Efficient Mendler-Style Lambda-Encodings in Cedille

Firsov, Denis; Blair, Richard; Stump, Aaron

doi:10.1007/978-3-319-94821-8_14

Cited by 10 publications

(22 citation statements)

References 18 publications

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“…RelTT may be compared with previous work of Stump et al on Cedille [25], [26], [27]. Both systems aim at a minimalistic extension of a small pure type system as a foundation for type theory.…”

Section: Related Workmentioning

confidence: 99%

Relational Type Theory (All Proofs)

Stump,

Delaware,

Jenkins

2021

Preprint

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This paper introduces Relational Type Theory (RelTT), a new approach to type theory with extensionality principles, based on a relational semantics for types. The type constructs of the theory are those of System F plus relational composition, converse, and promotion of application of a term to a relation. A concise realizability semantics is presented for these types. The paper shows how a number of constructions of traditional interest in type theory are possible in RelTT, including η-laws for basic types, inductive types with their induction principles, and positive-recursive types. A crucial role is played by a lemma called Identity Inclusion, which refines the Identity Extension property familiar from the semantics of parametric polymorphism. The paper concludes with a type system for RelTT, paving the way for implementation.

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Section: Related Workmentioning

confidence: 99%

Relational Type Theory (All Proofs)

Stump,

Delaware,

Jenkins

2021

Preprint

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“…Next, we consider the first step in our progression towards Cedille's recursion universe. This is a recursion universe for so-called Mendler-style recursion, an approach to terminating recursion originated by Mendler [Mendler 1991], and studied subsequently in a number of other works [Ahn and Sheard 2011;Firsov et al 2018;Vene 1999, 2000]. The basic idea proposed by Mendler is to change the form of algebras from…”

Section: A Mendler-style Recursion Universementioning

confidence: 99%

Strong functional pearl: Harper’s regular-expression matcher in Cedille

Stump

Jenkins

Spahn

et al. 2020

Proc. ACM Program. Lang.

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This paper describes an implementation of Harper's continuation-based regular-expression matcher as a strong functional program in Cedille; i.e., Cedille statically confirms termination of the program on all inputs. The approach uses neither dependent types nor termination proofs. Instead, a particular interface dubbed a recursion universe is provided by Cedille, and the language ensures that all programs written against this interface terminate. Standard polymorphic typing is all that is needed to check the code against the interface. This answers a challenge posed by Bove, Krauss, and Sozeau. CCS Concepts: • Software and its engineering → Functional languages; Recursion; • Theory of computation → Regular languages.

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“…For type families S and T of kind I → ⋆, Cast • I • S • T is the type of generalized identity functions in CDLE; its formation, introduction, and elimination rules are given in Figure 2a. This family of types was first introduced by Firsov et al in [8], wherein it is called Id, and only the non-indexed variant is given (for the related notion of zero-cost coercion in Haskell, see [5]). Since CDLE is Curry-style, an identity function from S to T might exists even if S and T are inconvertible types.…”

Section: Derived Constructsmentioning

confidence: 99%

“…Geuvers [12] showed the impossibility of deriving induction for them in second-order dependent type theory; Firsov and Stump [10] demonstrated how to generically derive the induction principle for them in CDLE. Parigot [27] showed that the Church-style of encoding has no better than linear-time data accessors (such as predecessor for natural numbers); Firsov et al [8] showed how to use the induction principle for a Mendler-style of encoding [24] to define efficient (constant-time) data accessors. Furthermore, Firsov et al [9] show how to further augment this with course-of-values induction, an expressive scheme wherein the inductive hypothesis can be invoked on subdata at unbounded depth.…”

Section: Introductionmentioning

confidence: 99%

Efficient lambda encodings for Mendler-style coinductive types in Cedille

Jenkins¹,

Stump²,

Diehl³

2020

Electron. Proc. Theor. Comput. Sci.

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In the calculus of dependent lambda eliminations (CDLE), it is possible to define inductive datatypes via lambda encodings that feature constant-time destructors and a course-of-values induction scheme. This paper begins to address the missing derivations for the dual, coinductive types. Our derivation utilizes new methods within CDLE, as there are seemingly fundamental difficulties in adapting previous known approaches for deriving inductive types. The lambda encodings we present implementing coinductive types feature constant-time constructors and a course-of-values corecursion scheme. Coinductive type families are also supported, enabling proofs for many standard coinductive properties such as stream bisimulation. All work is mechanically verified by the Cedille tool, an implementation of CDLE.

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Efficient Mendler-Style Lambda-Encodings in Cedille

Cited by 10 publications

References 18 publications

Relational Type Theory (All Proofs)

Relational Type Theory (All Proofs)

Strong functional pearl: Harper’s regular-expression matcher in Cedille

Efficient lambda encodings for Mendler-style coinductive types in Cedille

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