Introduction to higher order categorical logic
Introduction to higher order categorical logic
Algebraic approaches to program semantics
Algebraic approaches to program semantics
Notions of computation and monads
Information and Computation
Institutions: abstract model theory for specification and programming
Journal of the ACM (JACM)
Categories and computer science
Categories and computer science
New foundations for fixpoint computations: FIX-hyperdoctrines and the FIX-logic
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
Categorical programming with functorial strength
Categorical programming with functorial strength
Fundamentals of Algebraic Specification I
Fundamentals of Algebraic Specification I
A Typed Lambda Calculus with Categorical Type Constructors
Category Theory and Computer Science
A categorical programming language
A categorical programming language
Consistency of the theory of contexts
Journal of Functional Programming
Parameterizations and Fixed-Point Operators on Control Categories
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
Parameterizations and fixed-point operators on control categories
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
Van Kampen colimits as bicolimits in span
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Parameterizations and Fixed-Point Operators on Control Categories
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
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A specification, as we shall use it here, consists of a signature together with a collection of (non-conditional) equations; these equations involve terms in the ‘distributive type theory’ which is built on top of the signature. This type theory has finite product (x, 1) and coproduct (+, 0) types. Particular simple examples of such specifications are Hagino specifications, which are used to describe inductively defined types. Models of specifications are described in arbitrary distributive categories. In a more categorical approach, one describes models as structure preserving functors. It enables us to define in general what are (a) models of parametrized spefications (in terms of Kan extensions) and (b) models with parameters (in terms of so-called ‘simple slice’ categories). It is shown that in the special case of Hagino specifications, these general definitions specialize to ones in terms of algebras or coalgebras for associated ‘strong’ polynomial functors. Models with parameters of Hagino specifications were described earlier by Cockett and Spencer.