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theory Framework
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imports Main
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begin
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chapter {* The Isabelle/Isar Framework \label{ch:isar-framework} *}
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text {*
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Isabelle/Isar
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\cite{Wenzel:1999:TPHOL,Wenzel-PhD,Nipkow-TYPES02,Wenzel-Paulson:2006,Wenzel:2006:Festschrift}
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is intended as a generic framework for developing formal
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mathematical documents with full proof checking. Definitions and
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proofs are organized as theories; an assembly of theory sources may
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be presented as a printed document; see also
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\chref{ch:document-prep}.
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The main objective of Isar is the design of a human-readable
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structured proof language, which is called the ``primary proof
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format'' in Isar terminology. Such a primary proof language is
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somewhere in the middle between the extremes of primitive proof
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objects and actual natural language. In this respect, Isar is a bit
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more formalistic than Mizar
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\cite{Trybulec:1993:MizarFeatures,Rudnicki:1992:MizarOverview,Wiedijk:1999:Mizar},
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using logical symbols for certain reasoning schemes where Mizar
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would prefer English words; see \cite{Wenzel-Wiedijk:2002} for
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further comparisons of these systems.
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So Isar challenges the traditional way of recording informal proofs
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in mathematical prose, as well as the common tendency to see fully
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formal proofs directly as objects of some logical calculus (e.g.\
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@{text "\<lambda>"}-terms in a version of type theory). In fact, Isar is
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better understood as an interpreter of a simple block-structured
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language for describing data flow of local facts and goals,
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interspersed with occasional invocations of proof methods.
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Everything is reduced to logical inferences internally, but these
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steps are somewhat marginal compared to the overall bookkeeping of
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the interpretation process. Thanks to careful design of the syntax
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and semantics of Isar language elements, a formal record of Isar
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instructions may later appear as an intelligible text to the
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attentive reader.
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The Isar proof language has emerged from careful analysis of some
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inherent virtues of the existing logical framework of Isabelle/Pure
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\cite{paulson-found,paulson700}, notably composition of higher-order
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natural deduction rules, which is a generalization of Gentzen's
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original calculus \cite{Gentzen:1935}. The approach of generic
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inference systems in Pure is continued by Isar towards actual proof
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texts.
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Concrete applications require another intermediate layer: an
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object-logic. Isabelle/HOL \cite{isa-tutorial} (simply-typed
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set-theory) is being used most of the time; Isabelle/ZF
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\cite{isabelle-ZF} is less extensively developed, although it would
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probably fit better for classical mathematics.
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*}
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end
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