Light Functional Interpretation

Hernest, Mircea-Dan

doi:10.1007/11538363_33

Cited by 6 publications

(6 citation statements)

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“…12 This can be extended to fully classical proofs, modulo some double-negation translation, see [14]. 13 System WeZ ∃,nc+ was denoted WE−Z + in [13]. It is nevertheless much better presented, with complete comparative details in [14], just like its corresponding WeZ ∃ , see below.…”

Section: The Light Functional Dialectica Interpretationmentioning

confidence: 98%

“…14 System WeZ ∃ , which was denoted WE−Z − in [13], is a Natural Deduction formulation of the weakly extensional Heyting Arithmetic in all finite types WE−HA ω from Section 1.6.12 of [26]. See also [3,24] for the original corresponding fully extensional variant Z ∃ ≡ Z + ∃.…”

Section: The Light Functional Dialectica Interpretationmentioning

confidence: 99%

“…The free variables of A D are exactly the 10 Paper [1] provides a nice survey in English which includes the extensions to full Analysis. 11 In [13] we named these special existential and universal quantifiers "without (or non-) computational meaning", abbreviated ncm. We here continue to use our own terminology.…”

Section: The Light Functional Dialectica Interpretationmentioning

confidence: 99%

“…The main feature of "Dialectica Light" is the elimination already at extraction time of a number of relevant (for the Dialectica program extraction) Contractions which are identified as redundant and in consequence are isolated by means of an adaptation of Berger's quantifiers without computational content 11 (introduced in [2] as "uniform quantifiers"), here denoted ∀ and ∃, like in [13,14].…”

Section: The Light Functional Dialectica Interpretationmentioning

confidence: 99%

“…A repair of this situation can be provided for the BBS refined A-translation by eliminating the distortion from the proof at input 8 or by using its Kripke-style variant due to Berger in [2] 9 . The latter extraction technique actually produces exactly the same program as our Light Dialectica interpretation (originally introduced in [13], but see also [14] for a much larger and more unified exposition).…”

Section: Introductionmentioning

confidence: 99%

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Light Dialectica Program Extraction from a Classical Fibonacci Proof

Hernest¹

2007

Electronic Notes in Theoretical Computer Science

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We demonstrate program extraction by the Light Dialectica Interpretation (LDI) on a minimal logic proof of the classical existence of Fibonacci numbers. This semi-classical proof is available in MinLog's library of examples. The term of Gödel's T extracted by the LDI is, after strong normalization, exactly the usual recursive algorithm which defines the Fibonacci numbers (in pairs). This outcome of the Light Dialectica meta-algorithm is much better than the T-program extracted by means of the pure Gödel Dialectica Interpretation. It is also strictly less complex than the result obtained by means of the refined A-translation technique of Berger, Buchholz and Schwichtenberg on an artificially distorted variant of the input proof, but otherwise it is identical with the term yielded by Berger's Kripke-style refined A-translation. Although syntactically different, it also has the same computational complexity as the original program yielded by the refined A-translation from the undistorted input classical Fibonacci proof.

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Section: The Light Functional Dialectica Interpretationmentioning

confidence: 98%

Section: The Light Functional Dialectica Interpretationmentioning

confidence: 99%

Section: The Light Functional Dialectica Interpretationmentioning

confidence: 99%

Section: The Light Functional Dialectica Interpretationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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