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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