author | wenzelm |
Sat, 18 Mar 2000 19:11:34 +0100 | |
changeset 8517 | 062e6cd78534 |
parent 8507 | d22fcea34cb7 |
child 8547 | 93b8685d004b |
permissions | -rw-r--r-- |
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\chapter{Generic Tools and Packages}\label{ch:gen-tools} |
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\section{Axiomatic Type Classes}\label{sec:axclass} |
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\indexisarcmd{axclass}\indexisarcmd{instance}\indexisarmeth{intro-classes} |
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\begin{matharray}{rcl} |
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\isarcmd{axclass} & : & \isartrans{theory}{theory} \\ |
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\isarcmd{instance} & : & \isartrans{theory}{proof(prove)} \\ |
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intro_classes & : & \isarmeth \\ |
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\end{matharray} |
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Axiomatic type classes are provided by Isabelle/Pure as a \emph{definitional} |
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interface to type classes (cf.~\S\ref{sec:classes}). Thus any object logic |
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may make use of this light-weight mechanism of abstract theories. See |
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\cite{Wenzel:1997:TPHOL} for more information. There is also a tutorial on |
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\emph{Using Axiomatic Type Classes in Isabelle} that is part of the standard |
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Isabelle documentation. |
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%FIXME cite |
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\begin{rail} |
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'axclass' classdecl (axmdecl prop comment? +) |
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; |
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'instance' (nameref '<' nameref | nameref '::' simplearity) comment? |
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; |
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\end{rail} |
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\begin{descr} |
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\item [$\isarkeyword{axclass}~c < \vec c~axms$] defines an axiomatic type |
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class as the intersection of existing classes, with additional axioms |
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holding. Class axioms may not contain more than one type variable. The |
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class axioms (with implicit sort constraints added) are bound to the given |
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names. Furthermore a class introduction rule is generated, which is |
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employed by method $intro_classes$ to support instantiation proofs of this |
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class. |
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\item [$\isarkeyword{instance}~c@1 < c@2$ and $\isarkeyword{instance}~t :: |
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(\vec s)c$] setup up a goal stating the class relation or type arity. The |
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proof would usually proceed by $intro_classes$, and then establish the |
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characteristic theorems of the type classes involved. After finishing the |
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proof, the theory will be augmented by a type signature declaration |
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corresponding to the resulting theorem. |
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\item [$intro_classes$] repeatedly expands all class introduction rules of |
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this theory. |
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\end{descr} |
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\section{Calculational proof}\label{sec:calculation} |
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\indexisarcmd{also}\indexisarcmd{finally}\indexisaratt{trans} |
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\begin{matharray}{rcl} |
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\isarcmd{also} & : & \isartrans{proof(state)}{proof(state)} \\ |
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\isarcmd{finally} & : & \isartrans{proof(state)}{proof(chain)} \\ |
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trans & : & \isaratt \\ |
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\end{matharray} |
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Calculational proof is forward reasoning with implicit application of |
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transitivity rules (such those of $=$, $\le$, $<$). Isabelle/Isar maintains |
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an auxiliary register $calculation$\indexisarthm{calculation} for accumulating |
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results obtained by transitivity composed with the current result. Command |
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$\ALSO$ updates $calculation$ involving $this$, while $\FINALLY$ exhibits the |
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final $calculation$ by forward chaining towards the next goal statement. Both |
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commands require valid current facts, i.e.\ may occur only after commands that |
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produce theorems such as $\ASSUMENAME$, $\NOTENAME$, or some finished proof of |
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$\HAVENAME$, $\SHOWNAME$ etc. |
