“…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.…”
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.
“…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.…”
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.
“…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.…”
Abstract. The atomic lambda-calculus is a typed lambda-calculus with explicit sharing, which originates in a Curry-Howard interpretation of a deep-inference system for intuitionistic logic. It has been shown that it allows fully lazy sharing to be reproduced in a typed setting. In this paper we prove strong normalization of the typed atomic lambda-calculus using Tait's reducibility method.
“…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).…”
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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