doc-src/IsarRef/Thy/Framework.thy

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