There is paper which expresses lambda terms in the terms of logic programming http://www.cse.unt.edu/~tarau/teaching/PL/docs/dbx.pdf Is there conversion in the other direction - expressing definite clauses / Horn rules / logic programming sentences using the lambda terms and type calculus?
This question has the following context: definite clause grammars express its rules as definite clauses inside the logic programming formalism, but categorial grammars/type logical grammars use lambda calculus for their expression. Definite clause grammars have nice learnability (grammar induction) properties and algorithms - so - it would be nice to bring them to the culture of (abstract) categorial grammars/type logical grammars.
