Abstract
A type is inhabited (non-empty) in a typed calculus iff there is a closed term of this type. The inhabitation (emptiness) problem is to determine if a given type is inhabited. This paper provides direct, purely syntactic proofs of the following results: the inhabitation problem is PSPACE-complete for simply typed lambda-calculus and undecidable for the polymorphic second-order and higher-order lambda calculi (systems F and Fω).
Cite
CITATION STYLE
Urzyczyn, P. (1997). Inhabitation in typed lambda-calculi (A syntactic approach). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1210, pp. 373–389). Springer Verlag. https://doi.org/10.1007/3-540-62688-3_47
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