Isar
swMATH ID:  4599 
Software Authors:  Makarius Wenzel 
Description:  Theorem proving system supporting both interactive proof development and some degree of automation have become quite successful in sizable applications in recent years (e.g. Isabelle/Bali or VerifiCard). Typical examples of this kind of semiautomated reasoning systems include Coq, PVS, HOL, and Isabelle. Despite this success in actually formalizing parts of mathematics and computer science, there are still obstacles in addressing a broad range of people. Paradoxically, none of the existing semiautomated reasoning systems have an adequate primary notion of proof that is amenable to human understanding (for communication, or just maintenance).
The Intelligible semiautomated reasoning (Isar) approach to readable formal proof documents sets out to bridge the semantic gap between internal notions of proof given by stateoftheart interactive theorem proving systems and an appropriate level of abstraction for userlevel work. The Isar formal proof language has been designed to satisfy quite contradictory requirements, being both ’declarative’ and immediately ’executable’, by virtue of the Isar/VM interpreter. Compared to existing declarative theorem proving systems (like Mizar), Isar avoids several shortcomings: it is based on a few basic principles only, it is quite independent of the underlying logic, and integrates a broad range of automated proof methods. Interactive proof development is supported directly as well. The Isabelle system offers Isar as an alternative proof language interface layer, beyond traditional tactic scripts. The Isabelle/Isar system provides an interpreter for the Isar formal proof document language. Isabelle/Isar input consists either of proper document constructors, or improper auxiliary commands (for diagnostics, exploration etc.). Proof texts consisting of proper document constructors only admit a purely static reading, thus being intelligible later without requiring dynamic replay that is so typical for traditional proof scripts. Any of the Isabelle/Isar commands may be executed in singlesteps, so basically the interpreter has a proof text debugger already builtin. The Isar subsystem is tightly integrated into the Isabelle/Pure metalogic implementation. Theories, theorems, proof procedures etc. may be used interchangeably between Isabelleclassic proof scripts and Isabelle/Isar documents. Isar is as generic as Isabelle, able to support a wide range of objectlogics. The current enduser setup is mainly for Isabelle/HOL. Together with the Isabelle/Isar instantiation of Proof General, a generic (X)Emacs interface for interactive proof assistants, we arrive at a reasonable environment for live proof document editing. Thus proof texts may be developed incrementally by issuing proper document constructors, including forward and backward tracing of partial documents; intermediate states may be inspected by diagnostic commands. 
Homepage:  http://isabelle.in.tum.de/Isar/ 
Related Software:  Isabelle; Isabelle/HOL; Coq; Mizar; Isabelle/Isar; HOL; Archive Formal Proofs; Sledgehammer; PVS; HOL Light; ML; Proof General; z3; E Theorem Prover; VAMPIRE; TPTP; kepler98; LCF; OMDoc; Theorema 
Cited in:  156 Documents 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Calculational reasoning revisited. An Isabelle/Isar experience. Zbl 1005.68535 Bauer, Gertrud; Wenzel, Markus 
2001

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Cited by 238 Authors
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