MoL-2013-14: Grathwohl, Hans Bugge (2013) Programming with Classical Proofs. [Report]
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Abstract
This thesis is about extracting programs from classical proofs. In the
first part, we show conservativity of Peano arithmetic over Heyting
arithmetic for Π02-sentences, an old result of Kreisel, using
Friedman’s A-translation technique. Then we present some extensions by
Parigot and Krebbers of the lambda-calculus with control mechanisms,
that allow for some amount of classical reasoning via the Curry–Howard
correspondence.
In the second part of the thesis, we present a new system by Aschieri
and Berardi, HA + EM1 , a Curry–Howard system for an arithmetic with a
limited amount of classical reasoning that is based on ideas from
their Interactive Realizability semantics for classical arithmetic. We
show Aschieri’s recent proof of strong normalization of HA + EM1 that
uses a new technique based on non-deterministic choice.
Two non-trivial examples of proof terms in HA+EM1 are then worked out,
and their possible reduction paths are analyzed. On basis of this, an
operational natural semantics for HA + EM1 is developed and tested on
the previous examples.
| Item Type: | Report |
|---|---|
| Report Nr: | MoL-2013-14 |
| Series Name: | Master of Logic Thesis (MoL) Series |
| Year: | 2013 |
| Uncontrolled Keywords: | Logic; Mathematics |
| Date Deposited: | 12 Oct 2016 14:38 |
| Last Modified: | 12 Oct 2016 14:38 |
| URI: | https://eprints.illc.uva.nl/id/eprint/903 |
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