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arXiv · 1511.09324

Isomorphisms considered as equalities: Projecting functions and enhancing partial application through and implementation of lambda+

Alejandro Díaz-Caro·Pablo E. Martínez López
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Abstract

We propose an implementation of lambda+, a recently introduced simply typed lambda-calculus with pairs where isomorphic types are made equal. The rewrite system of lambda+ is a rewrite system modulo an equivalence relation, which makes its implementation non-trivial. We also extend lambda+ with natural numbers and general recursion and use Beki\'c's theorem to split mutual recursions. This splitting, together with the features of lambda+, allows for a novel way of program transformation by reduction, by projecting a function before it is applied in order to simplify it. Also, currying together with the associativity and commutativity of pairs gives an enhanced form of partial application.

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Alejandro Díaz-Caro, Pablo E. Martínez López. 2015-11-30. Isomorphisms considered as equalities: Projecting functions and enhancing partial application through and implementation of lambda+. https://doi.org/10.1145/2897336.2897346

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