Pattern Matching and Fixed Points

Barenbaum, Pablo; Bonelli, Eduardo; Mohamed, Kareem

doi:10.1145/3236950.3236972

Cited by 3 publications

(3 citation statements)

References 20 publications

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“…The definition of the system, in particular the extension of tight derivations to that setting, seems however far from being evident. Barembaum, Bonelli, and Mohamed also apply CbN multi types to a CbNeed calculus extended with pattern matching and fixpoints [15], that might be interesting to refine along the lines of our work.…”

Section: Discussionmentioning

confidence: 99%

“…Ehrhard adapted multi types to CbV [34], and very recently Accattoli and Guerrieri adapted de Carvalho's study of exact bounds to Ehrhard's system and CbV evaluation [8]. Kesner used de Carvalho's CbN multi types to obtain a simple proof that CbNeed is termination equivalent to CbN [40] (first proved with other techniques by Maraist, Odersky, and Wadler [48] and Ariola and Felleisen [11] in the nineties), and then Kesner and coauthors continued exploring the theory of CbNeed via CbN multi types [14,15,42].…”

Section: Introductionmentioning

confidence: 99%

“…The three evaluations are presented as strategies of Accattoli and Kesner's Linear Substitution Calculus (shortened to LSC) [1,6], a calculus with a simple but expressive form of explicit sharing. The LSC is strongly related to linear logic [2], and provides a neat and manageable presentation of CbNeed, introduced by Accattoli, Barenbaum, and Mazza in [3], and further developed by various authors in [4,5,10,14,15,40,42]. Our type systems count evaluation steps by annotating typing rules in the exact same way, and the proofs of correctness and completeness all follow the exact same structure.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Types by Need

Accattoli

Guerrieri

Leberle

2019

Programming Languages and Systems

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A cornerstone of the theory of λ-calculus is that intersection types characterise termination properties. They are a flexible tool that can be adapted to various notions of termination, and that also induces adequate denotational models. Since the seminal work of de Carvalho in 2007, it is known that multi types (i.e. non-idempotent intersection types) refine intersection types with quantitative information and a strong connection to linear logic. Typically, type derivations provide bounds for evaluation lengths, and minimal type derivations provide exact bounds. De Carvalho studied call-by-name evaluation, and Kesner used his system to show the termination equivalence of call-by-need and call-byname. De Carvalho's system, however, cannot provide exact bounds on call-by-need evaluation lengths. In this paper we develop a new multi type system for call-by-need. Our system produces exact bounds and induces a denotational model of callby-need, providing the first tight quantitative semantics of call-by-need.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Types by Need

Accattoli

Guerrieri

Leberle

2019

Programming Languages and Systems

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A simple and efficient implementation of strong call by need by an abstract machine

Biernacka

Charatonik

Drab

2022

Proc. ACM Program. Lang.

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We present an abstract machine for a strong call-by-need strategy in the lambda calculus. The machine has been derived automatically from a higher-order evaluator that uses the technique of memothunks to implement laziness. The derivation has been done with the use of an off-the-shelf transformation tool implementing the "functional correspondence" between higher-order interpreters and abstract machines, and it yields a simple and concise description of the machine. We prove that the resulting machine conservatively extends the lazy version of Krivine machine for the weak call-by-need strategy, and that it simulates the normal-order strategy in bilinear number of steps.

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Useful Open Call-By-Need

Accattoli

Leberle

2022

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Pattern Matching and Fixed Points

Cited by 3 publications

References 20 publications

Types by Need

Types by Need

A simple and efficient implementation of strong call by need by an abstract machine

Useful Open Call-By-Need

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