FUNCTIONAL PEARL Linear lambda calculus and PTIME-completeness
We give transparent proofs of the PTIME-completeness of two decision problems for terms in the λ-calculus. The first is a reproof of the theorem that type inference for the simply-typed λ-calculus is PTIME-complete. Our proof is interesting because it uses no more than the standard combinators Churc...
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| Veröffentlicht in: | Journal of functional programming Jg. 14; H. 6; S. 623 - 633 |
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| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge, UK
Cambridge University Press
01.11.2004
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| Schlagworte: | |
| ISSN: | 0956-7968, 1469-7653 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We give transparent proofs of the PTIME-completeness of two decision problems for terms in the λ-calculus. The first is a reproof of the theorem that type inference for the simply-typed λ-calculus is PTIME-complete. Our proof is interesting because it uses no more than the standard combinators Church knew of some 70 years ago, in which the terms are linear affine – each bound variable occurs at most once. We then derive a modification of Church's coding of Booleans that is linear, where each bound variable occurs exactly once. A consequence of this construction is that any interpreter for linear λ-calculus requires polynomial time. The logical interpretation of this consequence is that the problem of normalizing proofnets for multiplicative linear logic (MLL) is also PTIME-complete. |
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| Bibliographie: | ark:/67375/6GQ-X4WZ8T0Z-W istex:CF7807EFCF2886675D6CDC8B16E262372B2C402C PII:S0956796804005131 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 |
| ISSN: | 0956-7968 1469-7653 |
| DOI: | 10.1017/S0956796804005131 |