By David Gries, Fred B. Schneider
Uploader's Note: Ripped from SpringerLink.
Here, the authors try to alter the best way common sense and discrete math are taught in desktop technology and arithmetic: whereas many books deal with common sense easily as one other subject of analysis, this one is exclusive in its willingness to move one step extra. The ebook traets good judgment as a easy instrument that may be utilized in basically another region.
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Extra info for A Logical Approach to Discrete Math (Monographs in Computer Science)
MODELING ENGLISH PROPOSITIONS 35 into b -=/'- c , since the exclusive or of b and c is true exactly when one of them is true and the other false . c. DEALING WITH IMPLICATION Sentences of the form "If b then c" or "If b , c " are usually translated as b =} c . For example, consider the sentence "If you don't eat your spinach, I'll spank you" . es =} sy. e. es =} sy. This fact may seem strange at first. But note that the two sentences If you don't eat your spinach, I'll spank you Eat your spinach or I'll spank you have the same meaning.
Adhere carefully to this format; the more standard our communication mechanism, the easier time we have understanding each other. 6 The assignment statement In the previous section, we showed how textual substitution was inextricably intertwined with equality. We now show a correspondence between textual substitution and the assignment statement that allows programmers to reason about assignment. 6. 10) X:= E evaluates expression E and stores the result in variable x . 5 Assignment x:= E is read as "x becomes E".
X = E[z :=X]. 8) . L e1"b mz: X= y g. X _ y -g. Y. This fundamental property of equality and function application holds for any function g and expressions X and Y . In fact, any expression can (momentarily) be viewed as a function of one or more of its variables. y = x + y . 8) are just two different forms of the same rule. 5) allows us to "substitute equals for equals" in an expression without changing the value of that expression. It therefore gives a method for demonstrating that two expressions are equal.