A lambda-calculus with constructors

Ariel Arbiser (1) , Alexandre Miquel (2) , Alejandro Ríos (1)

1 Departamento de Computación [Buenos Aires]
2 PPS - Preuves, Programmes et Systèmes

We present an extension of the lambda(eta)-calculus with a case construct that propagates through functions like a head linear substitution, and show that this construction permits to recover the expressiveness of ML-style pattern matching. We then prove that this system enjoys the Church-Rosser property using a semi-automatic `divide and conquer' technique by which we determine all the pairs of commuting subsystems of the formalism (considering all the possible combinations of the nine primitive reduction rules). Finally, we prove a separation theorem similar to Böhm's theorem for the whole formalism.

Keywords: lambda calculus; pattern matching; separation theorem

Domains: Logic in Computer Science [cs.LO]

Ariel Arbiser, Alexandre Miquel, Alejandro Ríos. A lambda-calculus with constructors. RTA'06, 2006, Seattle, United States. pp.181-196. ⟨hal-00150884⟩