Soft lambda-calculus: a language for polynomial time computation.

Patrick Baillot (1) , Virgile Mogbil (1)

1 LIPN - Laboratoire d'Informatique de Paris-Nord

Soft linear logic ([Lafont02]) is a subsystem of linear logic characterizing the class PTIME. We introduce Soft lambda-calculus as a calculus typable in the intuitionistic and affine variant of this logic. We prove that the (untyped) terms of this calculus are reducible in polynomial time. We then extend the type system of Soft logic with recursive types. This allows us to consider non-standard types for representing lists. Using these datatypes we examine the concrete expressiveness of Soft lambda-calculus with the example of the insertion sort algorithm.

Mots clés: Linear logic; lambda-calculus; polynomial time complexity; Soft linear logic; implicit computational complexity; recursive types

Domaines: Logique en informatique [cs.LO]

Patrick Baillot, Virgile Mogbil. Soft lambda-calculus: a language for polynomial time computation.. 2004, pp.27-41. ⟨hal-00085129⟩