Semantic analysis of normalisation by evaluation for typed lambda calculus

Fiore, Marcelo

doi:10.1145/571157.571161

Cited by 63 publications

(89 citation statements)

References 18 publications

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“…Because that cogen uses a universal type, the fact that it never generates an ill-typed generating extension from a well-typed input program is only manifest when each generating extension is type-checked, and the fact that the generating extension never generates an ill-typed residual program from well-typed static input is only manifest when each residual program is type-checked. Similarly, the fact that the partial evaluator of Fiore (2002) and that of Balat et al (2004), both of which use delimited control operators, never turn well-typed code into ill-typed code is not assured by the metalanguage, whether or not as part of a typed family of interpreter modules.…”

Section: If_ (Abstr Eb) (Fun () -> Abstr (Et ())) (Fun () -> Abstr (Ementioning

confidence: 99%

Finally tagless, partially evaluated: Tagless staged interpreters for simpler typed languages

Carette¹,

Kiselyov²,

Shan³

2009

J. Funct. Prog.

234

216

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We have built the first family of tagless interpretations for a higher-order typed object language in a typed metalanguage (Haskell or ML) that require no dependent types, generalized algebraic data types, or postprocessing to eliminate tags. The statically type-preserving interpretations include an evaluator, a compiler (or staged evaluator), a partial evaluator, and call-by-name and call-by-value CPS transformers.Our principal technique is to encode de Bruijn or higher-order abstract syntax using combinator functions rather than data constructors. In other words, we represent object terms not in an initial algebra but using the coalgebraic structure of the λ -calculus. Our representation also simulates inductive maps from types to types, which are required for typed partial evaluation and CPS transformations. Our encoding of an object term abstracts uniformly over the family of ways to interpret it, yet statically assures that the interpreters never get stuck. This family of interpreters thus demonstrates again that it is useful to abstract over higher-kinded types.It should also be possible to define languages with a highly refined syntactic type structure.Ideally, such a treatment should be metacircular, in the sense that the type structure used in the defined language should be adequate for the defining language.

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Section: If_ (Abstr Eb) (Fun () -> Abstr (Et ())) (Fun () -> Abstr (Ementioning

confidence: 99%

Finally tagless, partially evaluated: Tagless staged interpreters for simpler typed languages

Carette¹,

Kiselyov²,

Shan³

2009

J. Funct. Prog.

234

216

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“…For this, instead of the category F, Fiore [Fio02], and Miculan and Scagnetto [MS03] took the comma category 1 F ↓ U for the index category. Now U is the set containing all type names used in syntax.…”

Section: F↓u ) U For Typed Abstract Syntax With Bindingmentioning

confidence: 99%

Polymorphic Abstract Syntax via Grothendieck Construction

Hamana

2011

Foundations of Software Science and Computational Structures

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Abstract. Abstract syntax with variable binding is known to be characterised as an initial algebra in a presheaf category. This paper extends it to the case of polymorphic typed abstract syntax with binding. We consider two variations, secondorder and higher-order polymorphic syntax. The central idea is to apply Fiore's initial algebra characterisation of typed abstract syntax with binding repeatedly, i.e. first to the type structure and secondly to the term structure of polymorphic system. In this process, we use the Grothendieck construction to combine differently staged categories of polymorphic contexts.

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“…It is a monad on J t , with the unit and Kleisli extension given by variables-as-terms and substitution, like in the case of Lam. Fiore et al [13] [26] investigated a generalization of the notion of containers [1] to a dependently typed setting and used it to show that strictly positive families can be reduced to W-types. Relative monads played a central role in this development.…”

Section: Definition 22mentioning

confidence: 99%

Monads Need Not Be Endofunctors

Altenkirch

Chapman

Uustalu

2010

Foundations of Software Science and Computational Structures

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Abstract. We introduce a generalization of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed λ-calculus syntax and indexed containers. We show that the Kleisli and Eilenberg-Moore constructions carry over to relative monads and are related to relative adjunctions. Under reasonable assumptions, relative monads are monoids in the functor category concerned and extend to monads, giving rise to a coreflection between relative monads and monads. Arrows are also an instance of relative monads.

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Semantic analysis of normalisation by evaluation for typed lambda calculus

Cited by 63 publications

References 18 publications

Finally tagless, partially evaluated: Tagless staged interpreters for simpler typed languages

Finally tagless, partially evaluated: Tagless staged interpreters for simpler typed languages

Polymorphic Abstract Syntax via Grothendieck Construction

Monads Need Not Be Endofunctors

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