Abstract
The notion of C-function is introduced to λ-calculus with η-convertibility as a generalization of normal forms. C is a function from the λ-expressions, Λ, onto a partially ordered set, ℂfin. The D∞-value of X ε Λ is characterized by C(X) ε ℂfin. Extending the syntactical structure of ℂfin into ℂinf, we generalize Λ to Λ∞, the infinite λ-expressions. The lattice topology of Λ and Λ∞ induced by D∞ is equivalent to the lattice topology of ℂinf Since ℂinf is deduced from Λ independent of D∞, ℂinf can be said to give a natural lattice structure of Λ.
This work was partially supported by National Science Foundation Grant GJ-34342X.
This paper is incomplete due to the space limitation. For the complete presentation, refer to [4].
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© 1975 Springer-Verlag Berlin Heidelberg
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Nakajima, R. (1975). Infinite normal forms for the λ-calculus. In: Böhm, C. (eds) λ-Calculus and Computer Science Theory. LCCST 1975. Lecture Notes in Computer Science, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029519
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DOI: https://doi.org/10.1007/BFb0029519
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