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).
This work was partly supported by NSF grant CCR-9417382, KBN Grant 8 T11C 034 10 and by ESPRIT BRA7232 “Gentzen”.
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Urzyczyn, P. (1997). Inhabitation in typed lambda-calculi (a syntactic approach). In: de Groote, P., Roger Hindley, J. (eds) Typed Lambda Calculi and Applications. TLCA 1997. Lecture Notes in Computer Science, vol 1210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62688-3_47
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DOI: https://doi.org/10.1007/3-540-62688-3_47
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