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Conference Papers Year : 2017

Separating Functional Computation from Relations

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Abstract

The logical foundations of arithmetic generally start with a quantificational logic of relations. Of course, one often wishes to have a formal treatment of functions within this setting. Both Hilbert and Church added to logic choice operators (such as the epsilon operator) in order to coerce relations that happen to encode functions into actual functions. Others have extended the term language with confluent term rewriting in order to encode functional computation as rewriting to a normal form. We take a different approach that does not extend the underlying logic with either choice principles or with an equality theory. Instead, we use the familiar two-phase construction of focused proofs and capture functional computation entirely within one of these phases. As a result, our logic remains purely relational even when it is computing functions
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Dates and versions

hal-01615683 , version 1 (12-10-2017)

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  • HAL Id : hal-01615683 , version 1

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Ulysse Gérard, Dale Miller. Separating Functional Computation from Relations. 26th EACSL Annual Conference on Computer Science Logic (CSL 2017), Aug 2017, Stockholm, Sweden. pp.23:1--23:17. ⟨hal-01615683⟩
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