Formal Definitions and Proofs for Partial (Co)Recursive Functions

Cheval, Horatiu; Nowak, David; Rusu, Vlad

Document type :

Pré-publication ou Document de travail

Title :

Formal Definitions and Proofs for Partial (Co)Recursive Functions

Author(s) :

Cheval, Horatiu [Auteur]
University of Bucharest [UniBuc]
Nowak, David [Auteur]

Extra Small Extra Safe [2XS]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Rusu, Vlad [Auteur]

Analyse symbolique et conception orientée composants pour des systèmes embarqués temps-réel modulaires [SYCOMORES]

English keyword(s) :

partial (co)recursive functions
Coq proof assistant

HAL domain(s) :

Informatique [cs]/Logique en informatique [cs.LO]

English abstract : [en]

Partial functions are a key concept in programming. Without partiality a programming language has limited expressiveness-it is not Turing-complete, hence, some programs cannot be written. In functional programming languages, ...
Show more >Partial functions are a key concept in programming. Without partiality a programming language has limited expressiveness-it is not Turing-complete, hence, some programs cannot be written. In functional programming languages, partiality mostly originates from the non-termination of recursive functions. Corecursive functions are another source of partiality: here, the issue is not non-termination, but the inability to produce arbitrary large, finite approximations of a theoretically infinite output. Partial functions have been formally studied in the branch of theoretical computer science called domain theory. In this paper we propose to step up the level of formality by using the Coq proof assistant. The main difficulty is that Coq requires all functions to be total, since partiality would break the soundness of its underlying logic. We propose practical solutions for this issue, and others, which appear when one attempts to define and reason about partial (co)recursive functions in a total functional language.Show less >

Language :

Anglais

European Project :

COST Action EuroProofNet CA20111, funded by COST (European Cooperation in Science and Technology).

Collections :

Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL

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