author paulson Wed, 13 Jan 1999 16:30:53 +0100 changeset 6120 f40d61cd6b32 parent 6119 7e3eb9b4df8e child 6121 5fe77b9b5185
removal of FOL and ZF
 doc-src/Logics/preface.tex file | annotate | diff | comparison | revisions doc-src/Logics/syntax.tex file | annotate | diff | comparison | revisions
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+%% $Id$
+\chapter*{Preface}
+Several logics come with Isabelle.  Many of them are sufficiently developed
+to serve as comfortable reasoning environments.  They are also good
+starting points for defining new logics.  Each logic is distributed with
+sample proofs, some of which are described in this document.
+
+The logics \texttt{FOL} (first-order logic) and \texttt{ZF} (axiomatic set
+theory) are described in a separate manual~\cite{isabelle-ZF}.  Here are the
+others:
+
+\begin{ttdescription}
+\item[\thydx{CCL}] is Martin Coen's Classical Computational Logic,
+  which is the basis of a preliminary method for deriving programs from
+  proofs~\cite{coen92}.  It is built upon classical~\FOL{}.
+
+\item[\thydx{LCF}] is a version of Scott's Logic for Computable
+  Functions, which is also implemented by the~{\sc lcf}
+  system~\cite{paulson87}.  It is built upon classical~\FOL{}.
+
+\item[\thydx{HOL}] is the higher-order logic of Church~\cite{church40},
+which is also implemented by Gordon's~{\sc hol} system~\cite{mgordon-hol}.
+This object-logic should not be confused with Isabelle's meta-logic, which is
+also a form of higher-order logic.
+
+\item[\thydx{HOLCF}] is a version of {\sc lcf}, defined as an
+  extension of \texttt{HOL}\@.
+
+\item[\thydx{CTT}] is a version of Martin-L\"of's Constructive Type
+Theory~\cite{nordstrom90}, with extensional equality.  Universes are not
+included.
+
+\item[\thydx{Cube}] is Barendregt's $\lambda$-cube.
+ \end{ttdescription}
+
+The directory \texttt{Sequents} contains several logics based
+  upon the sequent calculus.  Sequents have the form $A@1,\ldots,A@m\turn +B@1,\ldots,B@n$; rules are applied using associative matching.
+\begin{ttdescription}
+\item[\thydx{LK}] is classical first-order logic as a sequent calculus.
+
+\item[\thydx{Modal}] implements the modal logics $T$, $S4$, and~$S43$.
+
+\item[\thydx{ILL}] implements intuitionistic linear logic.
+\end{ttdescription}
+
+The logics \texttt{CCL}, \texttt{LCF}, \texttt{HOLCF}, \texttt{Modal}, \texttt{ILL} and {\tt
+  Cube} are undocumented.  All object-logics' sources are
+distributed with Isabelle (see the directory \texttt{src}).  They are
+also available for browsing on the WWW at
+\begin{ttbox}
+http://www4.informatik.tu-muenchen.de/~nipkow/isabelle/
+\end{ttbox}
+Note that this is not necessarily consistent with your local sources!
+
+  Isabelle} and performing some Isabelle proofs.  Consult the {\em Reference
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/doc-src/Logics/syntax.tex	Wed Jan 13 16:30:53 1999 +0100
@@ -0,0 +1,62 @@
+%% $Id$
+%% THIS FILE IS COMMON TO ALL LOGIC MANUALS
+
+\chapter{Syntax definitions}
+The syntax of each logic is presented using a context-free grammar.
+These grammars obey the following conventions:
+\begin{itemize}
+\item identifiers denote nonterminal symbols
+\item \texttt{typewriter} font denotes terminal symbols
+\item parentheses $(\ldots)$ express grouping
+\item constructs followed by a Kleene star, such as $id^*$ and $(\ldots)^*$
+can be repeated~0 or more times
+\item alternatives are separated by a vertical bar,~$|$
+\item the symbol for alphanumeric identifiers is~{\it id\/}
+\item the symbol for scheme variables is~{\it var}
+\end{itemize}
+To reduce the number of nonterminals and grammar rules required, Isabelle's
+syntax module employs {\bf priorities},\index{priorities} or precedences.
+Each grammar rule is given by a mixfix declaration, which has a priority,
+and each argument place has a priority.  This general approach handles
+infix operators that associate either to the left or to the right, as well
+as prefix and binding operators.
+
+In a syntactically valid expression, an operator's arguments never involve
+an operator of lower priority unless brackets are used.  Consider
+first-order logic, where $\exists$ has lower priority than $\disj$,
+which has lower priority than $\conj$.  There, $P\conj Q \disj R$
+abbreviates $(P\conj Q) \disj R$ rather than $P\conj (Q\disj R)$.  Also,
+$\exists x.P\disj Q$ abbreviates $\exists x.(P\disj Q)$ rather than
+$(\exists x.P)\disj Q$.  Note especially that $P\disj(\exists x.Q)$
+becomes syntactically invalid if the brackets are removed.
+
+A {\bf binder} is a symbol associated with a constant of type
+$(\sigma\To\tau)\To\tau'$.  For instance, we may declare~$\forall$ as
+a binder for the constant~$All$, which has type $(\alpha\To o)\To o$.
+This defines the syntax $\forall x.t$ to mean $All(\lambda x.t)$.  We
+can also write $\forall x@1\ldots x@m.t$ to abbreviate $\forall x@1. +\ldots \forall x@m.t$; this is possible for any constant provided that
+$\tau$ and $\tau'$ are the same type.  \HOL's description operator
+$\varepsilon x.P\,x$ has type $(\alpha\To bool)\To\alpha$ and can bind
+only one variable, except when $\alpha$ is $bool$.  \ZF's bounded
+quantifier $\forall x\in A.P(x)$ cannot be declared as a binder
+because it has type $[i, i\To o]\To o$.  The syntax for binders allows
+type constraints on bound variables, as in
+$\forall (x{::}\alpha) \; (y{::}\beta) \; z{::}\gamma. Q(x,y,z)$
+
+To avoid excess detail, the logic descriptions adopt a semi-formal style.
+Infix operators and binding operators are listed in separate tables, which
+include their priorities.  Grammar descriptions do not include numeric
+priorities; instead, the rules appear in order of decreasing priority.
+This should suffice for most purposes; for full details, please consult the
+actual syntax definitions in the {\tt.thy} files.
+
+Each nonterminal symbol is associated with some Isabelle type.  For
+example, the formulae of first-order logic have type~$o$.  Every
+Isabelle expression of type~$o$ is therefore a formula.  These include
+atomic formulae such as $P$, where $P$ is a variable of type~$o$, and more
+generally expressions such as $P(t,u)$, where $P$, $t$ and~$u$ have
+suitable types.  Therefore, expression of type~$o$' is listed as a
+separate possibility in the grammar for formulae.
+
+`