injection
1. <mathematics> A function, f : A -> B, is injective or one-one, or is
an injection, if and only if
for all a,b in A, f(a) = f(b) => a = b.
I.e. no two different inputs give the same output (contrast many-to-one).
This is sometimes called an embedding. Only
injective functions have left inverses f' where
f'(f(x)) = x, since if f were not an injection,
there would be elements of B for which the value of
f' was not unique. If an injective function is also
a surjection then is it a bijection.
2. <reduction> An injection function is one which takes objects of type T
and returns objects of type C(T) where C is some type constructor. An example is
f x = (x, 0).
The opposite of an injection function is a projection function which
extracts a component of a constructed object, e.g.
fst (x,y) = x.
We say that f injects its argument into the data type and fst projects it
out.
(1995-03-14)
Nearby terms:
Initial Program Load « Initial Program Loader «
initiator «
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