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Also note that the automatic term abbreviation ``$\dots$'' has its canonical |
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application with calculational proofs. It automatically refers to the |
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argument\footnote{The argument of a curried infix expression is its right-hand |
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side.} of the preceding statement. |
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Isabelle/Isar calculations are implicitly subject to block structure in the |
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sense that new threads of calculational reasoning are commenced for any new |
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block (as opened by a local goal, for example). This means that, apart from |
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being able to nest calculations, there is no separate \emph{begin-calculation} |
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command required. |
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\begin{rail} |
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('also' | 'finally') transrules? comment? |
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; |
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'trans' (() | 'add' | 'del') |
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; |
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transrules: '(' thmrefs ')' interest? |
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; |
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\end{rail} |
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\begin{descr} |
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\item [$\ALSO~(thms)$] maintains the auxiliary $calculation$ register as |
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follows. The first occurrence of $\ALSO$ in some calculational thread |
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initializes $calculation$ by $this$. Any subsequent $\ALSO$ on the same |
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level of block-structure updates $calculation$ by some transitivity rule |
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applied to $calculation$ and $this$ (in that order). Transitivity rules are |
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picked from the current context plus those given as $thms$ (the latter have |
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precedence). |
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\item [$\FINALLY~(thms)$] maintaining $calculation$ in the same way as |
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$\ALSO$, and concludes the current calculational thread. The final result |
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is exhibited as fact for forward chaining towards the next goal. Basically, |
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$\FINALLY$ just abbreviates $\ALSO~\FROM{calculation}$. Note that |
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``$\FINALLY~\SHOW{}{\Var{thesis}}~\DOT$'' and |
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``$\FINALLY~\HAVE{}{\phi}~\DOT$'' are typical idioms for concluding |
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calculational proofs. |
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\item [$trans$] maintains the set of transitivity rules of the theory or proof |
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context, by adding or deleting theorems (the default is to add). |
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\end{descr} |
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\section{Named local contexts (cases)}\label{sec:cases} |
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\indexisarcmd{case}\indexisarcmd{print-cases} |
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\indexisaratt{case-names}\indexisaratt{params} |
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\begin{matharray}{rcl} |
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\isarcmd{case} & : & \isartrans{proof(state)}{proof(state)} \\ |
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\isarcmd{print_cases}^* & : & \isarkeep{proof} \\ |
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case_names & : & \isaratt \\ |
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params & : & \isaratt \\ |
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\end{matharray} |
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Basically, Isar proof contexts are built up explicitly using commands like |
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$\FIXNAME$, $\ASSUMENAME$ etc.\ (see \S\ref{sec:proof-context}). In typical |
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verification tasks this can become hard to manage, though. In particular, a |
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large number of local contexts may emerge from case analysis or induction over |
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inductive sets and types. |
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\medskip |
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The $\CASENAME$ command provides a shorthand to refer to certain parts of |
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logical context symbolically. Proof methods may provide an environment of |
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named ``cases'' of the form $c\colon \vec x, \vec \phi$. Then the effect of |
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$\CASE{c}$ is exactly the same as $\FIX{\vec x}~\ASSUME{c}{\vec\phi}$. |
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It is important to note that $\CASENAME$ does \emph{not} provide any means to |
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peek at the current goal state, which is treated as strictly non-observable in |
