Automatic Dimensional Inference
نویسندگان
چکیده
1. While there have been a number of proposals to integrate dimensional analysis into existing compilers 1, 7, 8, 9], it appears that no one has made the easy observation that dimensional analysis ts neatly into the pattern of ML-style type inference 4, 5, 6]. In this paper we show how to add dimensions to the simply-typed lambda calculus, and we show that every typable dimension-preserving term has a principal type. The principal type is unique up to a choice of basis. 2. Let us x a number N of dimensions. Then we can deene a set of types by: Here we have added a new set of types Q(n 1 ; : : :; n N), representing dimensional quantities. If we set N = 3, and denote the dimensions using MLT in the usual way, then Q(n 1 ; : : :; n N) represents the dimension usually denoted M n 1 L n 2 T n 3 .
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