On algebraic modeling of computer programs

The article considers functional grammar in terms of algorithmic algebras. As a result, we have identified the simplest invariant basis (name - value pair), which can later serve as a unified basis for building more complex structures in computer memory when implementing declarations of complex objects in computer programs. It is obtained a lemma on commutativity of assignment operator transfer and valid state of program memory, which returns a value by the name of variable. The logical connection between the homomorphism of multibase data algebras and the homomorphism of valid memory states is established by the theorem of diagrams commutativity in Cartesian closed categories and expressed by an assignment operator. An example of computer modeling of classical dynamic system using functional grammars is presented as a system of ordinary differential equations with given initial conditions. To demonstrate the application of functional grammars we have used an algorithm that generates a solution to an ordinary differential equation.