Quasi-linear Dialectica Extraction

Trifonov, Trifon

doi:10.1007/978-3-642-13962-8_46

Cited by 1 publication

(7 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, m = ff, which contradicts with the premise m = tt → |C| x s , implying both A 1 and A 2 . Finally, assuming that T C is a variable bound by an external definition context as in [16], we see that T C t 1 t 2 ≤ t 1 + t 2 + K for some constant K, not dependent on C, t 1 or t 2 .…”

Section: Marked Counterexamplesmentioning

confidence: 94%

“…We will shortly outline the variant of the Dialectica interpretation, which was presented in [16]. It allows extraction of more efficient programs by avoiding syntactic repetition of subterms.…”

Section: Quasi-linear Dialectica Interpretationmentioning

confidence: 99%

“…where ξ := [x v := p + ]. Thus, as shown in [16], by avoiding recomputation we might improve worst time complexity of the program. However, in this special case we can optimise even further.…”

Section: A Special Case Of Recursionmentioning

confidence: 99%

“…Even though many automatic software systems for handling large proof objects are being actively developed, additional work is needed to identify and remove possible redundancies, so that the extracted programs are more readable, shorter and faster. Examples of such optimisations include uniform decorations [1,7,12], soundness-preserving program transformations [10], avoiding syntactic repetition [16]. In the present paper we suggest another such technique for the Dialectica interpretation, which marks computed counterexamples that are determined to be valid.…”

Section: Introductionmentioning

confidence: 99%

“…We demonstrate how in certain cases this approach can reduce the average time complexity of the obtained program by terminating recursive search immediately after a correct counterexample is found. The suggested change is an extension of the interpretation variant given in [16]. The reason is that even though counterexample marking can be formally applied directly to the original Dialectica interpretation, its practical effects are only visible when (at least) syntactic repetition is avoided.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Dialectica Interpretation with Marked Counterexamples

Trifonov¹

2011

Electron. Proc. Theor. Comput. Sci.

Self Cite

View full text Add to dashboard Cite

Goedel's functional "Dialectica" interpretation can be used to extract functional programs from non-constructive proofs in arithmetic by employing two sorts of higher-order witnessing terms: positive realisers and negative counterexamples. In the original interpretation decidability of atoms is required to compute the correct counterexample from a set of candidates. When combined with recursion, this choice needs to be made for every step in the extracted program, however, in some special cases the decision on negative witnesses can be calculated only once. We present a variant of the interpretation in which the time complexity of extracted programs can be improved by marking the chosen witness and thus avoiding recomputation. The achieved effect is similar to using an abortive control operator to interpret computational content of non-constructive principles

show abstract

Section: Marked Counterexamplesmentioning

confidence: 94%

Section: Quasi-linear Dialectica Interpretationmentioning

confidence: 99%

Section: A Special Case Of Recursionmentioning

confidence: 99%