Uniformity and the Taylor expansion of ordinary lambda-terms

Theoretical Computer Science

Volumn 403, Issue 2-3, 2008, Pages 347-372

  Ehrhard, Thomas ^a   Regnier, Laurent ^b  

^a UNIVERSITÉ PARIS DIDEROT   (France)

^b AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

Denotational semantics; Differential lambda calculus; Lambda calculus; Lambda calculus with multiplicities; Lambda calculus with resources; Linear logic

Indexed keywords

ARSENIC COMPOUNDS; DIFFERENTIATION (CALCULUS); EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL TECHNIQUES;

LAMBDA CALCULUS; LAMBDA-TERMS; LINEAR COMBINATION (LC); RATIONAL COEFFICIENTS; REDUCTS; TAYLOR EXPANSIONS;

CALCULATIONS;

EID: 48449106415     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2008.06.001     Document Type: Article

References (19)

1. Boudol G., Curien P.-L., and Lavatelli C. A semantics for lambda calculi with resource. Mathematical Structures in Computer Science 9 4 (1999) 437-482
2. Bucciarelli A., and Ehrhard T. On phase semantics and denotational semantics: The exponentials. Annals of Pure and Applied Logic 109 3 (2001) 205-241
3. Berry G. Stable models of typed lambda-calculi. Proceedings of the 5th International Colloquium on Automata, Languages and Programming. Lecture Notes in Computer Science vol. 62 (1978), Springer-Verlag
4. Gérard Boudol, The lambda calculus with multiplicities, Technical Report 2025, INRIA Sophia-Antipolis, 1993
5. De Bruijn N.G. Generalizing Automath by means of a lambda-typed lambda calculus. In: Kueker D.W., Lopez-Escobar E.G.K., and Smith C.H. (Eds). Mathematical Logic and Theoretical Computer Science. Lecture Notes in Pure and Applied Mathematics (1987), Marcel Dekker 71-92
6. De Bruijn N.G. Generalizing automath by means of a lambda-typed lambda calculus. In: Nederpelt R.P., Geuvers J.H., and De Vrijer R.C. (Eds). Selected Papers on Automath. Studies in Logic and The Foundations of Mathematics vol. 133 (1995), Elsevier Science 313-337
7. Danos V., and Regnier L. Reversible, irreversible and optimal lambda-machines. Theoretical Computer Science 227 1-2 (1999) 273-291
8. Ehrhard T. Finiteness spaces. Mathematical Structures in Computer Science 15 4 (2005) 615-646
9. Ehrhard T., and Regnier L. The differential lambda-calculus. Theoretical Computer Science 309 1-3 (2003) 1-41
10. Ehrhard T., and Regnier L. Böhm trees, Krivine machine and the Taylor expansion of ordinary lambda-terms. In: Beckmann A., Berger U., Löwe B., and Tucker J.V. (Eds). Logical Approaches to Computational Barriers. Lecture Notes in Computer Science vol. 3988 (2006), Springer-Verlag 186-197
11. Ehrhard T., and Regnier L. Differential interaction nets. Theoretical Computer Science 364 2 (2006) 166-195
12. Girard J.-Y. The system F of variable types, fifteen years later. Theoretical Computer Science 45 (1986) 159-192
13. Girard J.-Y. Linear logic. Theoretical Computer Science 50 (1987) 1-102
14. Girard J.-Y. Locus Solum. Mathematical Structures in Computer Science 11 3 (2001) 301-506
15. Girard J.-Y., Lafont Y., and Taylor P. Proofs and types. Cambridge Tracts in Theoretical Computer Science vol. 7 (1989), Cambridge University Press
16. Kfoury A.J. A linearization of the lambda-calculus. Journal of Logic and Computation 10 3 (2000) 411-436
17. Jean-Louis Krivine, Un interpréteur du lambda-calcul. Unpublished note, 1985
18. Krivine J.-L. A call-by-name lambda-calculus machine. Higher-Order and Symbolic Computation 20 2 (2007) 199-207
19. Vaux L. The differential lambda-mu calculus. Theoretical Computer Science 379 1-2 (2007) 166-209