In a logic grammar, such grammatical phenomena as long-distance dependencies, conjunctive constructions, etc., often present problems whose treatment results in a formulation of grammar rules which are both hard to write and control. Perspicuity in the grammar rules can be achieved by introducing various constraints explicitly rather than embedding them in the rules themselves. This paper presents a metainterpreter approach to introducing explicit constraints in a syntactic parser. Our approach, called Semantically Constrained Parsing (SCP), shows a general way of introducing a meta-interpreter which makes it possible to associate sets of constraints with specific categories of the object language. So the constraints are used as demons in SCP, making for efficiency. Since this formulation ensures the communicability of one component of grammar with another, the resultant parser can consist of several modules different in nature and yet communicable with one another. We will show how the modularity achieved by SCP leads to an efficient logic grammar solution to the problem of long-distance dependencies. The use of Lexical Functional Grammar as our linguistics framework also reveals the generality of the SCP formulation compared with the approach of Stabler [13, 14].