NDLI: A syntactic and functional correspondence between reduction semantics and reduction-free full normalisers (2013).

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A syntactic and functional correspondence between reduction semantics and reduction-free full normalisers (2013).

Content Provider	CiteSeerX
Author	García-Pérez, Álvaro Nogueira, Pablo
Abstract	Olivier Danvy and others have shown the syntactic correspondence machines, as well as the functional correspondence between reduction-free normalisers (a big-step semantics) and abstract machines. The correspondences are established by program transformation (so-called interderivation) techniques. A reduction semantics machine obtained from them is the same. However, the correspondences fail when the underlying reduction strategy is hybrid, i.e., relies on another sub-strategy. Hybridisation is an essential structural property of full-reducing and complete strategies. Hybridisation is unproblematic in the functional correspondence. But in the syntactic correspondence the refocusing and inlining-ofiterate-function steps become context sensitive, preventing the refunctionalisation of the abstract machine. We show how to solve the problem and showcase the interderivation of normalisers for normal order, the standard, full-reducing and complete strategy of the pure lambda calculus. Our solution makes it possible to interderive, rather than contrive, full-reducing abstract machines. As expected, the machine we obtain is a variant of Pierre Crégut’s full Krivine machine KN.
File Format	PDF
Publisher Date	2013-01-01
Access Restriction	Open
Subject Keyword	Functional Correspondence Reduction Semantics Reduction-free Full Normaliser Abstract Machine Complete Strategy Normal Order Full-reducing Abstract Machine Essential Structural Property Reduction Semantics Machine Inlining-ofiterate-function Step Reduction Strategy Reduction-free Normaliser Syntactic Correspondence Machine Big-step Semantics Program Transformation Syntactic Correspondence Pure Lambda Calculus Olivier Danvy So-called Interderivation
Content Type	Text

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