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Isar! Instead, the cases considered here usually emerge in a canonical way |
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from certain pieces of specification that appear in the theory somewhere else |
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(e.g.\ in an inductive definition, or recursive function). See also |
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\S\ref{sec:induct-method} for more details of how this works in HOL. |
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\medskip |
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Named cases may be exhibited in the current proof context only if both the |
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proof method and the corresponding rule support this. Case names and |
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parameters of basic rules may be declared by hand as well, by using |
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appropriate attributes. Thus variant versions of rules that have been derived |
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manually may be used in advanced case analysis later. |
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\railalias{casenames}{case\_names} |
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\railterm{casenames} |
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\begin{rail} |
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'case' nameref attributes? |
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; |
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casenames (name + ) |
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; |
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'params' ((name * ) + 'and') |
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; |
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\end{rail} |
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\begin{descr} |
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\item [$\CASE{c}$] invokes a named local context $c\colon \vec x, \vec \phi$, |
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as provided by an appropriate proof method (such as $cases$ and $induct$, |
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see \S\ref{sec:induct-method}). The command $\CASE{c}$ abbreviates |
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$\FIX{\vec x}~\ASSUME{c}{\vec\phi}$. |
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\item [$\isarkeyword{print_cases}$] prints all local contexts of the current |
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goal context, using Isar proof language notation. This is a diagnostic |
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command; $undo$ does not apply. |
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\item [$case_names~\vec c$] declares names for the local contexts of premises |
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of some theorem ($\vec c$ refers to the \emph{suffix} of the list premises). |
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\item [$params~\vec p@1 \dots \vec p@n$] renames the innermost parameters of |
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premises $1, \dots, n$ of some theorem. An empty list of names be be given |
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to skip positions, leaving the corresponding parameters unchanged. |
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\end{descr} |
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\section{Generalized existence} |
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\indexisarcmd{obtain} |
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\begin{matharray}{rcl} |
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\isarcmd{obtain} & : & \isartrans{proof(prove)}{proof(state)} \\ |
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\end{matharray} |
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Generalized existence reasoning means that additional elements with certain |
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properties are introduced, together with a soundness proof of that context |
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change (the rest of the main goal is left unchanged). |
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Syntactically, the $\OBTAINNAME$ language element is like a proof method to |
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the present goal, followed by a proof of its additional claim, followed by the |
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actual context commands (cf.\ $\FIXNAME$ and $\ASSUMENAME$, |
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\S\ref{sec:proof-context}). |
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\begin{rail} |
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'obtain' (vars + 'and') comment? \\ 'where' (assm comment? + 'and') |
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; |
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\end{rail} |
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$\OBTAINNAME$ is defined as a derived Isar command as follows, where the |
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preceding goal shall be $\psi$, with (optional) facts $\vec b$ indicated for |
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forward chaining. |
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\begin{matharray}{l} |
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\OBTAIN{\vec x}{a}{\vec \phi}~~\langle proof\rangle \equiv {} \\[0.5ex] |
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\quad \PROOF{succeed} \\ |
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\qquad \DEF{}{thesis \equiv \psi} \\ |
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\qquad \PRESUME{that}{\All{\vec x} \vec\phi \Imp thesis} \\ |
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\qquad \FROM{\vec b}~\SHOW{}{thesis}~~\langle proof\rangle \\ |
