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theory Introduction
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imports Main
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begin
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chapter {* Introduction *}
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section {* Overview *}
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text {*
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The \emph{Isabelle} system essentially provides a generic
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infrastructure for building deductive systems (programmed in
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Standard ML), with a special focus on interactive theorem proving in
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higher-order logics. Many years ago, even end-users would refer to
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certain ML functions (goal commands, tactics, tacticals etc.) to
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pursue their everyday theorem proving tasks.
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In contrast \emph{Isar} provides an interpreted language environment
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of its own, which has been specifically tailored for the needs of
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theory and proof development. Compared to raw ML, the Isabelle/Isar
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top-level provides a more robust and comfortable development
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platform, with proper support for theory development graphs, managed
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transactions with unlimited undo etc. The Isabelle/Isar version of
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the \emph{Proof~General} user interface
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\cite{proofgeneral,Aspinall:TACAS:2000} provides a decent front-end
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for interactive theory and proof development in this advanced
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theorem proving environment, even though it is somewhat biased
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towards old-style proof scripts.
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\medskip Apart from the technical advances over bare-bones ML
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programming, the main purpose of the Isar language is to provide a
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conceptually different view on machine-checked proofs
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\cite{Wenzel:1999:TPHOL,Wenzel-PhD}. \emph{Isar} stands for
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\emph{Intelligible semi-automated reasoning}. Drawing from both the
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traditions of informal mathematical proof texts and high-level
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programming languages, Isar offers a versatile environment for
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structured formal proof documents. Thus properly written Isar
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proofs become accessible to a broader audience than unstructured
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tactic scripts (which typically only provide operational information
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for the machine). Writing human-readable proof texts certainly
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requires some additional efforts by the writer to achieve a good
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presentation, both of formal and informal parts of the text. On the
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other hand, human-readable formal texts gain some value in their own
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right, independently of the mechanic proof-checking process.
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Despite its grand design of structured proof texts, Isar is able to
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assimilate the old tactical style as an ``improper'' sub-language.
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This provides an easy upgrade path for existing tactic scripts, as
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well as some means for interactive experimentation and debugging of
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structured proofs. Isabelle/Isar supports a broad range of proof
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styles, both readable and unreadable ones.
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\medskip The generic Isabelle/Isar framework (see
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\chref{ch:isar-framework}) works reasonably well for any Isabelle
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object-logic that conforms to the natural deduction view of the
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Isabelle/Pure framework. Specific language elements introduced by
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the major object-logics are described in \chref{ch:hol}
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(Isabelle/HOL), \chref{ch:holcf} (Isabelle/HOLCF), and \chref{ch:zf}
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(Isabelle/ZF). The main language elements are already provided by
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the Isabelle/Pure framework. Nevertheless, examples given in the
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generic parts will usually refer to Isabelle/HOL as well.
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\medskip Isar commands may be either \emph{proper} document
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constructors, or \emph{improper commands}. Some proof methods and
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attributes introduced later are classified as improper as well.
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Improper Isar language elements, which are marked by ``@{text
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"\<^sup>*"}'' in the subsequent chapters; they are often helpful
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when developing proof documents, but their use is discouraged for
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the final human-readable outcome. Typical examples are diagnostic
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commands that print terms or theorems according to the current
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context; other commands emulate old-style tactical theorem proving.
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*}
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end
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