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Using Commutativity Properties for Controlling Coercions
"... . This paper investigates some soundness conditions which have to be fulfilled in systems with coercions and generic operators. A result of Reynolds on unrestricted generic operators is extended to generic operators which obey certain constraints. We get natural conditions for such operators, whi ..."
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. This paper investigates some soundness conditions which have to be fulfilled in systems with coercions and generic operators. A result of Reynolds on unrestricted generic operators is extended to generic operators which obey certain constraints. We get natural conditions for such operators, which are expressed within the theoretic framework of category theory. However, in the context of computer algebra, there arise examples of coercions and generic operators which do not fulfil these conditions. We describe a framework  relaxing the above conditions  that allows distinguishing between cases of ambiguities which can be resolved in a quite natural sense and those which cannot. An algorithm is presented that detects such unresolvable ambiguities in expressions. 1 Introduction Reynolds [10] uses category theory to investigate the problems of the interaction of coercions (implicit conversions) and generic operators (also called overloaded operators) . He concludes with ...
HPGP: HighPerformance Generic Programming for Computational Mathematics by CompileTime Instantiation of Higher Order Functors
, 1997
"... A functor is a parameterized program module i.e. a function that takes modules as arguments and returns a module as its result. A higherorder functor deals in the same way with modules whose components are functors themselves. We propose to develop a generic compilation system for the construction ..."
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A functor is a parameterized program module i.e. a function that takes modules as arguments and returns a module as its result. A higherorder functor deals in the same way with modules whose components are functors themselves. We propose to develop a generic compilation system for the construction of highperformance mathematical software libraries for scientific and technical application domains. This system has the following features: 1. It is based on a powerful higherorder functor language. 2. It is an open library that can be retargeted to any core language. 3. It is able to resolve functor instantiation at compiletime. The functor language is expressive enough to build all types and type constructors without referring to the core language (thus maximizing flexibility) and to express all interactions between modules by parameterization (thus maximizing reusability). By compiletime instantiation, genericity does not cause any execution overhead; by automatically sharing instant...
The "Optical Formula Recognition" System for Handprinted Input
, 1995
"... this paper an integrated system  whose development started with (Marzinkewitsch, 1990)  will be presented, which offers the demanded facilities: Calculating by 07477171/90/000000 + 00 $03.00/0 c fl 1995 Academic Press Limited 2 J. Hartmann, G. Hotz, R. Loos, R. Marzinkewitsch, J. Quapp, F. W ..."
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this paper an integrated system  whose development started with (Marzinkewitsch, 1990)  will be presented, which offers the demanded facilities: Calculating by 07477171/90/000000 + 00 $03.00/0 c fl 1995 Academic Press Limited 2 J. Hartmann, G. Hotz, R. Loos, R. Marzinkewitsch, J. Quapp, F. Weigel, and A. Weber