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\quad \NEXT \\ |
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\qquad \FIX{\vec x}~\ASSUME{a}{\vec\phi} \\ |
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\end{matharray} |
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Typically, the soundness proof is relatively straight-forward, often just by |
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canonical automated tools such as $\BY{simp}$ (see \S\ref{sec:simp}) or |
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$\BY{blast}$ (see \S\ref{sec:classical-auto}). Note that the ``$that$'' |
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presumption above is usually declared as simplification and (unsafe) |
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introduction rule, somewhat depending on the object-logic's policy, |
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though.\footnote{Major object-logics such as HOL and HOLCF do this already.} |
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The original goal statement is wrapped into a local definition in order to |
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avoid any automated tools descending into it. Usually, any statement would |
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admit the intended reduction; only in very rare cases $thesis_def$ has to be |
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expanded to complete the soundness proof. |
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\medskip |
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In a sense, $\OBTAINNAME$ represents at the level of Isar proofs what would be |
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meta-logical existential quantifiers and conjunctions. This concept has a |
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broad range of useful applications, ranging from plain elimination (or even |
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introduction) of object-level existentials and conjunctions, to elimination |
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over results of symbolic evaluation of recursive definitions, for example. |
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\section{Miscellaneous methods and attributes} |
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\indexisarmeth{unfold}\indexisarmeth{fold} |
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\indexisarmeth{erule}\indexisarmeth{drule}\indexisarmeth{frule} |
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\indexisarmeth{fail}\indexisarmeth{succeed} |
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\begin{matharray}{rcl} |
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unfold & : & \isarmeth \\ |
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fold & : & \isarmeth \\[0.5ex] |
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erule^* & : & \isarmeth \\ |
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drule^* & : & \isarmeth \\ |
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frule^* & : & \isarmeth \\[0.5ex] |
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succeed & : & \isarmeth \\ |
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fail & : & \isarmeth \\ |
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\end{matharray} |
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\begin{rail} |
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('fold' | 'unfold' | 'erule' | 'drule' | 'frule') thmrefs |
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; |
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\end{rail} |
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\begin{descr} |
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\item [$unfold~thms$ and $fold~thms$] expand and fold back again the given |
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meta-level definitions throughout all goals; any facts provided are inserted |
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into the goal and subject to rewriting as well. |
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\item [$erule~thms$, $drule~thms$, and $frule~thms$] are similar to the basic |
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$rule$ method (see \S\ref{sec:pure-meth-att}), but apply rules by |
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elim-resolution, destruct-resolution, and forward-resolution, respectively |
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\cite{isabelle-ref}. These are improper method, mainly for experimentation |
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and emulating tactic scripts. |
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Different modes of basic rule application are usually expressed in Isar at |
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the proof language level, rather than via implicit proof state |
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modifications. For example, a proper single-step elimination would be done |
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using the basic $rule$ method, with forward chaining of current facts. |
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\item [$succeed$] yields a single (unchanged) result; it is the identity of |
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the ``\texttt{,}'' method combinator (cf.\ \S\ref{sec:syn-meth}). |
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\item [$fail$] yields an empty result sequence; it is the identity of the |
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``\texttt{|}'' method combinator (cf.\ \S\ref{sec:syn-meth}). |
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\end{descr} |
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\indexisaratt{standard} |
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\indexisaratt{elimify} |
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\indexisaratt{RS}\indexisaratt{COMP} |
