Behavioural specifications in type theory

Mylonakis, Nikos

doi:10.1007/3-540-61629-2_55

Cited by 2 publications

(1 citation statement)

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“…Important issues in algebraic specification refinement, such as the choice of input sorts [36] and the stability of constructors [39,37,10], are automatically resolved in the type-theoretic setting. Other work linking algebraic specification and type theory includes [28,34,2,41,40]. Relevant work using System F and parametricity includes [29,30] showing that the introduction of non-terminating recursion also breaks down the tight correspondence between the existence of a simulation relation and observational equivalence.…”

Section: Introductionmentioning

confidence: 99%

A Higher-Order Simulation Relation for System F

Hannay

2000

Lecture Notes in Computer Science

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The notion of data type specification refinement is discussed in a setting of System F and the logic for parametric polymorphism of Plotkin and Abadi. At first order, one gets a notion of specification refinement up to observational equivalence in the logic simply by using Luo's formalism. This paper generalises this notion to abstract data types whose signatures contain higher-order and polymorphic functions. At higher order, the tight connection in the logic between the existence of a simulation relation and observational equivalence ostensibly breaks down. We show that an alternative notion of simulation relation is suitable. This also gives a simulation relation in the logic that composes at higher order, thus giving a syntactic logical counterpart to recent advances on the semantic level.

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