Question

how to write a function where a postcondition that is violated

Answer 1

Answer:

Preconditions, postconditions, and assertions are forms of acceptance tests that are widely used in software engineering to improve software reliability. The precondition of a method (or function, or subroutine, depending on the programming language) is a logical condition that must be true when that method is called. For example, if we are operating in the domain of real numbers and invoke a method to calculate the square root of a number, an obvious precondition is that this number must be non-negative.

A postcondition associated with a method invocation is a condition that must be true when we return from a method. For example, if a natural logarithm method was called with input X, and the method returns Y, we must have eY = X (within the limits of the level of precision being used).

Preconditions and postconditions are often interpreted in contractual terms. The function invoking a method agrees to ensure that the preconditions are met for that method: if they are not, there is no guarantee that the invoked method will return the correct result. In return, the method agrees to ensure that the postconditions are satisfied upon returning from it.

Assertions are a generalization of preconditions and postconditions. An assertion tests for a condition that must be true at the point at which that assertion is made. For example, we know that the total node degree of an undirected graph must be an even number (since each edge is incident on exactly two nodes). So, we can assert at the point of computation of this quantity that it must be even. If it turns out not to be so, an error has occurred; the response to the failure of an assertion is usually to notify the user or carry out some other appropriate action.