Exploring the Regular Tree Types

Morris, Peter D.; Altenkirch, Thorsten; McBride, Conor

doi:10.1007/11617990_16

Cited by 24 publications

(24 citation statements)

References 19 publications

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“…We soon move to bigger universes which include infinite types in section 4, where we introduce a general technique how to represent universes which contain fixpoints of types -this section is based on [35]. We also discuss the tradeoff between the size of a universe and the number of generic operations it supports.…”

Section: Structure Of the Papermentioning

confidence: 99%

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Generic Programming with Dependent Types

Altenkirch

McBride

Morris

2007

Datatype-Generic Programming

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Section: Structure Of the Papermentioning

confidence: 99%

“…As observed by McBride [29], the zipper is closely related to the notion of the derivative of a datatype, which has many structural similarities to derivatives in calculus. This topic has been explored from a more categorical perspective in [5,7]; the presentation here is again based on [35].…”

Section: Structure Of the Papermentioning

confidence: 99%

Generic Programming with Dependent Types

Altenkirch

McBride

Morris

2007

Datatype-Generic Programming

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“…This work is an extension of previous work with a universe of regular tree types [23], a proper sub-set of the strictly positive types. We will revisit this work in the first section of this paper.…”

Section: Introductionmentioning

confidence: 90%

A Universe of Strictly Positive Families

Morris

Altenkirch

Ghani

2009

Int. J. Found. Comput. Sci.

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In order to represent, compute and reason with advanced data types one must go beyond the traditional treatment of data types as being inductive types and, instead, consider them as inductive families. Strictly positive types (SPTs) form a grammar for defining inductive types and, consequently, a fundamental question in the the theory of inductive families is what constitutes a corresponding grammar for inductive families. This paper answers this question in the form of strictly positive families or SPFs. We show that these SPFs can be used to represent and compute with a variety of advanced data types and that generic programs can naturally be written over the universe of SPFs.

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“…By defining functions over this universe we obtain generic functions that work for any datatypes representable in that universe. A Simple Universe The universe that underlies GMeta is based on a simplified version of the universe for regular tree types by Morris et al (2004). Morris et al's universe is expressive enough to represent recursive types using µ-types (Pierce 2002).…”

Section: Datatype Generic Programmingmentioning

confidence: 99%

“…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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Exploring the Regular Tree Types

Cited by 24 publications

References 19 publications

Generic Programming with Dependent Types

Generic Programming with Dependent Types

A Universe of Strictly Positive Families

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

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