NON-PRINCIPAL ULTRAFILTERS, PROGRAM EXTRACTION AND HIGHER-ORDER REVERSE MATHEMATICS

Non-principal Ultrafilters, Program Extraction and Higher Order Reverse Mathematics

We investigate the strength of the existence of a non-principal ultrafilter over fragments of higher order arithmetic. Let (U) be the statement that a non-principal ultrafilter on N exists and let ACA0 be the higher order extension of ACA0. We show that ACA0 + (U) is Π2-conservative over ACA0 and thus that ACA0 +(U) is conservative over PA. Moreover, we provide a program extraction method and s...

Higher Order Reverse Mathematics

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Examples for program extraction in Higher-Order Logic

Program Extraction in Simply-Typed Higher Order Logic

Based on a representation of primitive proof objects as λterms, which has been built into the theorem prover Isabelle recently, we propose a generic framework for program extraction. We show how this framework can be used to extract functional programs from proofs conducted in a constructive fragment of the object logic Isabelle/HOL. A characteristic feature of our implementation of program ext...

Higher-Order Program Generation

This dissertation addresses the challenges of embedding programming languages, specializing generic programs to specific parameters, and generating specialized instances of programs directly as executable code. Our main tools are higher-order programming techniques and automatic program generation. It is our thesis that they synergize well in the development of customizable software. Recent res...