Abstract | ||
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Some computations on a symbolic term M are more judicious than others, for instance the leftmost outermost derivations in the λ-calculus. In order to characterise generically that kind of judicious computations, [M] introduces the
notion of external derivations in its axiomatic description of Rewriting Systems: a derivation e : M → P is said to be external when the derivation e; f : M → Q is standard whenever the derivation f : P → Q is standard.
In this article, we show that in every Axiomatic Rewriting System [M,1] every derivation d : M → Q can be factorised as an external derivation e : M → P followed by an internal derivation m : P → Q. Moreover, this epi-mono factorisation is functorial (i.e there is a nice diagram) in the sense of Freyd and Kelly [FK].
Conceptually, the factorisation property means that the efficient part of a computation can always be separated from its junk.
Technically, the property is the key step towards our illuminating interpretation of Berry's stability (semantics) as a syntactic
phenomenon (rewriting). In fact, contrary to the usual Lévy derivation spaces, the external derivation spaces enjoy meets.
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Year | DOI | Venue |
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1997 | 10.1007/BFb0026981 | Category Theory and Computer Science |
Keywords | Field | DocType |
factorisation theorem,rewriting theory | Discrete mathematics,Lambda calculus,Axiomatic system,Axiom,Rewriting,Category theory,Factorization,Mathematics,Computation | Conference |
ISBN | Citations | PageRank |
3-540-63455-X | 8 | 0.67 |
References | Authors | |
5 | 1 |
Name | Order | Citations | PageRank |
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Paul-andré Melliès | 1 | 392 | 30.70 |