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Towards Merging Recursion and Comonads
, 2000
"... Comonads are mathematical structures that account naturally for effects that derive from the context in which a program is executed. This paper reports ongoing work on the interaction between recursion and comonads. Two applications are shown that naturally lead to versions of a comonadic fold op ..."
Abstract

Cited by 9 (2 self)
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Comonads are mathematical structures that account naturally for effects that derive from the context in which a program is executed. This paper reports ongoing work on the interaction between recursion and comonads. Two applications are shown that naturally lead to versions of a comonadic fold operator on the product comonad. Both versions capture functions that require extra arguments for their computation and are related with the notion of strong datatype. 1 Introduction One of the main features of recursive operators derivable from datatype definitions is that they impose a structure upon 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 socalled fusion laws, are particularly interesting in p...
On Categories of Asynchronous Circuits
, 1994
"... In this paper we describe a general categorical model of asynchronous circuits flexible enough to describe various paradigms of communication between circuit elements  each paradigm gives rise to a specific category of circuits. In each case the operations on circuits and semantics give an algebr ..."
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In this paper we describe a general categorical model of asynchronous circuits flexible enough to describe various paradigms of communication between circuit elements  each paradigm gives rise to a specific category of circuits. In each case the operations on circuits and semantics give an algebra of circuits akin to a process algebra in which series composition is the composition of the category. The essential aspects of the model are ffl a category of data types [Wal89]; ffl a category Circ whose objects are data types, and whose arrows are inputoutput circuits built from data types; ffl a semantic category Sem suitable to contain behaviours of the circuits; ffl operations on Circ and Sem (for example, cases, parallel, and feedback operations); ffl and a behaviour functor bhv : Circ ! Sem, which preserves the operations (compositionality of behaviour). The study of asynchrony in circuit theory is precisely the study of circuit categories and associated behaviour functors ...
Towards Merging Recursion and Comonads
, 2000
"... Comonads are mathematical structures that account naturally for effects that derive from the context in which a program is executed. This paper reports ongoing work on the interaction between recursion and comonads. Two applications are shown that naturally lead to versions of a comonadic fold op ..."
Abstract
 Add to MetaCart
Comonads are mathematical structures that account naturally for effects that derive from the context in which a program is executed. This paper reports ongoing work on the interaction between recursion and comonads. Two applications are shown that naturally lead to versions of a comonadic fold operator on the product comonad. Both versions capture functions that require extra arguments for their computation and are related with the notion of strong datatype. 1 Introduction One of the main features of recursive operators derivable from datatype definitions is that they impose a structure upon 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 socalled fusion laws, are particularly interesting in p...