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A Unified Approach to Fully Lazy Sharing
 In POPL
, 2012
"... We give an axiomatic presentation of sharingvialabelling for weak λcalculi, that allows to formally compare many different approaches to fully lazy sharing, and obtain two important results. We prove that the known implementations of full laziness are all equivalent in terms of the number of βre ..."
Abstract

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We give an axiomatic presentation of sharingvialabelling for weak λcalculi, that allows to formally compare many different approaches to fully lazy sharing, and obtain two important results. We prove that the known implementations of full laziness are all equivalent in terms of the number of βreductions performed, although they behave differently regarding the duplication of terms. We establish a link between the optimality theories of weak λcalculi and firstorder rewriting systems by expressing fully lazy λlifting in our framework, thus emphasizing the firstorder essence of weak reduction. This technical report extends [Bal12] with comprehensive proofs. 1
Minimality in a Linear Calculus with Iteration Abstract
"... System L is a linear version of Gödel’s System T, where the λcalculus is replaced with a linear calculus; or alternatively a linear λcalculus enriched with some constructs including an iterator. There is thus at the same time in this system a lot of freedom in reduction and a lot of information ab ..."
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System L is a linear version of Gödel’s System T, where the λcalculus is replaced with a linear calculus; or alternatively a linear λcalculus enriched with some constructs including an iterator. There is thus at the same time in this system a lot of freedom in reduction and a lot of information about resources, which makes it an ideal framework to start a fresh attempt at studying reduction strategies in λcalculi. In particular, we show that callbyneed, the standard strategy of functional languages, can be defined directly and effectively in System L, and can be shown minimal among weak strategies. 1