The relations of compatibility, consistency and identity are used to describe the semantics of the predicate programming language P. Recursive types are defined with the smallest fixed point. A generic type is described by a set of constraints. For expressions of duck type, the rules to define variable types are introduced. Algorithms for checking of recursion correctness, for determining the language construct types, and for checking the semantic correctness of constructs are developed.

The AVL-tree operators are usually presented in functional languages in compact and elegant stile. However functional programs for insertion and removal operators are ineffective. They implement the construction of new tree but not the modification of the source tree. The paper describes the predicate programs for two algorithms of insertions into an AVL-tree. The predicate program can be automatically transformed to effective imperative programs.

A review of the works that form the theoretical foundations of computation on Sleptsov nets and represent peculiarities of the drawing, compilation and linking of programs in the Sleptsov nets language, as well as massively parallel computing memory architectures for implementation of Sleptsov net processors is presented. The Petri net runs exponentially slower and represents a special case of the Sleptsov net. A universal Sleptsov net containing 13 places and 26 transitions is considered, which is a prototype of the Sleptsov net processor. Examples of programs in the Sleptsov nets language for efficient multiplication, RSA encryption / decryption, calculation of a fuzzy logic function, and solution of the Laplace equation are shown. The advantages of computations on Sleptsov nets are: visual graphical language, preserving the natural parallelism of domain, fine granulation of parallel computations, formal methods for parallel programs verification, and fast massively parallel architectures that implement the computation model.

In the predicate programming compiler, optimizing transformations of the list and tree operations are described. The set of rules for replacement of the original operation to its image in the target imperative language has been developed. The translated imperative program is as effective as if it would be written manually.