202212152212

Type :Note Tags : PLC

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Partial Functions

Note

A Partial Function is a function that has values on some arguments but not on all arguments The reason why a function would not return all values are :

• Error Termination: Evaluation of a function cannot proceed because of a conflict between the operator and an operand.
• Nontermination: Evaluation of a function proceeds indefinitely. An example of the first case would be the expression x:= 3 / 0, because devision by 0 is undefined. An example of the second scenario can be a function f(x: int) := if x = 0 then 0 else x + f(x-2), this function does not terminate when 3 is given as an argument.

A partial function is not a function as defined by the mathematical sense. A mathematical function $f:A\to B$ is a set of ordered pair $f\subset A\times B$ satisfying the following conditions:

1. If $(x,y)\in f$ and $(x,z)\in f$, then $y=z$.
2. For every $x\in A$, there exists a $y\in B$ such that $(x,y)\in f$. But a partial function only follows the first condition.

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Related Problems

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References