Extraction and verification of programs by analysis of formal proofs
Theoretical Computer Science
PX: a computational logic
Basic proof theory
Logic: from foundations to applications
Extracting constructive content from classical proofs
Extracting constructive content from classical proofs
A new method for establishing conservativity of classical systems over their intuitionistic version
Mathematical Structures in Computer Science
An arithmetic for polynomial-time computation
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
Quasi-linear Dialectica extraction
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Light functional interpretation
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
| Hi-index | 5.23 |
We give a quantitative analysis of Gödel's functional interpretation and its monotone variant. The two have been used for the extraction of programs and numerical bounds as well as for conservation results. They apply both to (semi-)intuitionistic as well as (combined with negative translation) classical proofs. The proofs may be formalized in systems ranging from weak base systems to arithmetic and analysis (and numerous fragments of these). We give upper bounds in basic proof data on the depth, size, maximal type degree and maximal type arity of the extracted terms as well as on the depth of the verifying proof. In all cases terms of size linear in the size of the proof at input can be extracted and the corresponding extraction algorithms have cubic worst-time complexity. The verifying proofs have depth linear in the depth of the proof at input and the maximal size of a formula of this proof.