Decomposing Typed Lambda Calculus into a Couple of Categorical Programming Languages
نویسنده
چکیده
We give two categorical programming languages with variable arrows and associated abstraction/reduction mechanisms, which extend the possibility of categorical programming Hag87, CF92] in practice. These languages are complementary to each other { one of them provides a rst-order programming style whereas the other does higher-order { and are \children" of the simply typed lambda calculus in the sense that we can decompose typed lambda calculus into them and, conversely , the combination of them is equivalent to typed lambda calculus. This decomposition is a consequence of a semantic analysis on typed lambda calculus due to C. Hermida and B. Jacobs HJ94].
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