# Mizar Analysis of Algorithms: Preliminaries

Formalized Mathematics (2007)

• Volume: 15, Issue: 3, page 87-110
• ISSN: 1426-2630

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## Abstract

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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.

## How to cite

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Grzegorz Bancerek. "Mizar Analysis of Algorithms: Preliminaries." Formalized Mathematics 15.3 (2007): 87-110. <http://eudml.org/doc/266833>.

@article{GrzegorzBancerek2007,
abstract = {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.},
author = {Grzegorz Bancerek},
journal = {Formalized Mathematics},
language = {eng},
number = {3},
pages = {87-110},
title = {Mizar Analysis of Algorithms: Preliminaries},
url = {http://eudml.org/doc/266833},
volume = {15},
year = {2007},
}

TY - JOUR
AU - Grzegorz Bancerek
TI - Mizar Analysis of Algorithms: Preliminaries
JO - Formalized Mathematics
PY - 2007
VL - 15
IS - 3
SP - 87
EP - 110
AB - 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.
LA - eng
UR - http://eudml.org/doc/266833
ER -

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