An inverse of the evaluation functional for typed lambda -calculus

Berger, Ulrich; Schwichtenberg, Helmut

doi:10.1109/lics.1991.151645

Cited by 160 publications

(158 citation statements)

References 4 publications

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“…With every initial algebra and final coalgebra are associated operators for (co)iteration and (co)recursion. Computation is implemented efficiently via normalization by evaluation [BS91,BES03]. Computation is extended to proofs via the Curry-Howard correspondence.…”

Section: The Interactive Proof System Minlogmentioning

confidence: 99%

Minlog - A Tool for Program Extraction Supporting Algebras and Coalgebras

Berger

Miyamoto

Schwichtenberg

et al. 2011

Algebra and Coalgebra in Computer Science

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Abstract. Minlog is an interactive system which implements prooftheoretic methods and applies them to verification and program extraction. We give an overview of Minlog and demonstrate how it can be used to exploit the computational content in (co)algebraic proofs and to develop correct and efficient programs. We illustrate this by means of two examples: one about parsing, the other about exact real numbers in signed digit representation.

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Section: The Interactive Proof System Minlogmentioning

confidence: 99%

Minlog - A Tool for Program Extraction Supporting Algebras and Coalgebras

Berger

Miyamoto

Schwichtenberg

et al. 2011

Algebra and Coalgebra in Computer Science

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“…Frameworks like type theories allow to lift a deep embedding into a shallow one. This operation is called reflection from a proof theoretic point of view; through a proofs-as-programs perspective it can be understood as a compilation operation and corresponds to one of the two steps of normalization by evaluation (NbE) [7]. In this work we adapt a previous formalization of NbE in Coq [12].…”

Section: Deep and Shallow Embeddingsmentioning

confidence: 99%

Importing HOL Light into Coq

Keller

Werner

2010

Interactive Theorem Proving

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Abstract. We present a new scheme to translate mathematical developments from HOL Light to Coq, where they can be re-used and rechecked. By relying on a carefully chosen embedding of Higher-Order Logic into Type Theory, we try to avoid some pitfalls of inter-operation between proof systems. In particular, our translation keeps the mathematical statements intelligible. This translation has been implemented and allows the importation of the HOL Light basic library into Coq.

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“…Normalization by evaluation (NbE) [BS91,Dan99] is a systematic method to perform βη-normalization. In a first step, the object t of type T is evaluated.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Typed Applicative Structures and Normalization by Evaluation for System F ω

Abel

2009

Computer Science Logic

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Abstract. We present a normalization-by-evaluation (NbE) algorithm for System F ω with βη-equality, the simplest impredicative type theory with computation on the type level. Values are kept abstract and requirements on values are kept to a minimum, allowing many different implementations of the algorithm. The algorithm is verified through a general model construction using typed applicative structures, called type and object structures. Both soundness and completeness of NbE are conceived as an instance of a single fundamental theorem.

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An inverse of the evaluation functional for typed lambda -calculus

Cited by 160 publications

References 4 publications

Minlog - A Tool for Program Extraction Supporting Algebras and Coalgebras

Minlog - A Tool for Program Extraction Supporting Algebras and Coalgebras

Importing HOL Light into Coq

Typed Applicative Structures and Normalization by Evaluation for System F ω

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