Logical Approaches to Computational Barriers

Principal Typings for Explicit Substitutions Calculi

Author(s): |
Daniel Ventura, Mauricio Ayala-Rincon and Fairouz Kamareddine |

Slot: |
Array, 16:30-16:50, col. 5 |

Having principal typings (for short PT) is an important property of type systems. In simply typed systems, this property guarantees the possibility of a complete and terminating type inference mechanism. It is well-known that the simply typed lambda-calculus has this property but recently J.B. Wells has introduced a system-independent definition of PT, which allows to prove that some type systems, e.g. the Hindley/Milner type system, do not satisfy PT. Explicit substitutions address a major computational drawback of the lambda-calculus and allow the explicit treatment of the substitution operation to formally correspond to its implementation. Several extensions of the lambda-calculus with explicit substitution have been given but some of which do not preserve basic properties such as the preservation of strong normalization. We consider two systems of explicit substitutions (lambda s_e and lambda sigma) and show that they can be accommodated with an adequate notion of PT. Specifically, our results are as follows: - We introduce PT notions for the simply typed versions of the lambda s_e- and the lambda-sigma-calculi and prove that they agree with Wells' notion of PT. - We show that these versions satisfy PT by revisiting previously introduced type inference algorithms.

websites: Arnold Beckmann | 2008-05-18 |