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Provable Isomorphisms of Types
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 1990
"... A constructive characterization is given of the isomorphisms which must hold in all models of the typed lambda calculus with surjective pairing. By the close relation between closed Cartesian categories and models of these calculi, we also produce a characterization of those isomorphisms which hold ..."
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Cited by 39 (8 self)
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A constructive characterization is given of the isomorphisms which must hold in all models of the typed lambda calculus with surjective pairing. By the close relation between closed Cartesian categories and models of these calculi, we also produce a characterization of those isomorphisms which hold in all CCC's. By the correspondence between these calculi and proofs in intuitionistic positive propositional logic, we thus provide a characterization of equivalent formulae of this logic, where the definition of equivalence of terms depends on having "invertible" proofs between the two terms. Rittri (1989), on types as search keys in program libraries, provides an interesting example of use of these characterizations.
Prelogical Relations
, 1999
"... this paper but which have some intriguing connections to some of our results and techniques, are [32] and [20]. We believe that the concept of prelogical relation would have a beneficial impact on the presentation and understanding of their results ..."
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Cited by 26 (5 self)
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this paper but which have some intriguing connections to some of our results and techniques, are [32] and [20]. We believe that the concept of prelogical relation would have a beneficial impact on the presentation and understanding of their results
Fully Complete Models for ML Polymorphic Types
 In Proc. of MFCS'2000
, 1999
"... We present an axiomatic characterization of models fullycomplete for MLpolymorphic types of system F. This axiomatization is given for hyperdoctrine models, which arise as adjoint models, i.e. coKleisli categories of suitable linear categories. Examples of adjoint models can be obtained from cate ..."
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We present an axiomatic characterization of models fullycomplete for MLpolymorphic types of system F. This axiomatization is given for hyperdoctrine models, which arise as adjoint models, i.e. coKleisli categories of suitable linear categories. Examples of adjoint models can be obtained from categories of Partial Equivalence Relations over Linear Combinatory Algebras. We show that a special linear combinatory algebra of partial involutions induces an hyperdoctrine which satisfies our axiomatization, and hence it provides a fullycomplete model for MLtypes. Introduction In this paper we address the problem of full completeness for system F. A categorical model of a type theory (or logic) is said to be fullycomplete ([AJ94a]) if, for all types (formulae) A; B, all morphisms f : [[A]] ! [[B]], from the interpretation of A into the interpretation of B, are denotations of a proofterm of the intailment A ` B. The notion of fullcompleteness is the counterpart of the notion of full...