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- W1489404987 abstract "In [1, §14E], a sequent calculus formulation ( L .-formulation) of type assignment (theory of functionality) is given for a system based either on a system of combinators with strong reduction or on a system of λη-calculus provided that the rule for subject conversion (which says that if X has type α and X cnv Y then Y has type α) is postulated for the system. This sequent calculus formulation does not work for a system based on the λβ-calculus. In [2] I introduced a sequent calculus formulation for a system without the rule of subject conversion based on any of the three systems mentioned above. Further, in [2, §5] I pointed out that if proper inclusions of the form of the statement that λ x · x is a function from α to β are postulated, then functions are identified with their restrictions in the λη-calculus but not in the λβ-calculus, and that therefore there is some interest in having a sequent calculus formulation of type assignment with the rule of subject conversion for systems based on the λβ-calculus. In this paper, such a system is presented, the elimination theorem (Gentzen's Hauptsatz ) is proved for it, and it is proved equivalent to the natural deduction formulation of [1, §14D]. I shall assume familiarity with the λβ-calculus, and shall use (with minor modifications) the notational conventions of [1]. Hence, the theory of type assignment (theory of functionality) will be based on an atomic constant F such that if α and β are types then Fαβ represents roughly the type of functions from α to β (more exactly it represents the type of functions whose domain includes α and under which the image of α is included in β)." @default.
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- W1489404987 date "1978-12-01" @default.
- W1489404987 modified "2023-09-27" @default.
- W1489404987 title "A sequent calculus formulation of type assignment with equality rules for the λβ-calculus " @default.
- W1489404987 doi "https://doi.org/10.2307/2273503" @default.
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