Subtyping Recursive Types
Identifieur interne : 001257 ( Crin/Curation ); précédent : 001256; suivant : 001258Subtyping Recursive Types
Auteurs : R. Amadio ; L. CardelliSource :
- ACM Transactions on Programming Languages and Systems ; 1993.
Abstract
We investigate the interactions of subtyping and recursive types in a simply typed lambda calculus. The two fundamental questions here are whether two (recursive) types are in the subtype relation and whether a term has a type. To address the first question, we relate various definitions of type equivalence and subtyping that are induced by a model, an ordering on infinite trees, an algorithm, and a set of type rules. We show soundness and completeness among the rules, the algorithm, and the tree semantics. We also prove soundness and a restricted form of completeness for the model. To address the second question, we show that to every pair of types in the subtype relation we can associate a term whose denotation is the uniquely determined coercion map between two types. Moreover we derive an algorithm that, when given a term with implicit coercions, can infer its least type whenever possible.
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