theory Introduction

imports Main

begin

chapter {* Introduction *}

section {* Overview *}

text {*

  The \emph{Isabelle} system essentially provides a generic

  infrastructure for building deductive systems (programmed in

  Standard ML), with a special focus on interactive theorem proving in

  higher-order logics.  Many years ago, even end-users would refer to

  certain ML functions (goal commands, tactics, tacticals etc.) to

  pursue their everyday theorem proving tasks.

  In contrast \emph{Isar} provides an interpreted language environment

  of its own, which has been specifically tailored for the needs of

  theory and proof development.  Compared to raw ML, the Isabelle/Isar

  top-level provides a more robust and comfortable development

  platform, with proper support for theory development graphs, managed

  transactions with unlimited undo etc.  The Isabelle/Isar version of

  the \emph{Proof~General} user interface

  \cite{proofgeneral,Aspinall:TACAS:2000} provides a decent front-end

  for interactive theory and proof development in this advanced

  theorem proving environment, even though it is somewhat biased

  towards old-style proof scripts.

  \medskip Apart from the technical advances over bare-bones ML

  programming, the main purpose of the Isar language is to provide a

  conceptually different view on machine-checked proofs

  \cite{Wenzel:1999:TPHOL,Wenzel-PhD}.  \emph{Isar} stands for

  \emph{Intelligible semi-automated reasoning}.  Drawing from both the

  traditions of informal mathematical proof texts and high-level

  programming languages, Isar offers a versatile environment for

  structured formal proof documents.  Thus properly written Isar

  proofs become accessible to a broader audience than unstructured

  tactic scripts (which typically only provide operational information

  for the machine).  Writing human-readable proof texts certainly

  requires some additional efforts by the writer to achieve a good

  presentation, both of formal and informal parts of the text.  On the

  other hand, human-readable formal texts gain some value in their own

  right, independently of the mechanic proof-checking process.

  Despite its grand design of structured proof texts, Isar is able to

  assimilate the old tactical style as an ``improper'' sub-language.

  This provides an easy upgrade path for existing tactic scripts, as

  well as some means for interactive experimentation and debugging of

  structured proofs.  Isabelle/Isar supports a broad range of proof

  styles, both readable and unreadable ones.

  \medskip The generic Isabelle/Isar framework (see

  \chref{ch:isar-framework}) works reasonably well for any Isabelle

  object-logic that conforms to the natural deduction view of the

  Isabelle/Pure framework.  Specific language elements introduced by

  the major object-logics are described in \chref{ch:hol}

  (Isabelle/HOL), \chref{ch:holcf} (Isabelle/HOLCF), and \chref{ch:zf}

  (Isabelle/ZF).  The main language elements are already provided by

  the Isabelle/Pure framework. Nevertheless, examples given in the

  generic parts will usually refer to Isabelle/HOL as well.

  \medskip Isar commands may be either \emph{proper} document

  constructors, or \emph{improper commands}.  Some proof methods and

  attributes introduced later are classified as improper as well.

  Improper Isar language elements, which are marked by ``@{text

  "\<^sup>*"}'' in the subsequent chapters; they are often helpful

  when developing proof documents, but their use is discouraged for

  the final human-readable outcome.  Typical examples are diagnostic

  commands that print terms or theorems according to the current

  context; other commands emulate old-style tactical theorem proving.

*}

end