Separating Functional Computation from Relations

Ulysse Gérard 1 Dale Miller 1
1 PARSIFAL - Proof search and reasoning with logic specifications
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
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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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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