A partial function from to assigns at most one value in to each element of ; it may be undefined outside a subset of .
A partial unary operation on a set is a partial function with specified domain and values in . A map preserving such operations must send each point of the source domain into the target domain and preserve its assigned value. It need not reflect whether the operation is defined.
Composition of partial functions is strict: is defined only if every is defined and is defined on the resulting tuple. An argument discarded by the outer function still has to be defined. A representation in a non-strict programming language therefore needs an explicit sequencing guard.
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A **partial function** is a concept in mathematics and computer science that refers to a function that is not defined for all possible inputs from its domain. In other words, a partial function can provide an output for some inputs, but there are some inputs for which it does not produce an output at all. ### Key Characteristics of Partial Functions: 1. **Partial Domain**: The set of inputs for which the function is defined is known as its domain.