## Mizar Analysis of Algorithms: Preliminaries

Algorithms and its parts - instructions - are formalized as elements of if-while algebras. An if-while algebra is a (1-sorted) universal algebra which has 4 operations: a constant - the empty instruction, a binary catenation of instructions, a ternary conditional instruction, and a binary while instruction. An execution function is defined on pairs (*s, I*), where *s* is a state (an element of certain set of states) and *I* is an instruction, and results in states. The execution function obeys control structures using the set of distinguished true states, i.e. a condition instruction is executed and the continuation of execution depends on if the resulting state is in true states or not. Termination is also defined for pairs (*s, I*) and depends on the execution function. The existence of execution function determined on elementary instructions and its uniqueness for terminating instructions are shown.

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