\chapter{Generic Tools and Packages}\label{ch:gen-tools}

\section{Axiomatic Type Classes}\label{sec:axclass}

%FIXME

% - qualified names

% - class intro rules;

% - class axioms;

\indexisarcmd{axclass}\indexisarcmd{instance}\indexisarmeth{intro-classes}

\begin{matharray}{rcl}

  \isarcmd{axclass} & : & \isartrans{theory}{theory} \\

  \isarcmd{instance} & : & \isartrans{theory}{proof(prove)} \\

  intro_classes & : & \isarmeth \\

\end{matharray}

Axiomatic type classes are provided by Isabelle/Pure as a \emph{definitional}

interface to type classes (cf.~\S\ref{sec:classes}).  Thus any object logic

may make use of this light-weight mechanism of abstract theories

\cite{Wenzel:1997:TPHOL}.  There is also a tutorial on using axiomatic type

classes in isabelle \cite{isabelle-axclass} that is part of the standard

Isabelle documentation.

\begin{rail}

  'axclass' classdecl (axmdecl prop comment? +)

  ;

  'instance' (nameref '<' nameref | nameref '::' simplearity) comment?

  ;

\end{rail}

\begin{descr}

\item [$\isarkeyword{axclass}~c < \vec c~axms$] defines an axiomatic type

  class as the intersection of existing classes, with additional axioms

  holding.  Class axioms may not contain more than one type variable.  The

  class axioms (with implicit sort constraints added) are bound to the given

  names.  Furthermore a class introduction rule is generated, which is

  employed by method $intro_classes$ to support instantiation proofs of this

  class.

\item [$\isarkeyword{instance}~c@1 < c@2$ and $\isarkeyword{instance}~t ::

  (\vec s)c$] setup a goal stating a class relation or type arity.  The proof

  would usually proceed by $intro_classes$, and then establish the

  characteristic theorems of the type classes involved.  After finishing the

  proof, the theory will be augmented by a type signature declaration

  corresponding to the resulting theorem.

\item [$intro_classes$] repeatedly expands all class introduction rules of

  this theory.

\end{descr}

\section{Calculational proof}\label{sec:calculation}

\indexisarcmd{also}\indexisarcmd{finally}

\indexisarcmd{moreover}\indexisarcmd{ultimately}

\indexisaratt{trans}

\begin{matharray}{rcl}

  \isarcmd{also} & : & \isartrans{proof(state)}{proof(state)} \\

  \isarcmd{finally} & : & \isartrans{proof(state)}{proof(chain)} \\

  \isarcmd{moreover} & : & \isartrans{proof(state)}{proof(state)} \\

  \isarcmd{ultimately} & : & \isartrans{proof(state)}{proof(chain)} \\

  trans & : & \isaratt \\

\end{matharray}

Calculational proof is forward reasoning with implicit application of

transitivity rules (such those of $=$, $\le$, $<$).  Isabelle/Isar maintains

an auxiliary register $calculation$\indexisarthm{calculation} for accumulating

results obtained by transitivity composed with the current result.  Command

$\ALSO$ updates $calculation$ involving $this$, while $\FINALLY$ exhibits the

final $calculation$ by forward chaining towards the next goal statement.  Both

commands require valid current facts, i.e.\ may occur only after commands that

produce theorems such as $\ASSUMENAME$, $\NOTENAME$, or some finished proof of

$\HAVENAME$, $\SHOWNAME$ etc.  The $\MOREOVER$ and $\ULTIMATELY$ commands are

similar to $\ALSO$ and $\FINALLY$, but only collect further results in

$calculation$ without applying any rules yet.

Also note that the automatic term abbreviation ``$\dots$'' has its canonical

application with calculational proofs.  It refers to the argument\footnote{The

  argument of a curried infix expression is its right-hand side.} of the

preceding statement.

