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Improving Angel's Parallel Operator: Gumtree's Approach
, 1997
"... We describe some features of the tactic language implemented in the theorem prover Ergo 5. This is a variant of the generic tactic language Angel. We have adapted the language by changing the semantics of its parallel composition operator, the operator by which different tactics are applied to di ..."
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We describe some features of the tactic language implemented in the theorem prover Ergo 5. This is a variant of the generic tactic language Angel. We have adapted the language by changing the semantics of its parallel composition operator, the operator by which different tactics are applied to different branches in a proof tree. The paper includes a denotational semantics for this operator, and a collection of derived tactics which use it, together with a collection of algebraic laws which they obey. Keywords Tactic, Tactical, Denotational Semantics, Algebraic Laws, Interactive theorem proving 1 Introduction Theoremproving tools have traditionally used their implementation language as a tactic language in which users can write procedures to assist in the discovery of proofs. In the LCF family of tools, this language is ML, with certain tactic combinators (tacticals) predefined. Various versions of Ergo (Nickson, Traynor, and Utting, 1996) have used QuProlog (Robinson and Ha...
Multithreading in an Interactive Theorem Prover
, 1999
"... s and compressed postscript files are available via http://svrc.it.uq.edu.au Multithreading in an Interactive Theorem Prover Phil Cook Peter Robinson Abstract The Ergo theorem prover is an interactive prover that is currently being used by the SVRC for carrying out proofs associated with the ..."
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s and compressed postscript files are available via http://svrc.it.uq.edu.au Multithreading in an Interactive Theorem Prover Phil Cook Peter Robinson Abstract The Ergo theorem prover is an interactive prover that is currently being used by the SVRC for carrying out proofs associated with the development of trusted software. The current version of Ergo is a singlethreaded prover. A multithreaded version would allow many possibilities for improving the effectiveness of the prover. For example, automatic tactics for simple subproofs and rule browsers could be run as background threads while the user is planning and carrying out more complex proof tasks. This paper describes some strategies for constructing a multithreaded prover using the highlevel communication and thread facilities found in QuProlog 5.0. 1 Introduction The Ergo theorem prover [1] is an interactive prover, developed by the Software Verification Research Centre, used to perform proofs associated with t...
A Monadic Interpretation of Tactics
, 2002
"... Many proof tools use `tactic languages' as programs to direct their proofs. We present a simplified idealised tactic language, and describe its denotational semantics. The language has many applications outside theoremproveo activ5QbG) The semantics is parametrised by a monad (plus additional ..."
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Many proof tools use `tactic languages' as programs to direct their proofs. We present a simplified idealised tactic language, and describe its denotational semantics. The language has many applications outside theoremproveo activ5QbG) The semantics is parametrised by a monad (plus additional structure). By instantiating this inv arious ways, the core semantics of a number of di#erent tactic languages is obtained. 1 Int roduct45 The notiB of a tactic as a program usedi the constructifi of a (machic[ assi46fi8 formal proof has become quie wie[S#fifi[ Tacti# orifi#z[ i the work of Gordon et al [GMW79] onEdi burgh LCF. The extent to whi h other`tacti4 based' systems istems[ t essentien[ the same style of programmifi faci#[I vari4 consi[I8#Bfi . InEdi burgh LCF, atacti does notit[8B construct a proof. Rather,i ti s usedi backwardreasoni[ to construct a vali#fiz[I functi[ whi h mayi46z8 prove thedesi6B property. Theoremhood i guarded by use of a `safe datatype', and only sound vali484[I functi[I may construct elements ofthi type. In other work, the type of theoremsi protected by havi8 the class oftacti icti protected, so thati i ia ossiSB tobui# unsound proofs. The account here tends towards the secondvion though the treatment oftacti6 i s actually so abstract that thi may not be an i[ edi# t to i[ appli#[IS# i eipli sense. Whie. tacti[ arewiSfi6[IS tacti programmi remai4 adiBfiBS task. Inthi paper, weconsi#[ abstractdescri[S#fi oftactifi[ wit the hope that modern algori desii techniSzS# such as thosedescri ed byBiS and de Moor [BdM97], can be brought to bear on thedi8Sfi[IS ontacti programmi#4 Earlia di#S[ISS oftacti6 i n the abstract (wiract operati6z[ bii to any parti[ISS proof tool)i)[SS those by SchmiB [Sch84] and Mi4#...
Transformation Rules for Z
"... Z is a formal specification language combining typed set theory, predicate calculus, and a schema calculus. This paper describes an extension of Z that allows transformation and reasoning rules to be written in a Zlike notation. This gives a highlevel, declarative, way of specifying transformation ..."
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Z is a formal specification language combining typed set theory, predicate calculus, and a schema calculus. This paper describes an extension of Z that allows transformation and reasoning rules to be written in a Zlike notation. This gives a highlevel, declarative, way of specifying transformations of Z terms, which makes it easier to build new Z manipulation tools. We describe the syntax and semantics of these rules, plus some example reasoning engines that use sets of rules to manipulate Z terms. The utility of these rules is demonstrated by discussing two sets of rules. One set defines expansion of Z schema expressions. The other set is used by the ZLive animator to preprocess Z expressions into a form more suitable for animation. 1
Implementing the Zc Logic in Ergo
, 1998
"... In this paper, we describe work we have been doing on implementing the logic in Ergo 5. Initially, we have chosen to implement the ZUM'98 version of the logic, which uses explicit Currystyle typing rules, rather than the more recent Churchstyle presentation, because the former is more suited ..."
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In this paper, we describe work we have been doing on implementing the logic in Ergo 5. Initially, we have chosen to implement the ZUM'98 version of the logic, which uses explicit Currystyle typing rules, rather than the more recent Churchstyle presentation, because the former is more suited to mechanization. Ergo 5 is the latest version of a series of interactive proof tools that have been designed and implemented at the Software Verification Research Centre (Brisbane, Australia) over the last ten years. It is implemented in QuProlog.
Under consideration for publication in Formal Aspects of Computing The Variety of Variables in Automated RealTime Refinement
, 2002
"... Keywords: Computeraided programming; Program refinement theory; Realtime programming ..."
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Keywords: Computeraided programming; Program refinement theory; Realtime programming