What is the the continuity criterion for graphs of functions studied in the Scott-Strachey model of computation

?

What is the graph of a function

?

The graph of a function is simply the set of all input output pairs for the function.

What is the relation between a procedure `p`

and a the notion of continuous functional?

We can prove that the graph of any physically realizable procedure p that behaves like a mathematical function as the limit of a continuous functional F such that:

In other words the graph of p is the limit of the n-fold compositions of F with Itself beginning with the empty graph.

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