Isabelle/Isar calculations are implicitly subject to block structure in the

sense that new threads of calculational reasoning are commenced for any new

block (as opened by a local goal, for example).  This means that, apart from

being able to nest calculations, there is no separate \emph{begin-calculation}

command required.

\medskip

The Isar calculation proof commands may be defined as

follows:\footnote{Internal bookkeeping such as proper handling of

  block-structure has been suppressed.}

\begin{matharray}{rcl}

  \ALSO@0 & \equiv & \NOTE{calculation}{this} \\

  \ALSO@{n+1} & \equiv & \NOTE{calculation}{trans~[OF~calculation~this]} \\

  \FINALLY & \equiv & \ALSO~\FROM{calculation} \\

  \MOREOVER & \equiv & \NOTE{calculation}{calculation~this} \\

  \ULTIMATELY & \equiv & \MOREOVER~\FROM{calculation} \\

\end{matharray}

\begin{rail}

  ('also' | 'finally') transrules? comment?

  ;

  ('moreover' | 'ultimately') comment?

  ;

  'trans' (() | 'add' | 'del')

  ;

  transrules: '(' thmrefs ')' interest?

  ;

\end{rail}

\begin{descr}

\item [$\ALSO~(\vec a)$] maintains the auxiliary $calculation$ register as

  follows.  The first occurrence of $\ALSO$ in some calculational thread

  initializes $calculation$ by $this$. Any subsequent $\ALSO$ on the same

  level of block-structure updates $calculation$ by some transitivity rule

  applied to $calculation$ and $this$ (in that order).  Transitivity rules are

  picked from the current context plus those given as explicit arguments (the

  latter have precedence).

\item [$\FINALLY~(\vec a)$] maintaining $calculation$ in the same way as

  $\ALSO$, and concludes the current calculational thread.  The final result

  is exhibited as fact for forward chaining towards the next goal. Basically,

  $\FINALLY$ just abbreviates $\ALSO~\FROM{calculation}$.  Note that

  ``$\FINALLY~\SHOW{}{\Var{thesis}}~\DOT$'' and

  ``$\FINALLY~\HAVE{}{\phi}~\DOT$'' are typical idioms for concluding

  calculational proofs.

\item [$\MOREOVER$ and $\ULTIMATELY$] are analogous to $\ALSO$ and $\FINALLY$,

  but collect results only, without applying rules.

\item [$trans$] declares theorems as transitivity rules.

\end{descr}

\section{Named local contexts (cases)}\label{sec:cases}

\indexisarcmd{case}\indexisarcmd{print-cases}

\indexisaratt{case-names}\indexisaratt{params}

\begin{matharray}{rcl}

  \isarcmd{case} & : & \isartrans{proof(state)}{proof(state)} \\

  \isarcmd{print_cases}^* & : & \isarkeep{proof} \\

  case_names & : & \isaratt \\

  params & : & \isaratt \\

\end{matharray}

Basically, Isar proof contexts are built up explicitly using commands like

$\FIXNAME$, $\ASSUMENAME$ etc.\ (see \S\ref{sec:proof-context}).  In typical

verification tasks this can become hard to manage, though.  In particular, a

large number of local contexts may emerge from case analysis or induction over

inductive sets and types.

\medskip

The $\CASENAME$ command provides a shorthand to refer to certain parts of

logical context symbolically.  Proof methods may provide an environment of

named ``cases'' of the form $c\colon \vec x, \vec \phi$.  Then the effect of

$\CASE{c}$ is exactly the same as $\FIX{\vec x}~\ASSUME{c}{\vec\phi}$.

It is important to note that $\CASENAME$ does \emph{not} provide any means to

peek at the current goal state, which is treated as strictly non-observable in

Isar!  Instead, the cases considered here usually emerge in a canonical way

from certain pieces of specification that appear in the theory somewhere else

(e.g.\ in an inductive definition, or recursive function).  See also

\S\ref{sec:induct-method} for more details of how this works in HOL.

