an:05994294
Zbl 1241.03011
Nakazawa, Koji; Tatsuta, Makoto; Kameyama, Yukiyoshi; Nakano, Hiroshi
Type checking and typability in domain-free lambda calculi
EN
Theor. Comput. Sci. 412, No. 44, 6193-6207 (2011).
00288605
2011
j
03B40
existential type; type checking; typability; undecidability; CPS translation; domain-free type system
Summary: This paper shows (1) the undecidability of type checking and the typability problems in the domain-free lambda calculus with negation, product, and existential types, (2) the undecidability of the typability problem in the domain-free polymorphic lambda calculus, and (3) the undecidability of type checking and the typability problems in the domain-free lambda calculus with function and existential types. The first and the third results are proved by the second result and CPS translations that reduce those problems in the domain-free polymorphic lambda calculus to those in the domain-free lambda calculi with existential types. The key idea is the conservativity of the domain-free lambda calculi with existential types over the images of the translations.