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Kripke Models and the (in)equational Logic of the SecondOrder LambdaCalculus
, 1995
"... . We define a new class of Kripke structures for the secondorder calculus, and investigate the soundness and completeness of some proof systems for proving inequalities (rewrite rules) as well as equations. The Kripke structures under consideration are equipped with preorders that correspond to an ..."
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, and Preor is the category of preorders). We make use of an explicit construction of the exponential of functors in the Cartesianclosed category Preor W , and we also define a kind of exponential Q \Phi (A s ) s2T to take care of type abstraction. However, we strive for simplicity, and we only use
Preliminary Version
, 1993
"... Kripke Models for the SecondOrder lambdaCalculus We define a new class of Kripke structures for the secondorder λcalculus, and investigate the soundness and completeness of some proof systems for proving inequalities (rewrite rules) or equations. The Kripke structures under consideration are equ ..."
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is a preorder, the set of worlds, and Preor is the category of preorders). We make use of an explicit construction of the exponential of functors in the Cartesianclosed category PreorW, and we also define a kind of exponential ∏Φ(As)s∈Τ to take care of type abstraction. We obtain soundness
Compactly generated stacks: a cartesianclosed theory of topological stacks
 MATH
, 2009
"... A convenient 2category of topological stacks is constructed which is both complete and Cartesian closed. This 2category, called the 2category of compactly generated stacks, is the analogue of classical topological stacks, but for a different Grothendieck topology. In fact, there is an equivalen ..."
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Cited by 4 (0 self)
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A convenient 2category of topological stacks is constructed which is both complete and Cartesian closed. This 2category, called the 2category of compactly generated stacks, is the analogue of classical topological stacks, but for a different Grothendieck topology. In fact
Cartesian Closed Categories of Domains
, 1988
"... Contents 1 Basic Concepts 11 1.1 Ordered sets, directed sets, and directedcomplete partial orders : : : 11 1.2 Algebraic and continuous posets : : : : : : : : : : : : : : : : : : : : : 15 1.3 Scotttopology and continuous functions : : : : : : : : : : : : : : : : 20 1.4 Bifinite domains : : : : : ..."
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Cited by 29 (1 self)
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cartesian closed categories of algebraic directedcomplete partial orders with a least element : : : : : : : : : : : : : : 63 3 Domains without least element 69 3.1 Disjoint
Cartesian Closed Dialectica Categories
"... When Gödel developed his functional interpretation, also known as the Dialectica interpretation, his aim was to prove (relative) consistency of first order arithmetic by reducing it to a quantifierfree theory with finite types. Like other functional interpretations (e.g. Kleene’s realizability in ..."
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interpretation gives rise to the Dialectica categories (described by V. de Paiva in [dP89] and J.M.E. Hyland in [Hyl02]). These categories are symmetric monoidal closed and have finite products and weak coproducts, but they are not Cartesian closed in general. We give an analysis of how to obtain weakly
Cartesian Closed Double Categories,
"... their LambdaNotation, and the PiCalculus We introduce the notion of cartesian closed double category to provide mobile calculi for communicating systems with specific semantic models: One dimension is dedicated to compose systems and the other to compose their computations and their observations. ..."
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their LambdaNotation, and the PiCalculus We introduce the notion of cartesian closed double category to provide mobile calculi for communicating systems with specific semantic models: One dimension is dedicated to compose systems and the other to compose their computations and their observations
The category of categories with pullbacks is cartesian closed
, 904
"... We show that the category of categories with pullbacks and pullback preserving functors is cartesian closed. ..."
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We show that the category of categories with pullbacks and pullback preserving functors is cartesian closed.
On the Interpretation of Type Theory in Locally Cartesian Closed Categories
 Proceedings of Computer Science Logic, Lecture Notes in Computer Science
, 1994
"... . We show how to construct a model of dependent type theory (category with attributes) from a locally cartesian closed category (lccc). This allows to define a semantic function interpreting the syntax of type theory in an lccc. We sketch an application which gives rise to an interpretation of exten ..."
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Cited by 57 (1 self)
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. We show how to construct a model of dependent type theory (category with attributes) from a locally cartesian closed category (lccc). This allows to define a semantic function interpreting the syntax of type theory in an lccc. We sketch an application which gives rise to an interpretation
Cartesian closed stable categories q
, 2004
"... The aim of this paper is to establish some Cartesian closed categories which are between the two Cartesian closed categories: SLP (the category of Ldomains and stable functions) and DI (the full subcategory of SLP whose objects are all dIdomains). First we show that the exponentials of every full ..."
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The aim of this paper is to establish some Cartesian closed categories which are between the two Cartesian closed categories: SLP (the category of Ldomains and stable functions) and DI (the full subcategory of SLP whose objects are all dIdomains). First we show that the exponentials of every full
Equations in locally cartesian closed categories
, 2006
"... It is wellknown how to model simply typed calculus using cartesian closed categories (Lambek and Scott 1986). Type theories with dependent types, e.g. MartinLof type theories, are much harder to give categorical models. Dependent types can be handled either using bered category theory (Jacobs 199 ..."
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It is wellknown how to model simply typed calculus using cartesian closed categories (Lambek and Scott 1986). Type theories with dependent types, e.g. MartinLof type theories, are much harder to give categorical models. Dependent types can be handled either using bered category theory (Jacobs
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