\medskip

Named cases may be exhibited in the current proof context only if both the

proof method and the rules involved support this.  Case names and parameters

of basic rules may be declared by hand as well, by using appropriate

attributes.  Thus variant versions of rules that have been derived manually

may be used in advanced case analysis later.

\railalias{casenames}{case\_names}

\railterm{casenames}

\begin{rail}

  'case' nameref attributes?

  ;

  casenames (name + )

  ;

  'params' ((name * ) + 'and')

  ;

\end{rail}

%FIXME bug in rail

\begin{descr}

\item [$\CASE{c}$] invokes a named local context $c\colon \vec x, \vec \phi$,

  as provided by an appropriate proof method (such as $cases$ and $induct$ in

  Isabelle/HOL, see \S\ref{sec:induct-method}).  The command $\CASE{c}$

  abbreviates $\FIX{\vec x}~\ASSUME{c}{\vec\phi}$.

\item [$\isarkeyword{print_cases}$] prints all local contexts of the current

  state, using Isar proof language notation.  This is a diagnostic command;

  $undo$ does not apply.

\item [$case_names~\vec c$] declares names for the local contexts of premises

  of some theorem; $\vec c$ refers to the \emph{suffix} of the list premises.

\item [$params~\vec p@1 \dots \vec p@n$] renames the innermost parameters of

  premises $1, \dots, n$ of some theorem.  An empty list of names may be given

  to skip positions, leaving the present parameters unchanged.

\end{descr}

\section{Generalized existence}

\indexisarcmd{obtain}

\begin{matharray}{rcl}

  \isarcmd{obtain} & : & \isartrans{proof(prove)}{proof(state)} \\

\end{matharray}

Generalized existence reasoning means that additional elements with certain

properties are introduced, together with a soundness proof of that context

change (the rest of the main goal is left unchanged).

Syntactically, the $\OBTAINNAME$ language element is like an initial proof

method to the present goal, followed by a proof of its additional claim,

followed by the actual context commands (using the syntax of $\FIXNAME$ and

$\ASSUMENAME$, see \S\ref{sec:proof-context}).

\begin{rail}

  'obtain' (vars + 'and') comment? \\ 'where' (assm comment? + 'and')

  ;

\end{rail}

$\OBTAINNAME$ is defined as a derived Isar command as follows; here the

preceding goal shall be $\psi$, with (optional) facts $\vec b$ indicated for

forward chaining.

\begin{matharray}{l}

  \OBTAIN{\vec x}{a}{\vec \phi}~~\langle proof\rangle \equiv {} \\[0.5ex]

  \quad \PROOF{succeed} \\

  \qquad \DEF{}{thesis \equiv \psi} \\

  \qquad \PRESUME{that}{\All{\vec x} \vec\phi \Imp thesis} \\

  \qquad \FROM{\vec b}~\SHOW{}{thesis}~~\langle proof\rangle \\

  \quad \NEXT \\

  \qquad \FIX{\vec x}~\ASSUME{a}{\vec\phi} \\

\end{matharray}

Typically, the soundness proof is relatively straight-forward, often just by

canonical automated tools such as $\BY{simp}$ (see \S\ref{sec:simp}) or

$\BY{blast}$ (see \S\ref{sec:classical-auto}).  Note that the ``$that$''

presumption above is usually declared as simplification and (unsafe)

introduction rule, depending on the object-logic's policy,

though.\footnote{HOL and HOLCF do this already.}

The original goal statement is wrapped into a local definition in order to

avoid any automated tools descending into it.  Usually, any statement would

admit the intended reduction anyway; only in very rare cases $thesis_def$ has

to be expanded to complete the soundness proof.

\medskip

In a sense, $\OBTAINNAME$ represents at the level of Isar proofs what would be

meta-logical existential quantifiers and conjunctions.  This concept has a

broad range of useful applications, ranging from plain elimination (or even

introduction) of object-level existentials and conjunctions, to elimination

over results of symbolic evaluation of recursive definitions, for example.

