attribute intro} | @@{attribute elim} | @@{attribute dest}) ('!' | () | '?') @{syntax nat}?
wenzelm@26782
   695
    ;
wenzelm@42596
   696
    @@{attribute rule} 'del'
wenzelm@26782
   697
    ;
wenzelm@42596
   698
    @@{attribute iff} (((() | 'add') '?'?) | 'del')
wenzelm@42596
   699
  "}
wenzelm@26782
   700
wenzelm@28760
   701
  \begin{description}
wenzelm@26782
   702
wenzelm@28760
   703
  \item @{command "print_claset"} prints the collection of rules
wenzelm@26782
   704
  declared to the Classical Reasoner, which is also known as
wenzelm@26782
   705
  ``claset'' internally \cite{isabelle-ref}.
wenzelm@26782
   706
  
wenzelm@28760
   707
  \item @{attribute intro}, @{attribute elim}, and @{attribute dest}
wenzelm@26782
   708
  declare introduction, elimination, and destruction rules,
wenzelm@26782
   709
  respectively.  By default, rules are considered as \emph{unsafe}
wenzelm@26782
   710
  (i.e.\ not applied blindly without backtracking), while ``@{text
wenzelm@26782
   711
  "!"}'' classifies as \emph{safe}.  Rule declarations marked by
wenzelm@26782
   712
  ``@{text "?"}'' coincide with those of Isabelle/Pure, cf.\
wenzelm@26782
   713
  \secref{sec:pure-meth-att} (i.e.\ are only applied in single steps
wenzelm@26782
   714
  of the @{method rule} method).  The optional natural number
wenzelm@26782
   715
  specifies an explicit weight argument, which is ignored by automated
wenzelm@26782
   716
  tools, but determines the search order of single rule steps.
wenzelm@26782
   717
wenzelm@28760
   718
  \item @{attribute rule}~@{text del} deletes introduction,
wenzelm@26782
   719
  elimination, or destruction rules from the context.
wenzelm@26782
   720
wenzelm@28760
   721
  \item @{attribute iff} declares logical equivalences to the
wenzelm@26782
   722
  Simplifier and the Classical reasoner at the same time.
wenzelm@26782
   723
  Non-conditional rules result in a ``safe'' introduction and
wenzelm@26782
   724
  elimination pair; conditional ones are considered ``unsafe''.  Rules
wenzelm@26782
   725
  with negative conclusion are automatically inverted (using @{text
wenzelm@26789
   726
  "\<not>"}-elimination internally).
wenzelm@26782
   727
wenzelm@26782
   728
  The ``@{text "?"}'' version of @{attribute iff} declares rules to
wenzelm@26782
   729
  the Isabelle/Pure context only, and omits the Simplifier
wenzelm@26782
   730
  declaration.
wenzelm@26782
   731
wenzelm@28760
   732
  \end{description}
wenzelm@26782
   733
*}
wenzelm@26782
   734
wenzelm@26782
   735
wenzelm@27040
   736
subsection {* Classical operations *}
wenzelm@26782
   737
wenzelm@26782
   738
text {*
wenzelm@26782
   739
  \begin{matharray}{rcl}
wenzelm@28761
   740
    @{attribute_def swapped} & : & @{text attribute} \\
wenzelm@26782
   741
  \end{matharray}
wenzelm@26782
   742
wenzelm@28760
   743
  \begin{description}
wenzelm@26782
   744
wenzelm@28760
   745
  \item @{attribute swapped} turns an introduction rule into an
wenzelm@26782
   746
  elimination, by resolving with the classical swap principle @{text
wenzelm@26782
   747
  "(\<not> B \<Longrightarrow> A) \<Longrightarrow> (\<not> A \<Longrightarrow> B)"}.
wenzelm@26782
   748
wenzelm@28760
   749
  \end{description}
wenzelm@26782
   750
*}
wenzelm@26782
   751
wenzelm@26782
   752
wenzelm@27044
   753
section {* Object-logic setup \label{sec:object-logic} *}
wenzelm@26790
   754
wenzelm@26790
   755
text {*
wenzelm@26790
   756
  \begin{matharray}{rcl}
wenzelm@28761
   757
    @{command_def "judgment"} & : & @{text "theory \<rightarrow> theory"} \\
wenzelm@28761
   758
    @{method_def atomize} & : & @{text method} \\
wenzelm@28761
   759
    @{attribute_def atomize} & : & @{text attribute} \\
wenzelm@28761
   760
    @{attribute_def rule_format} & : & @{text attribute} \\
wenzelm@28761
   761
    @{attribute_def rulify} & : & @{text attribute} \\
wenzelm@26790
   762
  \end{matharray}
wenzelm@26790
   763
wenzelm@26790
   764
  The very starting point for any Isabelle object-logic is a ``truth
wenzelm@26790
   765
  judgment'' that links object-level statements to the meta-logic
wenzelm@26790
   766
  (with its minimal language of @{text prop} that covers universal
wenzelm@26790
   767
  quantification @{text "\<And>"} and implication @{text "\<Longrightarrow>"}).
wenzelm@26790
   768
wenzelm@26790
   769
  Common object-logics are sufficiently expressive to internalize rule
wenzelm@26790
   770
  statements over @{text "\<And>"} and @{text "\<Longrightarrow>"} within their own
wenzelm@26790
   771
  language.  This is useful in certain situations where a rule needs
wenzelm@26790
   772
  to be viewed as an atomic statement from the meta-level perspective,
wenzelm@26790
   773
  e.g.\ @{text "\<And>x. x \<in> A \<Longrightarrow> P x"} versus @{text "\<forall>x \<in> A. P x"}.
wenzelm@26790
   774
wenzelm@26790
   775
  From the following language elements, only the @{method atomize}
wenzelm@26790
   776
  method and @{attribute rule_format} attribute are occasionally
wenzelm@26790
   777
  required by end-users, the rest is for those who need to setup their
wenzelm@26790
   778
  own object-logic.  In the latter case existing formulations of
wenzelm@26790
   779
  Isabelle/FOL or Isabelle/HOL may be taken as realistic examples.
wenzelm@26790
   780
wenzelm@26790
   781
  Generic tools may refer to the information provided by object-logic
wenzelm@26790
   782
  declarations internally.
wenzelm@26790
   783
wenzelm@42596
   784
  @{rail "
wenzelm@42596
   785
    @@{command judgment} @{syntax constdecl}
wenzelm@26790
   786
    ;
wenzelm@42596
   787
    @@{attribute atomize} ('(' 'full' ')')?
wenzelm@26790
   788
    ;
wenzelm@42596
   789
    @@{attribute rule_format} ('(' 'noasm' ')')?
wenzelm@42596
   790
  "}
wenzelm@26790
   791
wenzelm@28760
   792
  \begin{description}
wenzelm@26790
   793
  
