## International Journal of Computational and Mathematical Sciences 1;1 © www.waset.org Winter 2007 Abstract—Unified Algebra

by Unknown Authors

by Unknown Authors

@MISC{_internationaljournal,

author = {},

title = {International Journal of Computational and Mathematical Sciences 1;1 © www.waset.org Winter 2007 Abstract—Unified Algebra},

year = {}

}

unifies booleans and numbers, values and types, functions and function spaces. It incorporates basic structures, such as sets and lists, and advanced structures, such as quantifications and limits. It does so with an economy of symbols and rules. The presentation is basic and detailed enough to serve as a foundation of that part of mathematics that serves much of computer science, with comments on what constitutes good mathematical practice. Keywords—boolean algebra, foundation of computer science, foundation of mathematics, unified algebra

104 |
APractical Theory of Programming
- Hehner
- 1993
(Show Context)
Citation Context ...operator to a list, +L conveniently expresses the sum of the items of list L . The Function Inclusion Law, specialized to lists, says that a list includes all its extensions. [S; T]: [S] For example, =-=[3; 2; 4]-=- is not only a list of three items, but also all lists that start with those three items. The intuition is the same as for functions. If a context requires a list of three integers (perhaps because it... |

19 |
Transformational hierarchical reasoning
- Grundy
- 1996
(Show Context)
Citation Context ...actoring So a string of bunches is equal to a bunch of strings. Thus, for example, 0; 1; 2: nat; 1; (0,..10) because 0: nat and 1: 1 and 2: 0,..10 . D. Lists A list is a packaged string. For example, =-=[0; 1; 2]-=- is a list of three items. List formation [ ] distributes over bunch union. [null] = null base [A, B] = [A], [B] distribution, factoring Because of the distribution we can say [0; 1; 2]: [nat; 1; (0,.... |

10 |
A couple of novelties in the propositional calculus. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 31(2
- Hoare
- 1985
(Show Context)
Citation Context ...there is no danger of confusion, we may write Ln without a space between, but when we use multicharacter names, we must put a space between. The contents of a list is the string of items it contains. =-=[3; 5; 7; 4]-=- = 3; 5; 7; 4 The length of a list is the number of items it contains. #[3; 5; 7; 4] = 4 List indexes, like string indexes, start at 0 . An item can be selected from a list by juxtaposing (placing nex... |

6 | from Boolean Algebra to Unified Algebra
- Hehner
- 2004
(Show Context)
Citation Context ... designing the instrument, not playing the music. To appreciate the algebra, I rely on the reader's experience in using algebra. For motivations, justifications, and commentary, I refer the reader to =-=[2]-=-. The algebra is presented from the very beginning, leaving out nothing. That makes the early parts of Manuscript received April 5, 2006. Eric C. R. Hehner is the Bell Professor of Software Engineerin... |

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