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A Generalisation of Prelogical Predicates to Simply Typed Formal Systems
 In ICALP
, 2004
"... We generalise the notion of prelogical predicates [HS02] to arbitrary simply typed formal systems and their categorical models. We establish the basic lemma of prelogical predicates and composability of binary prelogical relations in this generalised setting. This generalisation takes place in ..."
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We generalise the notion of prelogical predicates [HS02] to arbitrary simply typed formal systems and their categorical models. We establish the basic lemma of prelogical predicates and composability of binary prelogical relations in this generalised setting. This generalisation takes place in a categorical framework for typed higherorder abstract syntax and semantics [Fio02,MS03].
Specification Refinement with System F, The HigherOrder Case
, 2000
"... . A typetheoretic counterpart to the notion of algebraic specification refinement is discussed for abstract data types with higherorder signatures. The typetheoretic setting consists of System F and the logic for parametric polymorphism of Plotkin and Abadi. For firstorder signatures, this setti ..."
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. A typetheoretic counterpart to the notion of algebraic specification refinement is discussed for abstract data types with higherorder signatures. The typetheoretic setting consists of System F and the logic for parametric polymorphism of Plotkin and Abadi. For firstorder signatures, this setting immediately gives a natural notion of specification refinement up to observational equivalence via the notion of simulation relation. Moreover, a proof strategy for proving observational refinements formalised by Bidoit, Hennicker and Wirsing can be soundly imported into the type theory. In lifting these results to the higherorder case, we find it necessary firstly to develop an alternative simulation relation and secondly to extend the parametric PERmodel interpretation, both in such a way as to observe data type abstraction barriers more closely. 1 Introduction One framework in algebraic specification that has particular appeal and applicability is that of stepwise specification refi...
Logical Relations, Data Abstraction, and Structured Fibrations
"... We develop a notion of equivalence between interpretations of the simply typed calculus together with an equationally dened abstract datatype, and we show that two interpretations are equivalent if and only if they are linked by a logical relation. We show that our construction generalises from th ..."
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We develop a notion of equivalence between interpretations of the simply typed calculus together with an equationally dened abstract datatype, and we show that two interpretations are equivalent if and only if they are linked by a logical relation. We show that our construction generalises from the simply typed calculus to include the linear calculus and calculi with additional type and term constructors, such as those given by sum types or by a strong monad for modelling phenomena such as partiality or nondeterminism. This is all done in terms of category theoretic structure, using  brations to model logical relations following Hermida, and adapting Jung and Tiuryn's logical relations of varying arity to provide the completeness results, which form the heart of the work.
Sketches
 JOURNAL OF PURE AND APPLIED ALGEBRA
, 1999
"... We generalise the notion of sketch. For any locally nitely presentable category, one can speak of algebraic structure on the category, or equivalently, a finitary monad on it. For any such finitary monad, we de ne the notions of sketch and strict model and prove that any sketch has a generic stric ..."
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We generalise the notion of sketch. For any locally nitely presentable category, one can speak of algebraic structure on the category, or equivalently, a finitary monad on it. For any such finitary monad, we de ne the notions of sketch and strict model and prove that any sketch has a generic strict model on it. This is all done with enrichment in any monoidal biclosed