Generic Programming within Dependently Typed Programming

Altenkirch, Thorsten; McBride, Conor

doi:10.1007/978-0-387-35672-3_1

Cited by 58 publications

(57 citation statements)

References 17 publications

(14 reference statements)

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“…An important application of dependent types is that of generic programming with universes, as in the work of Altenkirch and McBride [2003]; Benke et al [2003]. The basic idea is to represent the "universe" of types as data, and provide an interpretation function from values of this data type to types (in ).…”

Section: Generic Castmentioning

confidence: 99%

Parametricity and dependent types

2010

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract Reynolds' abstraction theorem shows how a typing judgement in System F can be translated into a relational statement (in second order predicate logic) about inhabitants of the type. We obtain a similar result for a single lambda calculus (a pure type system), in which terms, types and their relations are expressed. Working within a single system dispenses with the need for an interpretation layer, allowing for an unusually simple presentation. While the unification puts some constraints on the type system (which we spell out), the result applies to many interesting cases, including dependently-typed ones. Permanent

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Section: Generic Castmentioning

confidence: 99%

Parametricity and dependent types

2010

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“…The latter is based on the work by Dybjer and Setzer on Induction-Recursion [18,19] which can also be understood as universe constructions for non-dependent and dependent types. The first two authors of the present notes presented a universe construction for the first order fragment of Haskell datatypes including nested datatypes in [9] which was motivated by the work on generic Haskell [14,25].…”

Section: Related Workmentioning

confidence: 99%

Generic Programming with Dependent Types

Altenkirch

McBride

Morris

2007

Datatype-Generic Programming

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“…Setzer (1999, 2001) showed universe constructions within a type-theory with an axiomatization of inductionrecursion. Altenkirch and McBride (2003) proposed a universe capturing the datatypes and generic operations of Generic Haskell (Hinze and Jeuring 2003) and Norell (2008) shows how to do DGP with universes in Agda (Norell 2007). Verbruggen et al (2008Verbruggen et al ( , 2009) formalized a Generic Haskell (Hinze and Jeuring 2003) DGP style in Coq, which can also be used to do generic programming.…”

Section: Related Workmentioning

confidence: 99%

GMeta: A Generic Formal Metatheory Framework for First-Order Representations

Lee

Oliveira

Cho

et al. 2012

Programming Languages and Systems

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Abstract. This paper presents GMeta: a generic framework for firstorder representations of variable binding that provides once and for all many of the so-called infrastructure lemmas and definitions required in mechanizations of formal metatheory. The key idea is to employ datatypegeneric programming (DGP) and modular programming techniques to deal with the infrastructure overhead. Using a generic universe for representing a large family of object languages we define datatype-generic libraries of infrastructure for first-order representations such as locally nameless or de Bruijn indices. Modules are used to provide templates: a convenient interface between the datatype-generic libraries and the endusers of GMeta. We conducted case studies based on the POPLmark challenge, and showed that dealing with challenging binding constructs, like the ones found in System F<:, is possible with GMeta. All of GMeta's generic infrastructure is implemented in the Coq theorem prover. Furthermore, due to GMeta's modular design, the libraries can be easily used, extended, and customized by users.

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Generic Programming within Dependently Typed Programming

Cited by 58 publications

References 17 publications

Parametricity and dependent types

Parametricity and dependent types

Generic Programming with Dependent Types

GMeta: A Generic Formal Metatheory Framework for First-Order Representations

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