Polytypic properties and proofs in Coq

Verbruggen, Wendy; Vries, Edsko de; Hughes, Arthur

doi:10.1145/1596614.1596616

Cited by 7 publications

(3 citation statements)

References 29 publications

(22 reference statements)

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“…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. This approach allows conventional datatypes to be expressed, but it cannot be used to express meta-theoretical generic operations since there are no representations for variables or binders.…”

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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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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“…Chlipala [7] uses this technique in the Coq proof assistant to generically define and prove substitution properties of programming languages. Verbruggen et al [31,32] use Coq's dependent types to develop a framework for proving properties about generic programs.…”

Section: Related Workmentioning

confidence: 99%

Generic Programming with Dependent Types

Weirich

Casinghino

2012

Lecture Notes in Computer Science

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Abstract. Some programs are doubly generic. For example, map is datatype-generic in that many different data structures support a mapping operation. A generic programming language like Generic Haskell can use a single definition to generate map for each type. However, map is also arity-generic because it belongs to a family of related operations that differ in the number of arguments. For lists, this family includes familiar functions from the Haskell standard library (such as repeat, map, and zipWith).This tutorial explores these forms of genericity individually and together. These two axes are not orthogonal: datatype-generic versions of repeat, map and zipWith have different arities of kind-indexed types. We explore these forms of genericity in the context of the Agda programming language, using the expressiveness of dependent types to capture both forms of genericity in a common framework. Therefore, this tutorial serves as an introduction to dependently typed languages as well as generic programming.The target audience of this work is someone who is familiar with functional programming languages, such as Haskell or ML, but would like to learn about dependently typed languages. We do not assume prior experience with Agda, type-or arity-generic programming.

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“…Chlipala [4] uses this technique in the Coq proof assistant to generically define and prove substitution properties of programming languages. Verbruggen et al [27] use Coq's dependent types to develop a framework for proving properties about generic programs.…”

Section: Related Workmentioning

confidence: 99%

Arity-generic datatype-generic programming

Weirich

Casinghino

2010

Proceedings of the 4th ACM SIGPLAN Workshop on Programming Languages Meets Program Verification

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Some programs are doubly-generic. For example, map is datatypegeneric in that many different data structures support a mapping operation. A generic programming language like Generic Haskell can use a single definition to generate map for each type. However, map is also arity-generic because it belongs to a family of related operations that differ in the number of arguments. For lists, this family includes repeat, map, zipWith, zipWith3, zipWith4, etc. With dependent types or clever programming, one can unify all of these functions together in a single definition.However, no one has explored the combination of these two forms of genericity. These two axes are not orthogonal because the idea of arity appears in Generic Haskell: datatype-generic versions of repeat, map and zipWith have different arities of kind-indexed types. In this paper, we define arity-generic datatype-generic programs by building a framework for Generic Haskell-style generic programming in the dependently-typed programming language Agda 2.

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Polytypic properties and proofs in Coq

Cited by 7 publications

References 29 publications

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

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

Generic Programming with Dependent Types

Arity-generic datatype-generic programming

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