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\indexisaratt{where} |
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\indexisaratt{tag}\indexisaratt{untag} |
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\indexisaratt{transfer} |
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\indexisaratt{export} |
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\indexisaratt{unfold}\indexisaratt{fold} |
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\begin{matharray}{rcl} |
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tag & : & \isaratt \\ |
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untag & : & \isaratt \\[0.5ex] |
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RS & : & \isaratt \\ |
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COMP & : & \isaratt \\[0.5ex] |
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where & : & \isaratt \\[0.5ex] |
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unfold & : & \isaratt \\ |
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fold & : & \isaratt \\[0.5ex] |
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standard & : & \isaratt \\ |
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elimify & : & \isaratt \\ |
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export^* & : & \isaratt \\ |
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transfer & : & \isaratt \\[0.5ex] |
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\end{matharray} |
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\begin{rail} |
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'tag' (nameref+) |
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; |
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'untag' name |
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; |
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('RS' | 'COMP') nat? thmref |
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; |
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'where' (name '=' term * 'and') |
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; |
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('unfold' | 'fold') thmrefs |
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; |
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\end{rail} |
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\begin{descr} |
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\item [$tag~name~args$ and $untag~name$] add and remove $tags$ of some |
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theorem. Tags may be any list of strings that serve as comment for some |
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tools (e.g.\ $\LEMMANAME$ causes the tag ``$lemma$'' to be added to the |
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result). The first string is considered the tag name, the rest its |
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arguments. Note that untag removes any tags of the same name. |
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\item [$RS~n~thm$ and $COMP~n~thm$] compose rules. $RS$ resolves with the |
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$n$-th premise of $thm$; $COMP$ is a version of $RS$ that skips the |
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automatic lifting process that is normally intended (cf.\ \texttt{RS} and |
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\texttt{COMP} in \cite[\S5]{isabelle-ref}). |
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\item [$where~\vec x = \vec t$] perform named instantiation of schematic |
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variables occurring in a theorem. Unlike instantiation tactics (such as |
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\texttt{res_inst_tac}, see \cite{isabelle-ref}), actual schematic variables |
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have to be specified (e.g.\ $\Var{x@3}$). |
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\item [$unfold~thms$ and $fold~thms$] expand and fold back again the given |
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meta-level definitions throughout a rule. |
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\item [$standard$] puts a theorem into the standard form of object-rules, just |
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as the ML function \texttt{standard} (see \cite[\S5]{isabelle-ref}). |
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\item [$elimify$] turns an destruction rule into an elimination, just as the |
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ML function \texttt{make\_elim} (see \cite{isabelle-ref}). |
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\item [$export$] lifts a local result out of the current proof context, |
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generalizing all fixed variables and discharging all assumptions. Note that |
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(partial) export is usually done automatically behind the scenes. This |
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attribute is mainly for experimentation. |
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\item [$transfer$] promotes a theorem to the current theory context, which has |
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to enclose the former one. Normally, this is done automatically when rules |
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are joined by inference. |
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\end{descr} |
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\section{The Simplifier} |
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\subsection{Simplification methods}\label{sec:simp} |
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\indexisarmeth{simp}\indexisarmeth{simp-all} |
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\begin{matharray}{rcl} |
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simp & : & \isarmeth \\ |
