Abstract
We give two classes of sound and complete models for the computational λ-calculus, or λc-calculus. For the first, we generalise the notion of cartesian closed category to that of closed Freyd-category. For the second, we generalise simple indexed categories. The former gives a direct semantics for the computational λ-calculus. The latter corresponds to an idealisation of stack-based intermediate languages used in some approaches to compiling.
This work is supported by EPSRC grant GR/J84205: Frameworks for programming language semantics and logic.
Supported by EPSRC grant GR/L54639.
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References
R. Douence and P. Fradet. A Taxonomy of Functional Language Implementations Part I: Call-by-Value, INRIA Research Report No 2783, 1995.
M. Hasegawa. Decomposing typed lambda calculus into a couple of categorical programming languages, Proc. CTCS, Lect. Notes in Computer Science 953 (1995).
A. Jeffrey. Premonoidal categories and a graphical view of programs. http://www.cogs.susx.ac.uk/users/alanje/premon/paper-title.html.
G.M. Kelly. The basic concepts of enriched categories. CUP (1982).
X. Leroy. The ZINC experiment: an economical implementation of the ML language. Technical Report RT-0117, INRIA, Institut National de Recherche en Informatique et en Automatique, 1990.
P.B. Levy. Call-by-push-value: a subsuming paradigm (extended abstract). In J.-Y Girard, editor, Typed Lambda-Calculi and Applications, Lecture Notes in Computer Science, April 1999.
E. Moggi. Computational Lambda calculus and Monads, Proc. LICS 89, IEEE Press (1989) 14–23.
E. Moggi. Notions of computation and monads, Information and Computation 93 (1991) 55–92.
A.J. Power. Premonoidal categories as categories with algebraic structure (submitted).
A.J. Power and E.P. Robinson. Premonoidal categories and notions of computation, Proc. LDPL’ 96, Math Structures in Computer Science.
A.J. Power and H. Thielecke. Environments, Continuation Semantics and Indexed Categories, Proc. Theoretical Aspects of Computer Science, Lecture Notes in Computer Science (1997) 391–414.
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Power, J., Thielecke, H. (1999). Closed Freyd- and κ-categories. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_59
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DOI: https://doi.org/10.1007/3-540-48523-6_59
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