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Logical Predicates for Intuitionistic Linear Type Theories
 In Typed Lambda Calculi and Applications (TLCA'99), Lecture Notes in Computer Science 1581
, 1999
"... We develop a notion of Kripkelike parameterized logical predicates for two fragments of intuitionistic linear logic (MILL and DILL) in terms of their categorytheoretic models. Such logical predicates are derived from the categorical glueing construction combined with the free symmetric monoidal co ..."
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Cited by 11 (4 self)
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We develop a notion of Kripkelike parameterized logical predicates for two fragments of intuitionistic linear logic (MILL and DILL) in terms of their categorytheoretic models. Such logical predicates are derived from the categorical glueing construction combined with the free symmetric monoidal cocompletion. As applications, we obtain full completeness results of translations between linear type theories.
Girard Translation and Logical Predicates
, 2000
"... We present a short proof of a folklore result: the Girard translation from the simply typed lambda calculus to the linear lambda calculus is fully complete. The proof makes use of a notion of logical predicates for intuitionistic linear logic. While the main result is of independent interest, this p ..."
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Cited by 4 (3 self)
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We present a short proof of a folklore result: the Girard translation from the simply typed lambda calculus to the linear lambda calculus is fully complete. The proof makes use of a notion of logical predicates for intuitionistic linear logic. While the main result is of independent interest, this paper can be read as a tutorial on this proof technique for reasoning about relations between type theories.
A Semantic Formulation of ⊤⊤lifting and Logical Predicates for Computational Metalanguage
 In Proc. CSL 2005. LNCS 3634
, 2005
"... Abstract. A semantic formulation of Lindley and Stark’s ⊤⊤lifting is given. We first illustrate our semantic formulation of the ⊤⊤lifting in Set with several examples, and apply it to the logical predicates for Moggi’s computational metalanguage. We then abstract the semantic ⊤⊤lifting as the lif ..."
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Cited by 2 (0 self)
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Abstract. A semantic formulation of Lindley and Stark’s ⊤⊤lifting is given. We first illustrate our semantic formulation of the ⊤⊤lifting in Set with several examples, and apply it to the logical predicates for Moggi’s computational metalanguage. We then abstract the semantic ⊤⊤lifting as the lifting of strong monads across bifibrations with lifted symmetric monoidal closed structures. 1
Glueing Algebraic Structures on a 2Category
, 2000
"... We study the glueing constructions (comma objects) on general algebraic structures on a 2category, described in terms of 2monads and adjunctions. Specifically, lifting theorems for the comma objects and changeofbase results on both algebras of 2monads and adjunctions in a 2category are present ..."
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We study the glueing constructions (comma objects) on general algebraic structures on a 2category, described in terms of 2monads and adjunctions. Specifically, lifting theorems for the comma objects and changeofbase results on both algebras of 2monads and adjunctions in a 2category are presented. As a leading example, we take the 2monad on Cat whose algebras are symmetric monoidal categories, and show that many of the constructions in our previous work on models of linear type theories can be derived within this axiomatics. 1 Introduction In the previous work [2, 3] we have considered a glueing construction for symmetric monoidal (closed) categories, for studying the logical predicates for models of linear type theories. In that construction the glueing functor is supposed to be lax symmetric monoidal, thus preserves the structure only up to a few coherent morphisms, not up to isomorphisms or identity. From a view of the study of categories with algebraic structures [8] (which...