wenzelm@28760
   794
  \item @{command "judgment"}~@{text "c :: \<sigma> (mx)"} declares constant
wenzelm@28760
   795
  @{text c} as the truth judgment of the current object-logic.  Its
wenzelm@28760
   796
  type @{text \<sigma>} should specify a coercion of the category of
wenzelm@28760
   797
  object-level propositions to @{text prop} of the Pure meta-logic;
wenzelm@28760
   798
  the mixfix annotation @{text "(mx)"} would typically just link the
wenzelm@28760
   799
  object language (internally of syntactic category @{text logic})
wenzelm@28760
   800
  with that of @{text prop}.  Only one @{command "judgment"}
wenzelm@28760
   801
  declaration may be given in any theory development.
wenzelm@26790
   802
  
wenzelm@28760
   803
  \item @{method atomize} (as a method) rewrites any non-atomic
wenzelm@26790
   804
  premises of a sub-goal, using the meta-level equations declared via
wenzelm@26790
   805
  @{attribute atomize} (as an attribute) beforehand.  As a result,
wenzelm@26790
   806
  heavily nested goals become amenable to fundamental operations such
wenzelm@42626
   807
  as resolution (cf.\ the @{method (Pure) rule} method).  Giving the ``@{text
wenzelm@26790
   808
  "(full)"}'' option here means to turn the whole subgoal into an
wenzelm@26790
   809
  object-statement (if possible), including the outermost parameters
wenzelm@26790
   810
  and assumptions as well.
wenzelm@26790
   811
wenzelm@26790
   812
  A typical collection of @{attribute atomize} rules for a particular
wenzelm@26790
   813
  object-logic would provide an internalization for each of the
wenzelm@26790
   814
  connectives of @{text "\<And>"}, @{text "\<Longrightarrow>"}, and @{text "\<equiv>"}.
wenzelm@26790
   815
  Meta-level conjunction should be covered as well (this is
wenzelm@26790
   816
  particularly important for locales, see \secref{sec:locale}).
wenzelm@26790
   817
wenzelm@28760
   818
  \item @{attribute rule_format} rewrites a theorem by the equalities
wenzelm@28760
   819
  declared as @{attribute rulify} rules in the current object-logic.
wenzelm@28760
   820
  By default, the result is fully normalized, including assumptions
wenzelm@28760
   821
  and conclusions at any depth.  The @{text "(no_asm)"} option
wenzelm@28760
   822
  restricts the transformation to the conclusion of a rule.
wenzelm@26790
   823
wenzelm@26790
   824
  In common object-logics (HOL, FOL, ZF), the effect of @{attribute
wenzelm@26790
   825
  rule_format} is to replace (bounded) universal quantification
wenzelm@26790
   826
  (@{text "\<forall>"}) and implication (@{text "\<longrightarrow>"}) by the corresponding
wenzelm@26790
   827
  rule statements over @{text "\<And>"} and @{text "\<Longrightarrow>"}.
wenzelm@26790
   828
wenzelm@28760
   829
  \end{description}
wenzelm@26790
   830
*}
wenzelm@26790
   831
wenzelm@26782
   832
end