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W Reconstructed
"... An early version of the Z Standard included the deductive system W for reasoning about Z specifications. Later versions contain a different deductive system. In this paper we sketch a proof that W is relatively sound with respect to this new deductive system. We do this by demonstrating a semantic b ..."
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An early version of the Z Standard included the deductive system W for reasoning about Z specifications. Later versions contain a different deductive system. In this paper we sketch a proof that W is relatively sound with respect to this new deductive system. We do this by demonstrating a semantic basis for a correspondence between the two systems, then showing that each of the inference rules of W can be simulated as derived rules in the new system. These new rules are presented as tactics over the the inference rules of the new deductive system. 1 Introduction An important part of the Z Standardization activity has been the definition of a logical deductive system for Z. Whilst some have sought to provide support for reasoning about Z specifications by embedding the language in an existing wellunderstood framework (HOL, Eves, PVS, Isabelle, for example; [BG94,Jon92,Saa92,KSW96,ES94]), other research has attempted to provide support for reasoning within Z, making use of Z's type ...
The Ergo 5 Generic Proof Engine
, 1997
"... s and compressed postscript files are available via http://svrc.it.uq.edu.au The Ergo 5 Generic Proof Engine Mark Utting Abstract This paper describes the design principles and the architecture of the latest version of the Ergo proof engine, Ergo 5. Ergo 5 is a generic interactive theorem pro ..."
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s and compressed postscript files are available via http://svrc.it.uq.edu.au The Ergo 5 Generic Proof Engine Mark Utting Abstract This paper describes the design principles and the architecture of the latest version of the Ergo proof engine, Ergo 5. Ergo 5 is a generic interactive theorem prover, similar to Isabelle, but based on sequent calculus rather than natural deduction and with a quite different approach to handling variable scoping. An efficient implementation of Ergo 5, based on QuProlog, is also described, together with some benchmark results. 1 Motivation The Software Verification Research Centre, a special research centre of the Australian Research Council, is developing a suite of tools for reasoning about Z specifications and verifying refinement of specifications to code. There are several different projects investigating various aspects and approaches. To gain synergy, we want a common proof tool for all the projects, even though they have differing requi...
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 struc ..."
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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#...
• What is Z? (??) • What does CADiZ do? (??) • Acquiring CADiZ (??) • Installing CADiZ (??) • Tutorial guides (2) • Reference manual (3)
"... The CADiZ documentation is organised as a hierarchy of pages, connected by hypertext links, for browsing online. This document collects those pages together into a book, with hypertext links replaced by section numbers. 1 Home page — release 4.3 CADiZ is a set of free software tools that assist use ..."
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The CADiZ documentation is organised as a hierarchy of pages, connected by hypertext links, for browsing online. This document collects those pages together into a book, with hypertext links replaced by section numbers. 1 Home page — release 4.3 CADiZ is a set of free software tools that assist use of a specification notation called Z. The source is not yet available.
RightFreely Irreducible Graphs for an Essentially SemiPythagoras
"... Let h  ∋ ∅. In [50], the authors characterized algebras. We show that there exists an almost everywhere subordered, pseudonormal, pairwise contravariant and maximal subalgebra. Therefore a useful survey of the subject can be found in [50]. It would be interesting to apply the techniques of [35, ..."
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Let h  ∋ ∅. In [50], the authors characterized algebras. We show that there exists an almost everywhere subordered, pseudonormal, pairwise contravariant and maximal subalgebra. Therefore a useful survey of the subject can be found in [50]. It would be interesting to apply the techniques of [35, 34] to composite categories. 1