Concept Programming - Rule of Equivalence, Equivalence Breakdown

Rule of Equivalence, Equivalence Breakdown

The rule of equivalence is verified when the code behavior matches the original concept. This equivalence may break down in many cases. Integer overflow breaks the equivalence between the mathematical integer concept and the computerized approximation of the concept.

Many ways to break the equivalence have been given specific names, because they are very common:

• A domain error is a condition where code executes outside of the domain of equivalence, which is the domain where the concept and the implementation match. An integer overflow is an example of domain error.
• A concept cast is a rewrite of a concept as a different concept because the original concept cannot be represented by the tools. In C, using pointers for output arguments because C doesn't support output arguments explicitly is an example of concept cast.
• A priority inversion is a form of syntactic or semantic noise introduced by some language-enforced general rule. It is called a priority inversion because the language takes precedence over the concept. In Smalltalk, everything is an object, and that rule leads to the undesirable consequence that an expression like 2+3*5 doesn't obey the usual order of operations (Smalltalk interprets this as sending the message * to the number resulting from 2+3, which yields result 25 instead of 17).