On understanding types, data abstraction, and polymorphism
ACM Computing Surveys (CSUR) - The MIT Press scientific computation series
An ideal model for recursive polymorphic types
Information and Control
Domain theoretic models of polymorphism
Information and Computation
The semantics of second-order lambda calculus
Information and Computation
A modest model of records, inheritance, and unbounded quantification
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
Inheritance as implicit coercion
Information and Computation
PER models of subtyping, recursive types and higher-order polymorphism
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A denotational model for polymorphic lambda calculus with subtyping
A denotational model for polymorphic lambda calculus with subtyping
Algebraic domains of natural transformations
MFPS '92 Selected papers of the meeting on Mathematical foundations of programming semantics. Part II : lambda calculus and domain theory: lambda calculus and domain theory
An Extension of System F with Subtyping
TACS '91 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Relational Semantics for Recursive Types and Bounded Quantification
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Using category theory to design implicit conversions and generic operators
Semantics-Directed Compiler Generation, Proceedings of a Workshop
| Hi-index | 5.23 |
We present a denotational model for F, the extension of second-order lambda calculus with subtyping defined in Cardelli and Wegner (ACM Comput. Surveys 17(4) (1985) 471-522.) Types are interpreted as arbitrary cpos and elements of types as natural transformations. We prove the soundness of our model with respect to the equational theory of F (Cardelli et al. (Internat. Conf. on Theoretical Aspects of Computer Software, Lecture Notes in Computer Science, vol. 526, Springer, Berlin, 1991, pp. 750-770)) and show coherence. Our model is of independent interest, because it integrates ad hoc and parametric polymorphism in an elegant fashion, admits nontrivial records and record update operations, and formalizes an "order faithfulness" criterion for well-behaved multiple subtyping.