A compiled implementation of strong reduction

GrégoireBenjamin,; LeroyXavier,

doi:10.1145/583852.581501

Cited by 75 publications

(119 citation statements)

References 18 publications

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“…In the but last rule, we use the "monus" function on N where m − m = 0 if m ≥ m. Read-back is deterministic, so we introduce two partial functions by R nf m d = v iff m d v and R ne m e = n iff m ne e n. These correspond to the read-back function by Gregoire and Leroy [GL02] and own previous work [ACP09].…”

Section: Read-back (Aka Reification)mentioning

confidence: 99%

Towards Normalization by Evaluation for the βη-Calculus of Constructions

Abel

2010

Functional and Logic Programming

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Abstract. We consider the Calculus of Constructions with typed beta-eta equality and an algorithm which computes long normal forms. The normalization algorithm evaluates terms into a semantic domain, and reifies the values back to terms in normal form. To show termination, we interpret types as partial equivalence relations between values and type constructors as operators on PERs. This models also yields consistency of the beta-eta-Calculus of Constructions. The model construction can be carried out directly in impredicative type theory, enabling a formalization in Coq.

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Section: Read-back (Aka Reification)mentioning

confidence: 99%

Towards Normalization by Evaluation for the βη-Calculus of Constructions

Abel

2010

Functional and Logic Programming

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“…This leaves the freedom to implement values in different ways, e. g., β-normal forms, weak head normal forms (as in Pollack's constructive engine [Pol94]), closures (as in Coquand's type checker [Coq96]), tagged functions (Epigram 2 [CAM07]) or virtual machine instructions (compiled reduction in Coq [GL02]). All implementations of values that satisfy the interface given in the following can be used with our NbE algorithm, and in this article we provide a framework to prove all these implementations correct.…”

Section: Abstract Normalization By Evaluationmentioning

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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“…We provide some performance figures for the cvs version 8.0 of Coq with processor Intel Pentium 4 (3.60 GHz) and a RAM of 1Gb. Of course, this version of Coq uses the compilation scheme described in [7]. Figure 1 gives the time to build the certificates for the 100000 first primes, the size of the certificate and the time for the Coq system to check them.…”

Section: Performancesmentioning

confidence: 99%