Title :
A continuum of theories of lambda calculus without semantics
Author :
Salibra, Antonino
Author_Institution :
Dipt. di Inf., Venezia Univ., Italy
Abstract :
In this paper, we give a topological proof of the following result: there exist 2↑(ℵ0) lambda theories of the untyped lambda calculus without a model in any semantics based on D.S. Scott´s (1972, 1981) view of models as partially ordered sets and of functions as monotonic functions. As a consequence of this result, we positively solve the conjecture, stated by O. Bastonero and X. Gouy (1999) and by C. Berline (2000), that the strongly stable semantics is incomplete
Keywords :
functions; lambda calculus; set theory; incomplete semantics; lambda theories; models; monotonic functions; partially ordered sets; strongly stable semantics; topological proof; untyped lambda calculus; Algebra; Calculus; Context modeling; Equations; Lattices; Mathematical model; Topology;
Conference_Titel :
Logic in Computer Science, 2001. Proceedings. 16th Annual IEEE Symposium on
Conference_Location :
Boston, MA
Print_ISBN :
0-7695-1281-X
DOI :
10.1109/LICS.2001.932509
