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arXiv · 1806.09236

A concrete model for a typed linear algebraic lambda calculus

Alejandro Díaz-Caro·Octavio Malherbe
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Abstract

We give an adequate, concrete, categorical-based model for Lambda-S, which is a typed version of a linear-algebraic lambda calculus, extended with measurements. Lambda-S is an extension to first-order lambda calculus unifying two approaches of non-cloning in quantum lambda-calculi: to forbid duplication of variables, and to consider all lambda-terms as algebraic linear functions. The type system of Lambda-S have a superposition constructor S such that a type A is considered as the base of a vector space while SA is its span. Our model considers S as the composition of two functors in an adjunction relation between the category of sets and the category of vector spaces over C. The right adjoint is a forgetful functor U, which is hidden in the language, and plays a central role in the computational reasoning.

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Alejandro Díaz-Caro, Octavio Malherbe. 2018-06-24. A concrete model for a typed linear algebraic lambda calculus. https://doi.org/10.1017/s0960129523000361

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