Beta reduction constraints

The constraint language for lambda structures (CLLS) can model lambda terms that are known only partially. In this paper, we introduce beta reduction constraints to describe beta reduction steps between partially known lambda terms. We show that beta reduction constraints can be expressed in an extension of CLLS by group parallelism. We then extend a known semi-decision procedure for CLLS to also deal with group parallelism and thus with beta-reduction constraints

Context unification and traversal equations

Abstract. Context unification was originally defined by H. Comon in ICALP’92, as the problem of finding a unifier for a set of equations containing first-order variables and context variables. These context variables have arguments, and can be instantiated by contexts. In other words, they are second-order variables that are restricted to be instantiated by linear terms (a linear term is a λ-expression λx1 ···λxn.t where every xi occurs exactly once in t). In this paper, we prove that, if the so called rank-bound conjecture is true, then the context unification problem is decidable. This is done reducing context unification to solvability of traversal equations (a kind of word unification modulo certain permutations) and then, reducing traversal equations to word equations with regular constraints.

A New Clausal Class Decidable by Hyperresolution

In this paper we define a new clausal class, called BU, which can be decided by hyperresolution with splitting. We also consider the model generation problem for BU and show that hyperresolution plus splitting can also be used as a Herbrand model generation procedure for BU and, furthermore, that the addition of a local minimality test allows us to generate only minimal Herbrand models for clause sets in BU. In addition, we investigate the relationship of BU to other solvable classes