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Extensional equality

(Or extensionality).

Functions, f and g are extensionally equal if and only if

f x = g x

for all x.

where "=" means both expressions fail to terminate (under some given reduction strategy) or they both terminate with the same basic value.

Two functions may be extensionally equal but not inter-convertible (neither is reducible to the other).

E.g. \ x . x+x and \ x . 2*x.

See also observational equivalence, referential transparency.

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