Linear Logical Reasoning on Programming

In our paper we follow the development of our approach of regarding programming as logical reasoning in intuitionistic linear logic. We present basic notions of linear logic and its deduction system and we define categorical semantics of linear logic as a symmetric monoidal closed category. Then we construct linear type theory over linear Church’s types involving linear calculus with equational axioms. We conclude with the interpretation of the linear type theory in symmetric monoidal closed category. Defined entities included in our whole linear logical system give us a possible mean for deduction and reduction of problem solving in the framework of mathematics and computer science.