\section{Miscellaneous methods and attributes}

\indexisarmeth{unfold}\indexisarmeth{fold}

\indexisarmeth{erule}\indexisarmeth{drule}\indexisarmeth{frule}

\indexisarmeth{fail}\indexisarmeth{succeed}

\begin{matharray}{rcl}

  unfold & : & \isarmeth \\

  fold & : & \isarmeth \\[0.5ex]

  erule^* & : & \isarmeth \\

  drule^* & : & \isarmeth \\

  frule^* & : & \isarmeth \\[0.5ex]

  succeed & : & \isarmeth \\

  fail & : & \isarmeth \\

\end{matharray}

\begin{rail}

  ('fold' | 'unfold' | 'erule' | 'drule' | 'frule') thmrefs

  ;

\end{rail}

\begin{descr}

\item [$unfold~\vec a$ and $fold~\vec a$] expand and fold back again the given

  meta-level definitions throughout all goals; any facts provided are inserted

  into the goal and subject to rewriting as well.

\item [$erule~\vec a$, $drule~\vec a$, and $frule~\vec a$] are similar to the

  basic $rule$ method (see \S\ref{sec:pure-meth-att}), but apply rules by

  elim-resolution, destruct-resolution, and forward-resolution, respectively

  \cite{isabelle-ref}.  These are improper method, mainly for experimentation

  and emulating tactic scripts.

  Different modes of basic rule application are usually expressed in Isar at

  the proof language level, rather than via implicit proof state

  manipulations.  For example, a proper single-step elimination would be done

  using the basic $rule$ method, with forward chaining of current facts.

\item [$succeed$] yields a single (unchanged) result; it is the identity of

  the ``\texttt{,}'' method combinator (cf.\ \S\ref{sec:syn-meth}).

\item [$fail$] yields an empty result sequence; it is the identity of the

  ``\texttt{|}'' method combinator (cf.\ \S\ref{sec:syn-meth}).

\end{descr}

\indexisaratt{standard}

\indexisaratt{elimify}

\indexisaratt{RS}\indexisaratt{COMP}

\indexisaratt{where}

\indexisaratt{tag}\indexisaratt{untag}

\indexisaratt{transfer}

\indexisaratt{export}

\indexisaratt{unfold}\indexisaratt{fold}

\begin{matharray}{rcl}

  tag & : & \isaratt \\

  untag & : & \isaratt \\[0.5ex]

  RS & : & \isaratt \\

  COMP & : & \isaratt \\[0.5ex]

  where & : & \isaratt \\[0.5ex]

  unfold & : & \isaratt \\

  fold & : & \isaratt \\[0.5ex]

  standard & : & \isaratt \\

  elimify & : & \isaratt \\

  export^* & : & \isaratt \\

  transfer & : & \isaratt \\[0.5ex]

\end{matharray}

\begin{rail}

  'tag' (nameref+)

  ;

  'untag' name

  ;

  ('RS' | 'COMP') nat? thmref

  ;

  'where' (name '=' term * 'and')

  ;

  ('unfold' | 'fold') thmrefs

  ;

\end{rail}

\begin{descr}

\item [$tag~name~args$ and $untag~name$] add and remove $tags$ of some

  theorem.  Tags may be any list of strings that serve as comment for some

  tools (e.g.\ $\LEMMANAME$ causes the tag ``$lemma$'' to be added to the

  result).  The first string is considered the tag name, the rest its

  arguments.  Note that untag removes any tags of the same name.

\item [$RS~n~a$ and $COMP~n~a$] compose rules.  $RS$ resolves with the $n$-th

  premise of $a$; $COMP$ is a version of $RS$ that skips the automatic lifting

  process that is normally intended (cf.\ \texttt{RS} and \texttt{COMP} in

  \cite[\S5]{isabelle-ref}).

