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We sketch a constructive formal theory TCF of computable functionals, based on the partial continuous functionals as their intendend domain. Such a task had long ago been started by Dana Scott [12, 15], under the wellknown abbreviation LCF (logic of computable functionals). The present approach differs from Scott’s in two aspects. (i) The intended… (More)
We prove basic facts about the properties of atomicity and coherence for Scott information systems, and we establish direct connections between coherent information systems and well-known point-free structures.
• It is unlikely that there is an algorithm f that decides (1), i.e., returns tt if x = 0 and ff if x 6= 0: on input x = 0 it would run forever (think of the decimal representation of x); it would only semi-decide it, i.e., it would be a partial algorithm. • The algorithm as a mapping f : R→ B is discontinuous at 0. • Reals are Cauchy sequences of… (More)