A Functional Approach for Formalizing Regular Hardware Structures

circuits are used for formalizing regular hardware structures which can ] be expressed by means of primitive recursion. In general, . . . . . . . regular circuit structures lead to regular signal structures. If for example, a structure is described, that con~ ~ sists of n combinational circuits connected in parallel, then it would be appropriate to use the type list for : grouping together the input and the output signals. ~ The structure of the input signal determines the structure of the circuit and the structure of the output signal. Grouping signals together by recursive types such as list Fig. 8.: Regular circuit, is flexible, since the structure of the signals and especially the number of the individual signals depends on the value. Other types than list can be used for grouping signals. In the next example, signals are grouped together by a list and a binary tree. primitive_datatype "list = Wil I Cons of 'a # list"; primitive_datatype "btree = Blear of 'a I Bnode of btree # btree"; The semantics of the corresponding PRIMREC-functions is: PRIMRECJist Nil a f = a PRIMRECJist (Cons x y) a f = f = y (PRIMRECJist y a f ) PRIMREC_btree (Bleafz) f g = f x PRIMREC_btree (Bnode x y) f g = g x y (PRIMRECJotree z f g) (PRIMREC_btree y f g) boo1 list The input of the 2n:l-multiplexer consists of a group of data inputs and an address signal for selecting one of the data inputs. The data input signals have an arbitrary type tr and they are grouped together as (a btree). The address signals are represented by a list of booleans (see figure 8).