\item [$where~\vec x = \vec t$] perform named instantiation of schematic

  variables occurring in a theorem.  Unlike instantiation tactics (such as

  \texttt{res_inst_tac}, see \cite{isabelle-ref}), actual schematic variables

  have to be specified (e.g.\ $\Var{x@3}$).

\item [$unfold~\vec a$ and $fold~\vec a$] expand and fold back again the given

  meta-level definitions throughout a rule.

\item [$standard$] puts a theorem into the standard form of object-rules, just

  as the ML function \texttt{standard} (see \cite[\S5]{isabelle-ref}).

\item [$elimify$] turns an destruction rule into an elimination, just as the

  ML function \texttt{make\_elim} (see \cite{isabelle-ref}).

\item [$export$] lifts a local result out of the current proof context,

  generalizing all fixed variables and discharging all assumptions.  Note that

  proper incremental export is already done as part of the basic Isar

  machinery.  This attribute is mainly for experimentation.

\item [$transfer$] promotes a theorem to the current theory context, which has

  to enclose the former one.  This is done automatically whenever rules are

  joined by inference.

\end{descr}

\section{The Simplifier}

\subsection{Simplification methods}\label{sec:simp}

\indexisarmeth{simp}\indexisarmeth{simp-all}

\begin{matharray}{rcl}

  simp & : & \isarmeth \\

  simp_all & : & \isarmeth \\

\end{matharray}

\railalias{simpall}{simp\_all}

\railterm{simpall}

\railalias{noasm}{no\_asm}

\railterm{noasm}

\railalias{noasmsimp}{no\_asm\_simp}

\railterm{noasmsimp}

\railalias{noasmuse}{no\_asm\_use}

\railterm{noasmuse}

\begin{rail}

  ('simp' | simpall) ('!' ?) opt? (simpmod * )

  ;

  opt: '(' (noasm | noasmsimp | noasmuse) ')'

  ;

  simpmod: ('add' | 'del' | 'only' | 'split' (() | 'add' | 'del') | 'other') ':' thmrefs

  ;

\end{rail}

\begin{descr}

\item [$simp$] invokes Isabelle's simplifier, after declaring additional rules

  according to the arguments given.  Note that the \railtterm{only} modifier

  first removes all other rewrite rules, congruences, and looper tactics

  (including splits), and then behaves like \railtterm{add}.

  The \railtterm{split} modifiers add or delete rules for the Splitter (see

  also \cite{isabelle-ref}), the default is to add.  This works only if the

  Simplifier method has been properly setup to include the Splitter (all major

  object logics such HOL, HOLCF, FOL, ZF do this already).

  The \railtterm{other} modifier ignores its arguments.  Nevertheless,

  additional kinds of rules may be declared by including appropriate

  attributes in the specification.

\item [$simp_all$] is similar to $simp$, but acts on all goals.

\end{descr}

By default, the Simplifier methods are based on \texttt{asm_full_simp_tac}

internally \cite[\S10]{isabelle-ref}, which means that assumptions are both

simplified as well as used in simplifying the conclusion.  In structured

proofs this is usually quite well behaved in practice: just the local premises

of the actual goal are involved, additional facts may inserted via explicit

forward-chaining (using $\THEN$, $\FROMNAME$ etc.).  The full context of

assumptions is only included if the ``$!$'' (bang) argument is given, which

should be used with some care, though.

Additional Simplifier options may be specified to tune the behavior even

further: $(no_asm)$ means assumptions are ignored completely (cf.\ 

\texttt{simp_tac}), $(no_asm_simp)$ means assumptions are used in the

simplification of the conclusion but are not themselves simplified (cf.\ 

\texttt{asm_simp_tac}), and $(no_asm_use)$ means assumptions are simplified

but are not used in the simplification of each other or the conclusion (cf.

\texttt{full_simp_tac}).

\medskip

The Splitter package is usually configured to work as part of the Simplifier.

