A Theory of Explicit Substitutions with Safe and Full Composition

Details A Theory of Explicit Substitutions with Safe and Full Composition A Theory of Explicit Substitutions with Safe and Full Composition

2009-05-15

arxiv.org/abs/0905.2539v3

LMCS 5 (3:1) 2009

Computer Science

Programming Languages

29 pages Special Issue: Selected Papers of the Conference "International Colloquium on Automata, Languages and Programming 200

Scientific paper

10.2168/LMCS-5(3:1)2009

Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the first part of this paper. Then, very simple technology in named variable-style notation is used to establish a theory of explicit substitutions for the lambda-calculus which enjoys a whole set of useful properties such as full composition, simulation of one-step beta-reduction, preservation of beta-strong normalisation, strong normalisation of typed terms and confluence on metaterms. Normalisation of related calculi is also discussed.

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