A Universe of Strictly Positive Families

Morris, Peter D.; Altenkirch, Thorsten; Ghani, Neil

doi:10.1142/s0129054109006462

Cited by 18 publications

(14 citation statements)

References 12 publications

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“…The basic universe construction presented in Figure 7 is a simple variation of the regular tree types universe proposed by Morris et al (2004Morris et al ( , 2009 in Epigram. Nevertheless the extensions for representing variables and binders presented in Figure 8 are new.…”

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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“…This tutorial covers only one part of what is possible in a dependently typed language. In particular, our codes do not extend to all inductive families and so we cannot represent all types that are available (see Benke et al [3] and Morris et al [20] for more expressive universes). A dependently typed language also permits the definition of generic proofs 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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“…While demonstrating a new form of double genericity, this paper covers only one part of what is possible in a dependently typed language. In particular, our codes do not extend to all inductive families and so we cannot represent all types that are available (see Benke et al [2] and Morris et al [17] for more expressive universes). A dependently-typed language also permits the definition of generic proofs 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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A Universe of Strictly Positive Families

Cited by 18 publications

References 12 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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