Tetsuo Ida

FLATS, a machine for numerical, symbolic and associative computing

Functional aspects of a machine called FLATS are described. FLATS aims to efficiently run both numerical and algebraic programs. Overflow free and variable precision arithmetic, table look-up computation, and associative computation based on single-hit content addressed tables are introduced for advanced numerical, algebraic and symbolic computing. Hashing hardware, tag mechanism and hardware list processing are used to realize these features.

Some FP algebra with Currying operation

In the description of FP, Backus [l, p. 6231 carefully separated the universe of expressions consisting of functions and program forming operators (PFO’s, also called functional forms) from the universe of objects on which the expressions operate. Although the elimination of objects in the domain of functions are preferable to avoid type compatibility problems, as indicated in [l, p. 6311, we sometimes find awkwardness in expressing algorithms entirely without objects as we gain experiences with our FP system [2]. (bu f x) is incorporated in our system as is in [l]. ‘bu’ is a function form which converts a binary function f to a unary function by partially supplying an argument x. (bu f x) is regarded as the result of (i) first ‘Currying’ f, i.e., (curry f), and then (ii) applying the Curried function to x. Because (bu f x) is specified at the time of defining a function, it may be regarded as a ‘static partial’ function, where ‘partial’ in this case implies that the arguments of f are partially supplied and ‘static’ implies that the supplied arguments are fixed at the time of defining the function. In this article we further strengthen the power