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Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
Closed Freyd and κCategories
, 1999
"... We give two classes of sound and complete models for the computational λcalculus, or ccalculus. For the first, we generalise the notion of cartesian closed category to that of closed Freydcategory. For the second, we generalise simple indexed categories. The former gives a direct semantics fo ..."
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Cited by 8 (0 self)
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We give two classes of sound and complete models for the computational λcalculus, or ccalculus. For the first, we generalise the notion of cartesian closed category to that of closed Freydcategory. For the second, we generalise simple indexed categories. The former gives a direct semantics
On The Freyd Categories Of An Additive Category
, 2000
"... To any additive category C, we associate in a functorial way two additive categories A(C), B(C). The category A(C), resp. B(C), is the reflection of C in the category of additive categories with cokernels, resp. kernels, and cokernel, resp. kernel, preserving functors. Then the iteration AB(C) i ..."
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Cited by 10 (5 self)
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(C) is the reflection of C in the category of abelian categories and exact functors. We call A(C) and B(C) the Freyd categories of C since the first systematic study of these categories was done by Freyd in the midsixties. The purpose of the paper is to study further the Freyd categories and to indicate
Closed Freyd and kCategories
, 1999
"... . We give two classes of sound and complete models for the computational calculus, or ccalculus. For the first, we generalise the notion of cartesian closed category to that of closed Freydcategory. For the second, we generalise simple indexed categories. The former gives a direct semantics for t ..."
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. We give two classes of sound and complete models for the computational calculus, or ccalculus. For the first, we generalise the notion of cartesian closed category to that of closed Freydcategory. For the second, we generalise simple indexed categories. The former gives a direct semantics
Freyd is Kleisli, for arrows
 In C. McBride, T. Uustalu, Proc. of Wksh. on Mathematically Structured Programming, MSFP 2006, Electron. Wkshs. in Computing. BCS
, 2006
"... Arrows have been introduced in functional programming as generalisations of monads. They also generalise comonads. Fundamental structures associated with (co)monads are Kleisli categories and categories of (EilenbergMoore) algebras. Hence it makes sense to ask if there are analogous structures for ..."
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Cited by 6 (2 self)
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for Arrows. In this short note we shall take first steps in this direction, and identify for instance the Freyd
Cartesian effect categories are Freydcategories
, 2009
"... Most often, in a categorical semantics for a programming language, the substitution of terms is expressed by composition and finite products. However this does not deal with the order of evaluation of arguments, which may have major consequences when there are sideeffects. In this paper Cartesian e ..."
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Cited by 17 (14 self)
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. The universal property of the sequential product provides Cartesian effect categories with a powerful tool for constructions and proofs. To our knowledge, both effect categories and sequential products are new notions. Keywords. Categorical logic, computational effects, monads, Freydcategories, premonoidal
Theorems for free!
 FUNCTIONAL PROGRAMMING LANGUAGES AND COMPUTER ARCHITECTURE
, 1989
"... From the type of a polymorphic function we can derive a theorem that it satisfies. Every function of the same type satisfies the same theorem. This provides a free source of useful theorems, courtesy of Reynolds' abstraction theorem for the polymorphic lambda calculus. ..."
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Cited by 380 (8 self)
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From the type of a polymorphic function we can derive a theorem that it satisfies. Every function of the same type satisfies the same theorem. This provides a free source of useful theorems, courtesy of Reynolds' abstraction theorem for the polymorphic lambda calculus.
Natural language and natural selection
 Behavioral and Brain Sciences
, 1990
"... Pinker, S. & Bloom, P. (1990). Natural language and natural selection. Behavioral and Brain Sciences 13 ..."
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Cited by 373 (3 self)
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Pinker, S. & Bloom, P. (1990). Natural language and natural selection. Behavioral and Brain Sciences 13
Parameterised notions of computation
 In MSFP 2006: Workshop on mathematically structured functional programming, ed. Conor McBride and Tarmo Uustalu. Electronic Workshops in Computing, British Computer Society
, 2006
"... Moggi’s Computational Monads and Power et al’s equivalent notion of Freyd category have captured a large range of computational effects present in programming languages such as exceptions, sideeffects, input/output and continuations. We present generalisations of both constructs, which we call para ..."
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Cited by 52 (3 self)
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Moggi’s Computational Monads and Power et al’s equivalent notion of Freyd category have captured a large range of computational effects present in programming languages such as exceptions, sideeffects, input/output and continuations. We present generalisations of both constructs, which we call
Results 1  10
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1,699