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Abstract types have existential types
Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages - POPL '85, 1985Abstract data type declarations appear in typed programming languages like Ada, Alphard, CLU and ML. This form of declaration binds a list of identifiers to a type with associated operations, a composite “value” we call a data algebra . We use a second-order typed lambda calculus SOL to show how data algebras may be
John C. Mitchell, Gordon D. Plotkin
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1995
The purpose of this paper is threefold. First, we describe some basic ideas of constructive type theory, with emphasis on their value for specification. Second, we demonstrate the use of type theory as a specification language. This is done by means of a detailed example, namely, the specification of an abstract data type (ADT) for multisets.
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The purpose of this paper is threefold. First, we describe some basic ideas of constructive type theory, with emphasis on their value for specification. Second, we demonstrate the use of type theory as a specification language. This is done by means of a detailed example, namely, the specification of an abstract data type (ADT) for multisets.
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Type inference and type classes
1990Type classes were developed in association with the lazy functional programming language Haskell [1] to handle overloading since no satisfactory off-the-shelf solution was available. The motivation and description of type classes is given in [2].
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1997
We present two mutual encodings, respectively of the Calculus of Inductive Constructions in Zermelo-Fraenkel set theory and the opposite way. More precisely, we actually construct two families of encodings, relating the number of universes in the type theory with the number of inaccessible cardinals in the set theory.
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We present two mutual encodings, respectively of the Calculus of Inductive Constructions in Zermelo-Fraenkel set theory and the opposite way. More precisely, we actually construct two families of encodings, relating the number of universes in the type theory with the number of inaccessible cardinals in the set theory.
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Dependently Typed Records in Type Theory
Formal Aspects of Computing, 2002Abstract.The languagePebbleof Burstall and Lampson proposed dependent types as the underlying principle in a unified framework to explain facilities for programming in the large, such asmodulesandsignatures, as well as for programming in the small. This proposal soon extended to large scale formal proof development as well.
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Abstract Data Types and Type Theory: Theories as Types
Mathematical Logic Quarterly, 1991Ruy J. G. B. de Queiroz +1 more
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type++: Prohibiting Type Confusion with Inline Type Information
Proceedings 2025 Network and Distributed System Security SymposiumNicolas Badoux +3 more
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