This paper describes an implementation of some of the ideas presented by F.C.N. Pereira in [1]. Pereira uses a sequent-calculus like system to produce Montague semantics from natural language. The lefthand sequent can be interpreted as a set of constraints under which a given sentence fragment has a certain interpretation. Pereira presents a few complementary "discharge-rules" to reduce the number of such constraints. These conditional interpretations constitute a uniform way to represent partial knowledge during the parsing process. The implementation this paper describes is done in Lambda Prolog [2]. Lambda Prolog is a generalization of horn-clause logic to higher order logic, based on the higher order unification procedure of Huet [3]. It appears that the implementation of Pereira's system in Lambda Prolog becomes very natural. The higher order unification mechanism of Lambda takes care of the complicated binding mechanisms in Pereira's "discharge-rules" in a very simple and elegant way. Finally, the paper discusses some problems with the implementation and gives a few suggestions on how these could be overcome.