All Compact Hausdor
نویسنده
چکیده
The rst mathematical model of the untyped lambda calculus was discovered by DANA SCOTT in the category of algebraic lattices and Scott continuous maps. The question then arises as to which other cartesian closed categories contain a model of the calculus. In this paper we show that any compact Hausdor model of the calculus must satisfy the property that the semantic map from the calculus to the model is constant. In particular, any compact re BLOCKINexive object in the category of Hausdor k-spaces gives rise to a degenerate model of the calculus. We also explore the relationship of the results we derive to the notions of a combinatory model and of an environment model of the calculus. DEDICATION. Dedicated to Dana S. Scott on the occasion of his sixty-rst birthday on October 11, 1993 as an expression of our admiration and appreciation for the continuous inspiration coming from him to topology and algebra. He makes us think about theory while keeping applications in mind. 0. Introduction The lambda calculus of Church and Curry long has been an object of study by researchers in theoretical computer science. The reason is that the untyped lambda calculus is very much like a prototypical programming language without assignment.
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