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Under intensional equality, two functions f and g are considered equal if they have the same "internal structure". This kind of equality could be implemented in interpreted languages by comparing the source code of the function bodies (such as in Interpreted Lisp 1.5) or the object code in compiled languages. Intensional equality implies extensional equality (assuming the functions are deterministic and have no hidden inputs, such as the program counter or a mutable global variable.)

Given the impracticality of implementing extensional and intensional equality, most languages supporting testing functions for equality use reference equality. All functions or closures are assigned a unique identifier (usually the address of the function body or the closure) and equality is decided based on equality of the identifier. Two separately defined, but otherwise identical function definitions will be considered unequal. Referential equality implies intensional and extensional equality. Referential equality breaks referential transparency and is therefore not supported in pure languages, such as Haskell.

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