Generic conversions of abstract syntax representations

Keuchel, Steven; Jeuring, Johan

doi:10.1145/2364394.2364403

Cited by 9 publications

(10 citation statements)

References 15 publications

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“…An expressive type theory such as Agda's or Coq's caters for generic developments using universes populated by codes for types. Besides containers, universe-based developments include the works of Keuchel and Jeuring [2012] (using HOAS and nameless representations), Keuchel et al [2016], Licata and Harper [2009], Allais et al [2018], Lee et al [2012] (using nameless representations), and Copello et al [2018] (using a nameful representation). Some of these support formats for complex binder patterns and feature a substantial amount of infrastructure lemmas and formalized case studies.…”

Section: Proof Assistant Representations Of Bindingsmentioning

confidence: 99%

Bindings as bounded natural functors

Blanchette

Gheri

Popescu

et al. 2019

Proc. ACM Program. Lang.

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We present a general framework for specifying and reasoning about syntax with bindings. Abstract binder types are modeled using a universe of functors on sets, subject to a number of operations that can be used to construct complex binding patterns and binding-aware datatypes, including non-well-founded and infinitely branching types, in a modular fashion. Despite not committing to any syntactic format, the framework is łconcretež enough to provide definitions of the fundamental operators on terms (free variables, alpha-equivalence, and capture-avoiding substitution) and reasoning and definition principles. This work is compatible with classical higher-order logic and has been formalized in the proof assistant Isabelle/HOL.

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Section: Proof Assistant Representations Of Bindingsmentioning

confidence: 99%

Bindings as bounded natural functors

Blanchette

Gheri

Popescu

et al. 2019

Proc. ACM Program. Lang.

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“…In this section, we briefly review the techiniques on which our paper is based on, namely FliPpr [24] and the unembedding transformation [1,2,19].…”

Section: Preliminariesmentioning

confidence: 99%

“…Moreover, FliPpr features a conventional programming style, allowing function definitions, calls and pattern matching; the preservation of them in the embedding is a challenge that is of general interest. The key idea underpinning our approach is the use of a technique known as unembedding [1,2,19], which transforms syntax in a tagless-final style to de Bruijn terms. The original motivation of unembedding is to convert a userfriendly syntax to a program-manipulation-friendly form.…”

Section: Introductionmentioning

confidence: 99%

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Embedding invertible languages with binders: a case of the FliPpr language

Matsuda

Wang

2018

Proceedings of the 11th ACM SIGPLAN International Symposium on Haskell

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This paper describes a new embedding technique of invertible programming languages, through the case of the FliPpr language. Embedded languages have the advantage of inheriting host languages' features and supports; and one of the influential methods of embedding is the tagless-final style, which enables a high level of programmability and extensibility. However, it is not straightforward to apply the method to the family of invertible/reversible/bidirectional languages, due to the different ways functions in such domains are represented. We consider FliPpr, an invertible pretty-printing system, as a representative of such languages, and show that Atkey et al.'s unembedding technique can be used to address the problem. Together with a reformulation of FliPpr, our embedding achieves a high level of interoperability with the host language Haskell, which is not found in any other invertible languages. We implement the idea and demonstrate the benefits of the approach with examples.

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“…Moreover, a lot of functionality like variable substitutions and free variable calculations is defined for many languages. Licata and Harper [16] and Keuchel and Jeuring [13] define universes for datatypes with binding in Agda. Lee et al [15] develop a framework for first-order representations of variable binding in Coq that is based on the universe of regular tree types [23] and that provides many of the socalled infrastructure lemmas required when mechanizing programming language meta-theory.…”

Section: Related and Future Workmentioning

confidence: 99%

Generic datatypes à la carte

Keuchel

Schrijvers

2013

Proceedings of the 9th ACM SIGPLAN Workshop on Generic Programming

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Formal reasoning in proof assistants, also known as mechanization, has high development costs. Building modular reusable components is a key issue in reducing these costs. A stumbling block for reuse is that inductive definitions and proofs are closed to extension. This is a manifestation of the expression problem that has been addressed by the Meta-Theoryà la Carte (MTC) framework in the context of programming language meta-theory. However, MTC's use of extensible Church-encodings is unsatisfactory.This paper takes a better approach to the problem with datatypegeneric programming (DGP). It applies well-known DGP techniques to represent modular datatypes, to build functions from functor algebras with folds and to compose proofs from proof algebras by means of induction. Moreover, for certain functionality and proofs our approach can achieve more reuse than MTC: instead of composing modular components we provide a single generic definition once and for all.

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Generic conversions of abstract syntax representations

Cited by 9 publications

References 15 publications

Bindings as bounded natural functors

Bindings as bounded natural functors

Embedding invertible languages with binders: a case of the FliPpr language

Generic datatypes à la carte

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