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A New Paradox in Type Theory
 Logic, Methodology and Philosophy of Science IX : Proceedings of the Ninth International Congress of Logic, Methodology, and Philosophy of Science
, 1994
"... this paper is to present a new paradox for Type Theory, which is a typetheoretic refinement of Reynolds' result [24] that there is no settheoretic model of polymorphism. We discuss then one application of this paradox, which shows unexpected connections between the principle of excluded middle and ..."
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this paper is to present a new paradox for Type Theory, which is a typetheoretic refinement of Reynolds' result [24] that there is no settheoretic model of polymorphism. We discuss then one application of this paradox, which shows unexpected connections between the principle of excluded middle and the axiom of description in impredicative Type Theories. 1 Minimal and Polymorphic HigherOrder Logic
Subtransitive CFA using Types
, 1998
"... We present an experimental evaluation of Heintze and McAllester's lineartime subtransitive CFA algorithm, in the context of SML/NJ v110.7. As described in [9], lineartime termination of the algorithm depends on the existence of a simple typing of the program such that the type tree at each node ..."
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We present an experimental evaluation of Heintze and McAllester's lineartime subtransitive CFA algorithm, in the context of SML/NJ v110.7. As described in [9], lineartime termination of the algorithm depends on the existence of a simple typing of the program such that the type tree at each node has a bounded size. We show that this condition is violated by many programs, especially heavily functorized ones, and so the typedirected version of the algorithm (which explores a program's entire type structure) is only practical on small programs. We also show that the demanddriven variant of the algorithm does not always terminate for programs with polymorphic type. Our main result is that a hybrid algorithm that combines both approaches avoids both the problems. Whereas Heintze and McAllester's original formulation relied on the existence of types to bound the runtime of the algorithm, our work shows that an effective implementation must actually use the types to control termination.