An algorithm for optimal lambda calculus reduction

Lamping, John

doi:10.1145/96709.96711

Cited by 191 publications

(120 citation statements)

References 4 publications

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“…The same line of argument applies to establish the associativity of append: X = append(append( [1,3,5], [7,9]), [11,13,15]) X = append( [1,3,5],append( [7,9], [11,13,15]…”

Section: Examplementioning

confidence: 99%

“…Most previous work in this approach adopted Interaction Nets [8] to represent and manipulate graphs ( [9][11] [12], to name a few). Many of the encodings of the λ-calculus into Interaction Nets pursued optimal sharing or efficiency, and resulted in more or less involved representation of λ-terms to achieve the objective.…”

Section: Encoding the Pure Lambda Calculus Into Hyperlmntalmentioning

confidence: 99%

“…Color comparison was based on whether one color was a prefix of the other, whose practical cost is yet to be studied. Lamping's optimal sharing [9] also employed many colors (called levels), and further employed tokens called croissants and brackets (both coming with many colors as well) to achieve sharing and complicated level management. Our encoding pursues a different direction: the size of the rewrite system.…”

Section: Properties Of the Encodingmentioning

confidence: 99%

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Towards a Substrate Framework of Computation

Ueda

2014

Lecture Notes in Computer Science

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Abstract. A grand challenge in computing is to establish a substrate computational model that encompasses diverse forms of non-sequential computation. This paper demonstrates how a hypergraph rewriting framework nicely integrates various forms and ingredients of concurrent computation and how simple static analyses help the understanding and optimization of programs. Hypergraph rewriting treats processes and messages in a unified manner, and treats message sending and parameter passing as symmetric reaction between two entities. Specifically, we show how fine-grained strong reduction of the λ-calculus can be concisely encoded into hypergraph rewriting with a small set of primitive operations.

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“…The same line of argument applies to establish the associativity of append: X = append(append( [1,3,5], [7,9]), [11,13,15]) X = append( [1,3,5],append( [7,9], [11,13,15]…”

Section: Examplementioning

confidence: 99%

Section: Encoding the Pure Lambda Calculus Into Hyperlmntalmentioning

confidence: 99%

Section: Properties Of the Encodingmentioning

confidence: 99%

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Towards a Substrate Framework of Computation

Ueda

2014

Lecture Notes in Computer Science

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“…It is a leading principle behind, among others, explicit substitution calculi [1,18,8,9,15,2], term calculi with strategies or higher-order transformations [14,3], and sharing graphs in the style of Lamping [17,4,21]. The atomic lambda-calculus represents a novel category in this range.…”

Section: Introductionmentioning

confidence: 99%

A Proof of Strong Normalisation of the Typed Atomic Lambda-Calculus

Gundersen

Heijltjes

Parigot

2013

Logic for Programming, Artificial Intelligence, and Reasoning

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“…T h i s i s f a r from e cient i f A contains function applications that s till need to be evaluated. Some optimizations of lambdacalculus, involving sharing of a rguments by di erent functions, have b e e n p r oposed by W adsworth (1971) and Lamping (1990).…”

Section: Introductionmentioning

confidence: 99%

Graph rewriting semantics for functional programming languages

Eekelen

Smetsers

Plasmeijer

1997

Computer Science Logic

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Abstract. The lambda calculus forms without any q uestion *the* theoretical backbone o f f u n ctional programming languages. For the design and implementation of the lazy functional language Concurrent C l e a n w e have used a related computational model: Term Graph Rewriting Systems (TGRS's). T h is paper wraps up our main conclusions after 10 years of experience with graph rewriting semantics for functional programming languages. TGRS's are not a direct extension of the l a m bdacalculus, so one sometimes has to re-establish known theoretical results. But T G R S 's are that much closer to the world of functional programming t h at its use has been proven to be very worthwhile. In TGRS's functions h a ve names, there are constants, pattern matching and one can choose to either share expressions or copy t h e m . Graph reduction very accurately models the essential behaviour o f m ost implementations of functional languages and therefore it forms a g o o d base for reasoning about reduction properties as well as the time and space consumption of functional applications. With uniqueness typing important information can be derived for ecient i m plementation and for purely functional interfacing w i t h i m perative programs.

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An algorithm for optimal lambda calculus reduction

Cited by 191 publications

References 4 publications

Towards a Substrate Framework of Computation

Towards a Substrate Framework of Computation

A Proof of Strong Normalisation of the Typed Atomic Lambda-Calculus

Graph rewriting semantics for functional programming languages

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