Closed Freyd- and κ-categories
We give two classes of sound and complete models for the computational λ-calculus, or λc-calculus. For the first, we generalise the notion of cartesian closed category to that of closed Freyd-category. For the second, we generalise simple indexed categories. The former gives a direct semantics for the computational λ-calculus. The latter corresponds to an idealisation of stack-based intermediate languages used in some approaches to compiling.
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