On Logic Programming Representations of Lambda Terms: de Bruijn Indices, Compression, Type Inference, Combinatorial Generation, Normalization

We introduce a compressed de Bruijn representation of lambda terms and define its bijections to standard representations. Compact combinatorial generation algorithms are given for several families of lambda terms, including open, closed, simply typed and linear terms as well as type inference and normal order reduction algorithms. We specify our algorithms as a literate Prolog program. In the process, we rely in creative ways on unification of logic variables, cyclic terms, backtracking and definite clause grammars.