A PolyTime Functional Language from Light Linear Logic

Patrick Baillot (1) , Marco Gaboardi (2, 3) , Virgile Mogbil (4)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 Dipartimento di Informatica [Torino]
3 FOCUS - Foundations of Component-based Ubiquitous Systems
4 LIPN - Laboratoire d'Informatique de Paris-Nord

We introduce a typed functional programming language LPL (acronym for Light linear Programming Language) in which all valid programs run in polynomial time, and which is complete for polynomial time functions. LPL is based on lambda-calculus, with constructors for algebraic data-types, pattern matching and recursive definitions, and thus allows for a natural programming style. The validity of LPL programs is checked through typing and a syntactic criterion on recursive definitions. The higher order type system is designed from the ideas of Light linear logic: stratification, to control recursive calls, and weak exponential connectives §, !, to control duplication of arguments.

Mots clés: Functional Language; Light linear logic; Polynomial Time; Implicit Computational Complexity; Type System

Domaines: Logique en informatique [cs.LO]; Langage de programmation [cs.PL]; Complexité [cs.CC]

Patrick Baillot, Marco Gaboardi, Virgile Mogbil. A PolyTime Functional Language from Light Linear Logic. 19th European Symposium on Programming (ESOP 2010), Mar 2010, Paphos, Cyprus. pp. 104-124, ⟨10.1007/978-3-642-11957-6⟩. ⟨hal-00443944⟩