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Continuation Semantics and Self-adjointness

โœ Scribed by Hayo Thielecke

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
989 KB
Volume
6
Category
Article
ISSN
1571-0661

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โœฆ Synopsis

We give an abstract categorical presentation of continuation semantics by taking the continuation type constructor : (or cont in Standard ML of New Jersey) as primitive. This constructor on types extends to a contravariant functor on terms which is adjoint to itself on the left restricted to the subcategory of those programs that do not manipulate the current continuation, it is adjoint to itself on the right.

The motivating example of such a category is built from (equivalence classes of typing judgements for) continuation passing style (CPS) terms.

A call-by-value -calculus with the control operator callcc as well as a call-byname -calculus can be interpreted. Arrow t ypes are broken down into continuation types for argument/result-continuations pairs. Specialising the semantics to the CPS term model allows a reconstruction of CPS transforms.

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