Handbook of logic in computer science (vol. 3)
What do types mean?: from intrinsic to extrinsic semantics
Programming methodology
Domains and Lambda-Calculi (Cambridge Tracts in Theoretical Computer Science)
Domains and Lambda-Calculi (Cambridge Tracts in Theoretical Computer Science)
Coinduction for Exact Real Number Computation
Theory of Computing Systems
From coinductive proofs to exact real arithmetic
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
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We study the domain-theoretic semantics of a Church-style typed @l-calculus with constructors, pattern matching and recursion, and show that it is closely related to the semantics of its untyped counterpart. The motivation for this study comes from program extraction from proofs via realizability where one has the choice of extracting typed or untyped terms from proofs. Our result shows that under a certain regularity condition, the choice is irrelevant. The regularity condition is that in every use of a fixed point type fix @a.@r, @a occurs only positively in @r.