Proof Systems for Retracts in Simply Typed Lambda Calculus

Stirling, Colin

doi:10.1007/978-3-642-39212-2_36

Cited by 8 publications

(7 citation statements)

References 14 publications

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“…While retractions between datatypes are a common tool in theoretical computer science (see e.g. [30]), we have been unable to find a version of Proposition 1 in the computer science literature. Nonetheless, we suspect this to be widely known.…”

Section: Proof Simple Structural Inductionmentioning

confidence: 81%

Unraveling Recursion: Compiling an IR with Recursion to System F

Jones¹,

Gkoumas²,

Kireev³

et al. 2019

Lecture Notes in Computer Science

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Lambda calculi are often used as intermediate representations for compilers. However, they require extensions to handle higherlevel features of programming languages. In this paper we show how to construct an IR based on System F µ ω which supports recursive functions and datatypes, and describe how to compile it to System F µ ω . Our IR was developed for commercial use at the IOHK company, where it is used as part of a compilation pipeline for smart contracts running on a blockchain.

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Section: Proof Simple Structural Inductionmentioning

confidence: 81%

Unraveling Recursion: Compiling an IR with Recursion to System F

Jones¹,

Gkoumas²,

Kireev³

et al. 2019

Lecture Notes in Computer Science

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“…We plan to investigate retractions in standard intersection types without conditions on right inverses, and in intersection and union types. The problem for the λβη-calculus is surely more difficult as shown by the papers [7,13,[20][21][22]26] and it is left for future work.…”

Section: Discussionmentioning

confidence: 99%

“…The problem of retraction solved in [13] is shown to be NP-complete in [22]. [26] gives a proof system which leads to an exponential decision procedure to characterise retraction for Curry types in the λβη-calculus.…”

Section: Related Workmentioning

confidence: 99%

Retractions in Intersection Types

Coppo

Dezani‐Ciancaglini

Díaz-Caro

et al. 2017

Electron. Proc. Theor. Comput. Sci.

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This paper deals with retraction - intended as isomorphic embedding - in intersection types building left and right inverses as terms of a lambda calculus with a bottom constant. The main result is a necessary and sufficient condition two strict intersection types must satisfy in order to assure the existence of two terms showing the first type to be a retract of the second one. Moreover, the characterisation of retraction in the standard intersection types is discussed.Comment: In Proceedings ITRS 2016, arXiv:1702.0187

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“…Retractions were considered as well, together with isomorphisms or separately. See, for example, Bruce and Longo (1985), Stirling (2013) and Coppo et al (2016) ‡ .…”

Section: Retractions Isomorphisms and Automorphisms Of Typesmentioning

confidence: 99%