EWD249 - 40

"table p"                                                           1a
"fill table p with first thousand prime numbers"                    1b
"print table p"                                                     1c

code numbers, starting with 1, because description 1 is expressed in terms of them, and "a", "b" and "c" being attached for the purpose of distinction.

Now we have to describe our convention chosen for the representation of the information to be contained in "table p", but this convention pertains to all three elements 1a, 1b and 1c. Therefore we call this description 2; it should contain the descriptions of the three separate elements (I use the equality sign as separator)

description 2:
1a    =   "integer array p[1:1000]"
1b    =   "make for k from 1 through 1000  p[k] equal to the k-th prime number"
1c    =   "print p[k] for k from 1 through 1000"   .

Description 2 is expressed in terms of three named entities to which we give (in the obvious order) the codes 2a, 2b and 2c. (In code numbers, description 2 is very meagre: it just states that for 1a, 1b and 1c, we have chosen the refinements 2a, 2b and 2c respectively.)

Remark. In the representation of the information to be contained in "table p", we have chosen not to exploit the fact that each of the values to be printed occurs only once, nor that they occur in the order of increasing magnitude. Conversely, this implies that the action that has to take place under the name of 2c is regarded as a specific instance of printing any set of thousand integer values (it could be a table of monthly wages of thousand numbered employees!). The net effect of the printing action in this example is as uniquely defined as the first thousand prime numbers are: we conceive it, however, as a specific instance of a larger class of occurrences. In the further refinement of 2c we deal with this whole class, the specific instance in this class being defined by the values of the elements of the array p. When people talk about "defining an interface" I often get the feeling that they overlook the presupposed generalization, the conception of the class of "possible" actions.

When 2b and 2c occur among the well-understood repertoire of instructions