There is no separate $split$ method available.  The effect of repeatedly

applying \texttt{split_tac} can be simulated by

$(simp~only\colon~split\colon~\vec a)$.

\subsection{Declaring rules}

\indexisarcmd{print-simpset}

\indexisaratt{simp}\indexisaratt{split}\indexisaratt{cong}

\begin{matharray}{rcl}

  print_simpset & : & \isarkeep{theory~|~proof} \\

  simp & : & \isaratt \\

  split & : & \isaratt \\

  cong & : & \isaratt \\

\end{matharray}

\begin{rail}

  ('simp' | 'split' | 'cong') (() | 'add' | 'del')

  ;

\end{rail}

\begin{descr}

\item [$print_simpset$] prints the collection of rules declared to the

  Simplifier, which is also known as ``simpset'' internally

  \cite{isabelle-ref}.  This is a diagnostic command; $undo$ does not apply.

\item [$simp$] declares simplification rules.

\item [$split$] declares split rules.

\item [$cong$] declares congruence rules.

\end{descr}

\subsection{Forward simplification}

\indexisaratt{simplify}\indexisaratt{asm-simplify}

\indexisaratt{full-simplify}\indexisaratt{asm-full-simplify}

\begin{matharray}{rcl}

  simplify & : & \isaratt \\

  asm_simplify & : & \isaratt \\

  full_simplify & : & \isaratt \\

  asm_full_simplify & : & \isaratt \\

\end{matharray}

These attributes provide forward rules for simplification, which should be

used only very rarely.  There are no separate options for declaring

simplification rules locally.

See the ML functions of the same name in \cite[\S10]{isabelle-ref} for more

information.

\section{The Classical Reasoner}

\subsection{Basic methods}\label{sec:classical-basic}

\indexisarmeth{rule}\indexisarmeth{intro}

\indexisarmeth{elim}\indexisarmeth{default}\indexisarmeth{contradiction}

\begin{matharray}{rcl}

  rule & : & \isarmeth \\

  intro & : & \isarmeth \\

  elim & : & \isarmeth \\

  contradiction & : & \isarmeth \\

\end{matharray}

\begin{rail}

  ('rule' | 'intro' | 'elim') thmrefs?

  ;

\end{rail}

\begin{descr}

\item [$rule$] as offered by the classical reasoner is a refinement over the

  primitive one (see \S\ref{sec:pure-meth-att}).  In case that no rules are

  provided as arguments, it automatically determines elimination and

  introduction rules from the context (see also \S\ref{sec:classical-mod}).

  This is made the default method for basic proof steps, such as $\PROOFNAME$

  and ``$\DDOT$'' (two dots), see also \S\ref{sec:proof-steps} and

  \S\ref{sec:pure-meth-att}.

\item [$intro$ and $elim$] repeatedly refine some goal by intro- or

  elim-resolution, after having inserted any facts.  Omitting the arguments

  refers to any suitable rules declared in the context, otherwise only the

  explicitly given ones may be applied.  The latter form admits better control

  of what actually happens, thus it is very appropriate as an initial method

  for $\PROOFNAME$ that splits up certain connectives of the goal, before

  entering the actual sub-proof.

\item [$contradiction$] solves some goal by contradiction, deriving any result

  from both $\neg A$ and $A$.  Facts, which are guaranteed to participate, may

  appear in either order.

\end{descr}

\subsection{Automated methods}\label{sec:classical-auto}

\indexisarmeth{blast}

\indexisarmeth{fast}\indexisarmeth{best}\indexisarmeth{slow}\indexisarmeth{slow-best}

\begin{matharray}{rcl}

 blast & : & \isarmeth \\

 fast & : & \isarmeth \\

 best & : & \isarmeth \\

 slow & : & \isarmeth \\

 slow_best & : & \isarmeth \\

\end{matharray}

\railalias{slowbest}{slow\_best}

\railterm{slowbest}

\begin{rail}

  'blast' ('!' ?) nat? (clamod * )

  ;

  ('fast' | 'best' | 'slow' | slowbest) ('!' ?) (clamod * )

  ;

  clamod: (('intro' | 'elim' | 'dest') (() | '?' | '??') | 'del') ':' thmrefs

  ;

\end{rail}

\begin{descr}

\item [$blast$] refers to the classical tableau prover (see \texttt{blast_tac}

  in \cite[\S11]{isabelle-ref}).  The optional argument specifies a

  user-supplied search bound (default 20).

