Toward the maturity of software engineering: Universal, formal, and mathematical definition for type and object as two disjoint basic concepts

Software engineering has not reached maturity level as classic engineering. Theoretical foundation for software engineering lacks the precision and universal agreement of terms. By contrast, classic engineering are founded on the seven base dimensions that are precise and universally agreed. This paper aims to bring software engineering into maturity, in terms of the precision of terms by establishing and mathematically defining two basic concepts: type and object. Just like the seven base dimensions in physics be part of theoretical foundation for classic engineering, the two basic concepts type and object are the theoretical foundation for software engineering. This paper lists twelve problems with current definitions of type and object. The proposed definition and concepts are linguistically tested and mathematically formulated using thirty five formulas. Each concept - type, object - is unique and has single interpretation. This paper shows that class is a derived concept - not a basic concept - and that class can be defined on the proposed disjoint basic concepts: type and object.