A function in intension is a finite program or formal construction description. Its associated function in extension is the partial or total input-output map it denotes. A Gödel number records the description rather than identifying all descriptions with the same extension.
A function in extension is a function specified by its domain and the value at each input in that domain. Distinct functions in intension can have this same extension. Properties of the extension of an arbitrary program are semantic properties, to which Rice theorem applies when the property is nontrivial.
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