J. Gibbons, Lecture notes on algebraic and coalgebraic methods for calculating functional programs, from Estonian Winter School on Computer Science, 1999. Home/Search Document Not in Database Summary Related Articles Check |
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A Calculational Approach to Program Inversion - Linacre (2003) (1 citation) (Correct)
....h, there exists a unique homomorphism, which we will denote, adopting the concise banana bracket notation, by ( h] F . The condition for ( h] F to be a homomorphism reads: h] F [wrap, cons] h ( h] F ) Since a coproduct forming arrow can be represented as a coproduct of arrows [35], we can assume h has form [g , f ] without loss of generality. If we split it to pointwise style and write foldrn f g for ( g , f ] for this particular F) we obtain the characterisation of fold on non empty lists, which should look familiar: foldrn f g (wrap a) g a foldrn f g (cons (a, ....
J. Gibbons. Lecture notes on algebraic and coalgebraic methods for calculating functional programs. In Estonian Winter School on Computer Science, 1999.
Generic Accumulations - Pardo (2002) (5 citations) (Correct)
.... framework for reasoning algebraically about programs and is the basis for current developments in generic programming (see e.g. 2, 19] In this section we review the relevant concepts around the categorical approach to recursive types [23, 25, 21] and its application to program calculation [24, 27, 11, 22, 5, 16]. The category theoretic explanation of (recursive) types is based on the idea that types constitute objects of a category C, programs are modelled by arrows of the category, and type constructors are functors on C. In this setting, a datatype T is understood as a solution (a fixed point) of a ....
J. Gibbons. Lecture Notes on Algebraic and Coalgebraic Methods for Calculating Functional Programs. In Summer School on Algebraic and Coalgebraic Methods in the Mathematics of Program Construction, Oxford, UK, April 2000.
Towards Merging Recursion and Comonads - Pardo (2000) (3 citations) (Correct)
....programs which can be exploited for program transformation. Recursive operators structure functional programs according to the data structures they traverse or generate and come equipped with a battery of algebraic laws, also derivable from type definitions, which are used in program calculations [24, 11, 5, 15]. Some of these laws, the so called fusion laws, are particularly interesting in practice since they enclose specific cases of deforestation, a program transformation technique that permits to remove intermediate data structures from programs. Functional programs can also be structured according ....
....is based on and fixes some notation. We describe the essentials of the category theoretic explanation of inductive and coinductive datatypes, the definition of structural recursive functions in that setting and some of their algebraic laws. Further details on these topics can be found in e.g. [22, 11, 5, 1, 15]. 2.1 Preliminaries In the categorical approach to recursive types, types are modeled by objects of a category C, and functions (operations, programs) are modelled by morphisms of this category. In this setting, type constructors correspond to endofunctors on C (i.e. functors from C to C) We ....
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J. Gibbons. Lecture Notes on Algebraic and Coalgebraic Methods for Calculating Functional Programs. In Summer School on Algebraic and Coalgebraic Methods in the Mathematics of Program Construction, Oxford, UK, April 2000.
Distributivity of Categories of Coalgebras H. Peter Gumm - Jesse Hughes And (Correct)
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J. Gibbons, Lecture notes on algebraic and coalgebraic methods for calculating functional programs, from Estonian Winter School on Computer Science, 1999.
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