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An Axiomatic Approach to Binary Logical Relations with Applications to Data Refinement
 Proc. TACS'97, Springer LNCS 1281
, 1997
"... We introduce an axiomatic approach to logical relations and data refinement. We consider a programming language and the monad on the category of small categories generated by it. We identify abstract data types for the language with sketches for the associated monad, and define an axiomatic notion o ..."
Abstract

Cited by 18 (1 self)
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We introduce an axiomatic approach to logical relations and data refinement. We consider a programming language and the monad on the category of small categories generated by it. We identify abstract data types for the language with sketches for the associated monad, and define an axiomatic notion of "relation" between models of such a sketch in a semantic category. We then prove three results: (i) such models lift to the whole language together with the sketch; (ii) any such relation satisfies a soundness condition, and (iii) such relations compose. We do this for both equality of data representations and for an ordered version. Finally, we compare our formulation of data refinement with that of Hoare. This work has been done with the support of the MITI Cooperative Architecture Project. This author also acknowledges the support of Kakenhi. y This author achnowledges the support of the MITI Cooperative Architecture Project. z This author acknowledges the support of EPSRC grant...
A General Completeness Result in Refinement
 in: Proceedings of the 14th International Workshop on Algebraic Development Techniques, no. 1827 in Lecture Notes in Computer Science
, 1999
"... . In a paper in 1986, Hoare, He and Sanders proposed a formulation of refinement for a system equivalent to the #calculus using a relation based semantics. To give a proof method to show that one program is a refinement of another, they introduced downward simulation and upward simulation, but the ..."
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Cited by 1 (1 self)
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. In a paper in 1986, Hoare, He and Sanders proposed a formulation of refinement for a system equivalent to the #calculus using a relation based semantics. To give a proof method to show that one program is a refinement of another, they introduced downward simulation and upward simulation, but the proof method based upon either of them is not complete with respect to their notion of refinement, so they claimed "joint" completeness based upon both notions of simulation with respect to their notion of refinement. We give a new definition of refinement in terms of structure respecting lax transformations, and show that the proof method based upon downward simulation is complete with respect to this notion of refinement. Although our theory works for the #calculus, we present the result for the calculus to make the presentation simpler. We use results in enriched category theory to show this, and the central notion here is that of algebraic structure on locally ordered categories, not o...