3 Several logics come with Isabelle. Many of them are sufficiently developed
4 to serve as comfortable reasoning environments. They are also good
5 starting points for defining new logics. Each logic is distributed with
6 sample proofs, some of which are described in this document.
8 \texttt{HOL} is currently the best developed Isabelle object-logic, including
9 an extensive library of (concrete) mathematics, and various packages for
10 advanced definitional concepts (like (co-)inductive sets and types,
11 well-founded recursion etc.). The distribution also includes some large
12 applications. See the separate manual \emph{Isabelle's Logics: HOL}. There
13 is also a comprehensive tutorial on Isabelle/HOL available.
15 \texttt{ZF} provides another starting point for applications, with a slightly
16 less developed library than \texttt{HOL}. \texttt{ZF}'s definitional packages
17 are similar to those of \texttt{HOL}. Untyped \texttt{ZF} set theory provides
18 more advanced constructions for sets than simply-typed \texttt{HOL}.
19 \texttt{ZF} is built on \texttt{FOL} (first-order logic), both are described
20 in a separate manual \emph{Isabelle's Logics: FOL and ZF}~\cite{isabelle-ZF}.
22 \medskip There are some further logics distributed with Isabelle:
24 \item[\thydx{CCL}] is Martin Coen's Classical Computational Logic,
25 which is the basis of a preliminary method for deriving programs from
26 proofs~\cite{coen92}. It is built upon classical~FOL.
28 \item[\thydx{LCF}] is a version of Scott's Logic for Computable
29 Functions, which is also implemented by the~{\sc lcf}
30 system~\cite{paulson87}. It is built upon classical~FOL.
32 \item[\thydx{HOLCF}] is a version of {\sc lcf}, defined as an extension of
33 \texttt{HOL}\@. See \cite{MuellerNvOS99} for more details on \texttt{HOLCF}.
35 \item[\thydx{CTT}] is a version of Martin-L\"of's Constructive Type
36 Theory~\cite{nordstrom90}, with extensional equality. Universes are not
39 \item[\thydx{Cube}] is Barendregt's $\lambda$-cube.
42 The directory \texttt{Sequents} contains several logics based
43 upon the sequent calculus. Sequents have the form $A@1,\ldots,A@m\turn
44 B@1,\ldots,B@n$; rules are applied using associative matching.
46 \item[\thydx{LK}] is classical first-order logic as a sequent calculus.
48 \item[\thydx{Modal}] implements the modal logics $T$, $S4$, and~$S43$.
50 \item[\thydx{ILL}] implements intuitionistic linear logic.
53 The logics \texttt{CCL}, \texttt{LCF}, \texttt{Modal}, \texttt{ILL} and {\tt
54 Cube} are undocumented. All object-logics' sources are distributed with
55 Isabelle (see the directory \texttt{src}). They are also available for
56 browsing on the WWW at
60 \url{http://www.cl.cam.ac.uk/Research/HVG/Isabelle/library/} \\
61 \url{http://isabelle.in.tum.de/library/} \\
65 Note that this is not necessarily consistent with your local sources!
67 \medskip Do not read the \emph{Isabelle's Logics} manuals before reading
68 \emph{Isabelle/HOL --- The Tutorial} or \emph{Introduction to Isabelle}, and
69 performing some Isabelle proofs. Consult the {\em Reference Manual} for more
70 information on tactics, packages, etc.
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