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simp_all & : & \isarmeth \\ |
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\end{matharray} |
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\railalias{simpall}{simp\_all} |
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\railterm{simpall} |
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\begin{rail} |
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('simp' | simpall) ('!' ?) (simpmod * ) |
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; |
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simpmod: ('add' | 'del' | 'only' | 'split' (() | 'add' | 'del') | 'other') ':' thmrefs |
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; |
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\end{rail} |
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\begin{descr} |
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\item [$simp$] invokes Isabelle's simplifier, after modifying the context by |
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adding or deleting rules as specified. The \railtoken{only} modifier first |
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removes all other rewrite rules, congruences, and looper tactics (including |
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splits), and then behaves like \railtoken{add}. |
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The \railtoken{split} modifiers add or delete rules for the Splitter (see |
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also \cite{isabelle-ref}), the default is to add. This works only if the |
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Simplifier method has been properly setup to include the Splitter (all major |
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object logics such HOL, HOLCF, FOL, ZF do this already). |
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The \railtoken{other} modifier ignores its arguments. Nevertheless there |
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may be side-effects on the context via attributes.\footnote{This provides a |
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back door for arbitrary context manipulation.} |
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\item [$simp_all$] is similar to $simp$, but acts on all goals. |
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\end{descr} |
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The $simp$ methods are based on \texttt{asm_full_simp_tac} |
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\cite[\S10]{isabelle-ref}, but is much better behaved in practice. Just the |
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local premises of the actual goal are involved by default. Additional facts |
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may be inserted via forward-chaining (using $\THEN$, $\FROMNAME$ etc.). The |
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full context of assumptions is only included in the $simp!$ versions, which |
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should be used with some care, though. |
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Note that there is no separate $split$ method. The effect of |
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\texttt{split_tac} can be simulated by $(simp~only\colon~split\colon~thms)$. |
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394 |
||
395 |
\subsection{Declaring rules} |
|
396 |
||
397 |
\indexisaratt{simp}\indexisaratt{split} |
|
7321 | 398 |
\begin{matharray}{rcl} |
399 |
simp & : & \isaratt \\ |
|
8483 | 400 |
split & : & \isaratt \\ |
7321 | 401 |
\end{matharray} |
402 |
||
403 |
\begin{rail} |
|
8483 | 404 |
('simp' | 'split') (() | 'add' | 'del') |
7321 | 405 |
; |
406 |
\end{rail} |
|
407 |
||
408 |
\begin{descr} |
|
7466 | 409 |
\item [$simp$] adds or deletes rules from the theory or proof context (the |
410 |
default is to add). |
|
8483 | 411 |
\item [$split$] is similar to $simp$, but refers to split rules. |
7321 | 412 |
\end{descr} |
7319 | 413 |
|
7315 | 414 |
|
415 |
\subsection{Forward simplification} |
|
416 |
||
7391 | 417 |
\indexisaratt{simplify}\indexisaratt{asm-simplify} |
418 |
\indexisaratt{full-simplify}\indexisaratt{asm-full-simplify} |
|
7315 | 419 |
\begin{matharray}{rcl} |
420 |
simplify & : & \isaratt \\ |
|
421 |
asm_simplify & : & \isaratt \\ |
|
422 |
full_simplify & : & \isaratt \\ |
|
423 |
asm_full_simplify & : & \isaratt \\ |
|
424 |
\end{matharray} |
|
425 |
||
7321 | 426 |
These attributes provide forward rules for simplification, which should be |
7905 | 427 |
used only very rarely. There are no separate options for adding or deleting |
428 |
simplification rules locally. |
|
429 |
||
430 |
See the ML functions of the same name in \cite[\S10]{isabelle-ref} for more |
|
431 |
information. |
|
7315 | 432 |
|
433 |
||
7135 | 434 |
\section{The Classical Reasoner} |
435 |
||
7335 | 436 |
\subsection{Basic methods}\label{sec:classical-basic} |
7321 | 437 |
|
7974 | 438 |
\indexisarmeth{rule}\indexisarmeth{intro} |
439 |
\indexisarmeth{elim}\indexisarmeth{default}\indexisarmeth{contradiction} |
|
7321 | 440 |
\begin{matharray}{rcl} |
441 |
rule & : & \isarmeth \\ |
|
442 |
intro & : & \isarmeth \\ |
|
443 |
elim & : & \isarmeth \\ |
|
444 |
contradiction & : & \isarmeth \\ |
|
445 |
\end{matharray} |
|
446 |
||
447 |
\begin{rail} |
|
448 |
('rule' | 'intro' | 'elim') thmrefs |
|
449 |
; |
|
450 |
\end{rail} |
|
451 |
||
452 |
\begin{descr} |
|
7466 | 453 |
\item [$rule$] as offered by the classical reasoner is a refinement over the |
8517 | 454 |
primitive one (see \S\ref{sec:pure-meth-att}). In case that no rules are |
7466 | 455 |
provided as arguments, it automatically determines elimination and |
7321 | 456 |
introduction rules from the context (see also \S\ref{sec:classical-mod}). |
8517 | 457 |
This is made the default method for basic proof steps, such as $\PROOFNAME$ |
458 |
