We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In particular, weak call-by-value beta-reduction can be simulated by an orthogonal constructor term rewrite system in the same number of reduction steps. Conversely, each reduction in a term rewrite system can be simulated by a constant number of beta-reduction steps. This is relevant to implicit computational complexity, because the number of beta steps to normal form is polynomially related to the actual cost (that is, as performed on a Turing machine) of normalization, under weak call-by-value reduction. Orthogonal constructor term rewrite systems and lambda-calculus are thus both polynomially related to Turing machines, taking as notion of cost their natural parameters.

Dal Lago U., Martini S. (2009). On Constructor Rewrite Systems and the Lambda-Calculus. HEIDELBERG : Springer Verlag.

On Constructor Rewrite Systems and the Lambda-Calculus

DAL LAGO, UGO;MARTINI, SIMONE
2009

Abstract

We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In particular, weak call-by-value beta-reduction can be simulated by an orthogonal constructor term rewrite system in the same number of reduction steps. Conversely, each reduction in a term rewrite system can be simulated by a constant number of beta-reduction steps. This is relevant to implicit computational complexity, because the number of beta steps to normal form is polynomially related to the actual cost (that is, as performed on a Turing machine) of normalization, under weak call-by-value reduction. Orthogonal constructor term rewrite systems and lambda-calculus are thus both polynomially related to Turing machines, taking as notion of cost their natural parameters.
2009
Automata, Languages and Programming, Vol II
163
174
Dal Lago U., Martini S. (2009). On Constructor Rewrite Systems and the Lambda-Calculus. HEIDELBERG : Springer Verlag.
Dal Lago U.; Martini S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/79046
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