A theory of finite maps

Collins, Georgina; Syme, Don

doi:10.1007/3-540-60275-5_61

Cited by 9 publications

(4 citation statements)

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“…However, it does not provide an induction principle for finite maps, and forward reasoning is often needed to use the library. We found we did not need induction to reason on finite maps, though there are natural induction principles we might have proved [11,18]. The fact that the library does not provide for extensional equality of finite maps means that, for example, the following simple lemma does not hold:…”

Section: Implementing Substitutions As Finite Mapsmentioning

confidence: 99%

A Machine Checked Model of Idempotent MGU Axioms For Lists of Equational Constraints

Kothari

Caldwell

2010

Electron. Proc. Theor. Comput. Sci.

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We present formalized proofs verifying that the first-order unification algorithm defined over lists of satisfiable constraints generates a most general unifier (MGU), which also happens to be idempotent. All of our proofs have been formalized in the Coq theorem prover. Our proofs show that finite maps produced by the unification algorithm provide a model of the axioms characterizing idempotent MGUs of lists of constraints. The axioms that serve as the basis for our verification are derived from a standard set by extending them to lists of constraints. For us, constraints are equalities between terms in the language of simple types. Substitutions are formally modeled as finite maps using the Coq library Coq.FSets.FMapInterface. Coq's method of functional induction is the main proof technique used in proving many of the axioms

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Section: Implementing Substitutions As Finite Mapsmentioning

confidence: 99%

A Machine Checked Model of Idempotent MGU Axioms For Lists of Equational Constraints

Kothari

Caldwell

2010

Electron. Proc. Theor. Comput. Sci.

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“…This is formalised using finite maps, which have not been adequately defined in HOL before. This is described elsewhere [5].…”

Section: Semanticsmentioning

confidence: 99%

Supporting Reasoning about Functional Programs: An Operational Approach

Collins

1995

Electronic Workshops in Computing

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Some existing systems for supporting reasoning about functional programs have been constructed without first formalising the semantics of the language. This paper discusses how a reasoning system can be built, within the HOL theorem proving environment, based on an operational semantics for the language and using a fully definitional approach. The theoretical structure of the system is based on work by Andrew Gordon, where applicative bisimulation is used to define program equivalence. We discuss how this theory can be embedded in HOL and the type of tools which can be built on top of this theoretical framework to make reasoning possible in practice.

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“…The PVS theorem-prover [ 1 I] has an undocumented decision procedure for a theory of arrays [12], and HOL has some automatic support for a theory of arrays via a library for finite partial functions [3].…”

Section: Introductionmentioning

confidence: 99%