\item [$fast$, $best$, $slow$, $slow_best$] refer to the generic classical

  reasoner (see \cite[\S11]{isabelle-ref}, tactic \texttt{fast_tac} etc).

\end{descr}

Any of above methods support additional modifiers of the context of classical

rules.  Their semantics is analogous to the attributes given in

\S\ref{sec:classical-mod}.  Facts provided by forward chaining are

inserted\footnote{These methods usually cannot make proper use of actual rules

  inserted that way, though.} into the goal before doing the search.  The

``!''~argument causes the full context of assumptions to be included as well.

This is slightly less hazardous than for the Simplifier (see

\S\ref{sec:simp}).

\subsection{Combined automated methods}

\indexisarmeth{auto}\indexisarmeth{force}

\begin{matharray}{rcl}

  force & : & \isarmeth \\

  auto & : & \isarmeth \\

\end{matharray}

\begin{rail}

  ('force' | 'auto') ('!' ?) (clasimpmod * )

  ;

  clasimpmod: ('simp' (() | 'add' | 'del' | 'only') | 'other' |

    ('split' (() | 'add' | 'del')) |

    (('intro' | 'elim' | 'dest') (() | '?' | '??') | 'del')) ':' thmrefs

\end{rail}

\begin{descr}

\item [$force$ and $auto$] provide access to Isabelle's combined

  simplification and classical reasoning tactics.  See \texttt{force_tac} and

  \texttt{auto_tac} in \cite[\S11]{isabelle-ref} for more information.  The

  modifier arguments correspond to those given in \S\ref{sec:simp} and

  \S\ref{sec:classical-auto}.  Just note that the ones related to the

  Simplifier are prefixed by \railtterm{simp} here.

  Facts provided by forward chaining are inserted into the goal before doing

  the search.  The ``!''~argument causes the full context of assumptions to be

  included as well.

\end{descr}

\subsection{Declaring rules}\label{sec:classical-mod}

\indexisarcmd{print-claset}

\indexisaratt{intro}\indexisaratt{elim}\indexisaratt{dest}

\indexisaratt{iff}\indexisaratt{delrule}

\begin{matharray}{rcl}

  print_claset & : & \isarkeep{theory~|~proof} \\

  intro & : & \isaratt \\

  elim & : & \isaratt \\

  dest & : & \isaratt \\

  iff & : & \isaratt \\

  delrule & : & \isaratt \\

\end{matharray}

\begin{rail}

  ('intro' | 'elim' | 'dest') (() | '?' | '??')

  ;

  'iff' (() | 'add' | 'del')

\end{rail}

\begin{descr}

\item [$print_claset$] prints the collection of rules declared to the

  Classical Reasoner, which is also known as ``simpset'' internally

  \cite{isabelle-ref}.  This is a diagnostic command; $undo$ does not apply.

\item [$intro$, $elim$, and $dest$] declare introduction, elimination, and

  destruct rules, respectively.  By default, rules are considered as

  \emph{safe}, while a single ``?'' classifies as \emph{unsafe}, and ``??'' as

  \emph{extra} (i.e.\ not applied in the search-oriented automated methods,

  but only in single-step methods such as $rule$).

\item [$iff$] declares equations both as rules for the Simplifier and

  Classical Reasoner.

\item [$delrule$] deletes introduction or elimination rules from the context.

  Note that destruction rules would have to be turned into elimination rules

  first, e.g.\ by using the $elimify$ attribute.

\end{descr}

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