and ``$\DDOT$'' (two dots), see also \S\ref{sec:proof-steps} and |
|
459 |
\S\ref{sec:pure-meth-att}. |
|
7321 | 460 |
|
7466 | 461 |
\item [$intro$ and $elim$] repeatedly refine some goal by intro- or |
7905 | 462 |
elim-resolution, after having inserted any facts. Omitting the arguments |
7321 | 463 |
refers to any suitable rules from the context, otherwise only the explicitly |
7335 | 464 |
given ones may be applied. The latter form admits better control of what |
465 |
actually happens, thus it is very appropriate as an initial method for |
|
466 |
$\PROOFNAME$ that splits up certain connectives of the goal, before entering |
|
7987 | 467 |
the actual sub-proof. |
7458 | 468 |
|
7466 | 469 |
\item [$contradiction$] solves some goal by contradiction, deriving any result |
470 |
from both $\neg A$ and $A$. Facts, which are guaranteed to participate, may |
|
471 |
appear in either order. |
|
7321 | 472 |
\end{descr} |
473 |
||
474 |
||
7981 | 475 |
\subsection{Automated methods}\label{sec:classical-auto} |
7315 | 476 |
|
7321 | 477 |
\indexisarmeth{blast} |
7391 | 478 |
\indexisarmeth{fast}\indexisarmeth{best}\indexisarmeth{slow}\indexisarmeth{slow-best} |
7321 | 479 |
\begin{matharray}{rcl} |
480 |
blast & : & \isarmeth \\ |
|
481 |
fast & : & \isarmeth \\ |
|
482 |
best & : & \isarmeth \\ |
|
483 |
slow & : & \isarmeth \\ |
|
484 |
slow_best & : & \isarmeth \\ |
|
485 |
\end{matharray} |
|
486 |
||
487 |
\railalias{slowbest}{slow\_best} |
|
488 |
\railterm{slowbest} |
|
489 |
||
490 |
\begin{rail} |
|
7905 | 491 |
'blast' ('!' ?) nat? (clamod * ) |
7321 | 492 |
; |
7905 | 493 |
('fast' | 'best' | 'slow' | slowbest) ('!' ?) (clamod * ) |
7321 | 494 |
; |
495 |
||
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|
496 |
clamod: (('intro' | 'elim' | 'dest') (() | '?' | '??') | 'del') ':' thmrefs |
7321 | 497 |
; |
498 |
\end{rail} |
|
499 |
||
500 |
\begin{descr} |
|
501 |
\item [$blast$] refers to the classical tableau prover (see \texttt{blast_tac} |
|
7335 | 502 |
in \cite[\S11]{isabelle-ref}). The optional argument specifies a |
7321 | 503 |
user-supplied search bound (default 20). |
504 |
\item [$fast$, $best$, $slow$, $slow_best$] refer to the generic classical |
|
7335 | 505 |
reasoner (see \cite[\S11]{isabelle-ref}, tactic \texttt{fast_tac} etc). |
7321 | 506 |
\end{descr} |
507 |
||
508 |
Any of above methods support additional modifiers of the context of classical |
|
8517 | 509 |
rules. Their semantics is analogous to the attributes given in |
7987 | 510 |
\S\ref{sec:classical-mod}. Facts provided by forward chaining are inserted |
511 |
into the goal before doing the search. The ``!''~argument causes the full |
|
512 |
context of assumptions to be included as well.\footnote{This is slightly less |
|
513 |
hazardous than for the Simplifier (see \S\ref{sec:simp}).} |
|
7321 | 514 |
|
7315 | 515 |
|
7981 | 516 |
\subsection{Combined automated methods} |
7315 | 517 |
|
7321 | 518 |
\indexisarmeth{auto}\indexisarmeth{force} |
519 |
\begin{matharray}{rcl} |
|
520 |
force & : & \isarmeth \\ |
|
521 |
auto & : & \isarmeth \\ |
|
522 |
\end{matharray} |
|
523 |
||
524 |
\begin{rail} |
|
7905 | 525 |
('force' | 'auto') ('!' ?) (clasimpmod * ) |
7321 | 526 |
; |
7315 | 527 |
|
8483 | 528 |
clasimpmod: ('simp' (() | 'add' | 'del' | 'only') | 'other' | |
529 |
('split' (() | 'add' | 'del')) | |
|
8203
2fcc6017cb72
intro/elim/dest attributes: changed ! / !! flags to ? / ??;
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diff
changeset
|
530 |
(('intro' | 'elim' | 'dest') (() | '?' | '??') | 'del')) ':' thmrefs |
7321 | 531 |
\end{rail} |
7315 | 532 |
|
7321 | 533 |
\begin{descr} |
534 |
\item [$force$ and $auto$] provide access to Isabelle's combined |
|
535 |
simplification and classical reasoning tactics. See \texttt{force_tac} and |
|
536 |
\texttt{auto_tac} in \cite[\S11]{isabelle-ref} for more information. The |
|
537 |
modifier arguments correspond to those given in \S\ref{sec:simp} and |
|
7905 | 538 |
\S\ref{sec:classical-auto}. Just note that the ones related to the |
539 |
Simplifier are prefixed by \railtoken{simp} here. |
|
7987 | 540 |
|
541 |
Facts provided by forward chaining are inserted into the goal before doing |
|
542 |
the search. The ``!''~argument causes the full context of assumptions to be |
|
543 |
included as well. |
|
7321 | 544 |
\end{descr} |
545 |
||
7987 | 546 |
|
8483 | 547 |
\subsection{Declaring rules}\label{sec:classical-mod} |
7135 | 548 |
|
7391 | 549 |
\indexisaratt{intro}\indexisaratt{elim}\indexisaratt{dest} |
550 |
\indexisaratt{iff}\indexisaratt{delrule} |
|
7321 | 551 |
\begin{matharray}{rcl} |
552 |
intro & : & \isaratt \\ |
|
553 |
elim & : & \isaratt \\ |
|
554 |
dest & : & \isaratt \\ |
|
7391 | 555 |
iff & : & \isaratt \\ |
7321 | 556 |
delrule & : & \isaratt \\ |
557 |
\end{matharray} |
|
7135 | 558 |
|
7321 | 559 |
\begin{rail} |
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|
560 |
('intro' | 'elim' | 'dest') (() | '?' | '??') |
7321 | 561 |
; |
562 |
\end{rail} |
|
7135 | 563 |
|
7321 | 564 |
\begin{descr} |
8517 | 565 |
\item [$intro$, $elim$, and $dest$] declare introduction, elimination, and |
566 |
destruct rules, respectively. By default, rules are considered as |
|
567 |
\emph{safe}, while a single ``?'' classifies as \emph{unsafe}, and ``??'' as |
|
568 |
\emph{extra} (i.e.\ not applied in the search-oriented automated methods, |
|
569 |
but only in single-step methods such as $rule$). |
|
7335 | 570 |
|
7391 | 571 |
\item [$iff$] declares equations both as rewrite rules for the simplifier and |
572 |
classical reasoning rules. |
|
573 |
||
7335 | 574 |
\item [$delrule$] deletes introduction or elimination rules from the context. |
575 |
Note that destruction rules would have to be turned into elimination rules |
|
7321 | 576 |
first, e.g.\ by using the $elimify$ attribute. |
577 |
\end{descr} |
|
7135 | 578 |
|
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|
579 |
|
7135 | 580 |
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