Computational interpretations of analysis via products of selection functions

We show that the computational interpretation of full comprehension via two wellknown functional interpretations (dialectica and modified realizability) corresponds to two closely related infinite products of selection functions

Abstract Datatypes for Real Numbers in Type Theory

Abstract. We propose an abstract datatype for a closed interval of real numbers to type theory, providing a representation-independent approach to programming with real numbers. The abstract datatype requires only function types and a natural numbers type for its formulation, and so can be added to any type theory that extends Gödel’s System datatype is equivalent in power to programming intensionally with representations of real numbers. We also consider representing arbitrary real numbers using a mantissa-exponent representation in which the mantissa is taken from the abstract interval.

Calculus in Coinductive Form

artment of Computer Science, University of Edinburgh, Edinburgh. E-mail: [email protected] tions (2) and (1) normalize the integral with respect to the subintegral function and the interval of integration. 1 Reapplying equation (3) yields the Taylor (Maclaurin) expansion f = f(0) :: f 0 = f(0) :: f 0 (0) :: f 00 . . . = f(0) :: f 0 (0) :: \Delta \Delta \Delta :: f (n) (0) :: \Delta \Delta \Delta Unfolding the above definition of ::, which amounts to iterated integration, one finally gets f(x) = f(0) + f 0 (0)x + \Delta \Delta \Delta + f (n) (0)x n<F

The Peirce translation and the double negation shift

Abstract. We develop applications of selection functions to proof theory and computational extraction of witnesses from proofs in classical analysis. The main novelty is a translation of classical minimal logic into minimal logic, which we refer to as the Peirce translation, and which we apply to interpret both a strengthening of the double-negation shift and the axioms of countable and dependent choice, via infinite products of selection functions

The Space of Measurement Outcomes as a Spectral Invariant for Non-Commutative Algebras

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