The Meaning of Types From Intrinsic to Extrinsic Semantics

Forfattere

  • John C. Reynolds

DOI:

https://doi.org/10.7146/brics.v7i32.20167

Resumé

A definition of a typed language is said to be "intrinsic" if it assigns
meanings to typings rather than arbitrary phrases, so that ill-typed
phrases are meaningless. In contrast, a definition is said to be "extrinsic"
if all phrases have meanings that are independent of their typings,
while typings represent properties of these meanings.
For a simply typed lambda calculus, extended with recursion, subtypes,
and named products, we give an intrinsic denotational semantics
and a denotational semantics of the underlying untyped language. We
then establish a logical relations theorem between these two semantics,
and show that the logical relations can be "bracketed" by retractions
between the domains of the two semantics. From these results, we
derive an extrinsic semantics that uses partial equivalence relations.

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Publiceret

2000-06-02

Citation/Eksport

Reynolds, J. C. (2000). The Meaning of Types From Intrinsic to Extrinsic Semantics. BRICS Report Series, 7(32). https://doi.org/10.7146/brics.v7i32.20167

Nummer

Nr. 32 (2000): RS-32 The Meaning of Types From Intrinsic to Extrinsic Semantics

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