Classical Extraction in Continuation Models

Valentin Blot (1)

1 Department of Computer Science [Bath]

We use the control features of continuation models to interpret proofs in first-order classical theories. This interpretation is suitable for extracting algorithms from proofs of Π 0 2 formulas. It is fundamentally different from the usual direct interpretation, which is shown to be equivalent to Friedman's trick. The main difference is that atomic formulas and natural numbers are interpreted as distinct objects. Nevertheless, the control features inherent to the continuation models permit extraction using a special " channel " on which the extracted value is transmitted at toplevel without unfolding the recursive calls. We prove that the technique fails in Scott domains, but succeeds in the refined setting of Laird's bistable bicpos, as well as in game semantics.

Domaines: Logique en informatique [cs.LO]

Valentin Blot. Classical Extraction in Continuation Models. 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016), Jun 2016, Porto, Portugal. pp.13:1-13:17, ⟨10.4230/LIPIcs.FSCD.2016.13⟩. ⟨hal-01766872⟩