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A new type assignment for $$\lambda$$-terms. (English) Zbl 0418.03010

##### MSC:
 03B40 Combinatory logic and lambda calculus
##### Keywords:
lambda-terms; type assignment; proving termination; normal form
Full Text:
##### References:
 [1] Birkhoff, G.: Lattice theory. American Mathematical Society Colloquium Publications25 (1940). · Zbl 0063.00402 [2] Böhm, C., Groß, W.: Introduction to the CUCH. In: Caianiello, E. R. (ed.): Automata Theory, pp. 35–65. Amsterdam: North-Holland 1966. [3] Böhm, C., Dezani-Ciancaglini, M.: $$\lambda$$-Terms as total or partial function on normal forms. In: Böhm, C. (ed.): $$\lambda$$-Calculus and computer science theory. Lecture Notes in Computer Science, Vol. 37, pp. 96–121. Berlin, Heidelberg, New York: Springer 1975. · Zbl 0342.02017 [4] Böhm, C., Coppo, M., Dezani-Ciancaglini, M.: Termination test inside $$\lambda$$-calculus. In: Salomaa, A. and Steinby, M. (eds.): Lecture Notes in Computer Science, Vol. 52, pp. 95–110. Berlin, Heidelberg, New York: Springer 1977. · Zbl 0358.02025 [5] Church, A.: Combinatory logic as a semigroup. Bull. Amer. Math. Soc. (Abstract)43 333 (1937). [6] Church, A.: A formalization of the simple theory of types. J. Symbol. Logic5, 56–58 (1950). · Zbl 0023.28901 · doi:10.2307/2266170 [7] Curry, H. B., Feys, R.: Combinatory logic, Vol. 1. Amsterdam: North-Holland 1958. · Zbl 0081.24104 [8] Curry, H. B., Hindley, J. R., Seldin, J. P.: Combinatory logic, Vol. 2. Amsterdam: North-Holland 1972. · Zbl 0242.02029 [9] Dezani-Ciancaglini, M.: A type theory for $$\lambda$$-$$\beta$$-normal forms. Proc. of the Symposium Informatica75, BLED (1975). · Zbl 0342.02017 [10] Gentzen, G.: Investigations into logical reductions. In: The Collected Papers of Gerard Gentzen. Amsterdam: North-Holland 1969. [11] Hindley, R., Lercher, B., Seldin, J. P.: Introduction to combinatory logic. London North. Soc. Lecture Note Series7 (1972). · Zbl 0269.02005 [12] Seldin, J. P.: The theory of generalized functionality. I. Unpublished manuscript (1976).
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