A simply typed context calculus with first-class environments

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2024, Issue , 2001, Pages 359-374

  Sato, Masahiko ^a   Sakurai, Takafumi ^b   Kameyama, Yukiyoshi ^a  

^a KYOTO UNIVERSITY   (Japan)

^b CHIBA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIATION (CALCULUS); FUNCTIONAL PROGRAMMING; LOGIC PROGRAMMING;

ABSTRACTION MECHANISM; CONSERVATIVE EXTENSIONS; FIRST-CLASS ENVIRONMENTS; FUNCTIONAL APPLICATIONS; HOLE FILLING; IN CONTEXTS; SIMPLY TYPED LAMBDA CALCULUS; SUBJECT REDUCTION;

CALCULATIONS;

EID: 84944045517     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44716-4_23     Document Type: Conference Paper

References (16)

1. Barendregt, H. P., The Lambda Calculus, Its Syntax and Semantics, North-Holland, 1981.
2. Bloo, R. and Rose, K.H., Preservation of Strong Normalization in Named Lambda Calculi with Explicit Substitution and Garbage Collection, Proceedings of CSN'95 (Computer Science in Netherlands), van Vliet J.C. (ed.), 1995. (ftp://ftp.diku.dk/diku/semantics/papers/D-246.ps)
3. Bognar, M. and de Vrijer, R., A calculus of lambda calculus contexts, available at: http://www.cs.vu.nl/~mirna/new.ps.gz.
4. de Bruijn, D. G., Lambda Calculus Notation with Nameless Dummies, a Tool for Automatic Formula Manipulation, with Application to the Church-Rosser Theorem, Indag. Math. 34, pp. 381-392, 1972.
5. Dami, L., A Lambda-Calculus for Dynamic Binding, pp. 201-231, Theoretical Computer Science 192, 1998.
6. Fiore, M., Plotkin, G., and Turi, D., Abstract Syntax and Variable Binding (Extended Abstract), Proc. 14th Symposium on Logic in Computer Science, pp. 193-202, 1999.
7. Hashimoto, M. and Ohori, A., A typed context calculus, Preprint RIMS-1098, Res. Inst. for Math. Sci., Kyoto Univ., 1996, Journal version is to appear in Theoretical Computer Science.
8. Lee, S.-R., and D. P. Friedman, Enriching the Lambda Calculus with Contexts: Toward a Theory of Incremental Program Construction, ACM SIGPLAN Notices, Proc. International Conference on Functional Programming, pp. 239-250, 1996.
9. Mason, I., Computing with Contexts, Higher-Order and Symbolic Computation 12, pp. 171-201, 1999.
10. Melliés, P.-A., Typed λ-calculi with explicit substitutions may not terminate, Typed Lambda Calculi and Applications, Lecture Notes in Computer Science 902, pp. 328-349, 1995.
11. Pitts, A.M., Some notes on inductive and co-inductive techniques in the semantics of functional programs, Notes Series BRICS-NS-94-5, Department of Computer Science, University of Aarhus, 1994.
12. Sakurada, H., An interpretation of a context calculus in an environment calculus, Master Thesis, Dept. of Information Science, Kyoto Univ., 1999 (in Japanese).
13. Sands, D., Computing with Contexts - a simple approach, Proc. Higher-Order Operational Techniques in Semantics, HOOTS II, 16 pages, Electronic Notes in Theoretical Computer Science 10, 1998.
14. Sato, M., Theory of Symbolic Expressions, II, Publ. of Res. Inst. for Math. Sci., Kyoto Univ., 21, pp. 455-540, 1985.
15. Sato, M., Sakurai T., and Burstall, R., Explicit Environments, Typed Lambda Calculi and Applications, Lecture Notes in Computer Science 1581, pp. 340-354, 1999.
16. Talcott, C., A Theory of binding structures and applications to rewriting, Theoretical Computer Science 112:1, pp. 99-143, 1993.