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Introduced in Python 2.2 as an optional feature and finalized in version 2.3, generators are Python's mechanism for lazy evaluation of a function that would otherwise return a space-prohibitive or computationally intensive list. This is an example to lazily generate the prime numbers:
where x 2, ⋯ , x n−2 are fresh variables not occurring elsewhere. Although the two formulas are not logically equivalent, they are equisatisfiable. The formula resulting from transforming all clauses is at most 3 times as long as its original; that is, the length growth is polynomial. [10]
This statement expresses the idea "' if and only if '". In particular, the truth value of p ↔ q {\displaystyle p\leftrightarrow q} can change from one model to another. On the other hand, the claim that two formulas are logically equivalent is a statement in metalanguage , which expresses a relationship between two statements p {\displaystyle ...
The eval() vs. exec() built-in functions (in Python 2, exec is a statement); the former is for expressions, the latter is for statements Statements cannot be a part of an expression—so list and other comprehensions or lambda expressions , all being expressions, cannot contain statements.
An important set of problems in computational complexity involves finding assignments to the variables of a Boolean formula expressed in conjunctive normal form, such that the formula is true. The k -SAT problem is the problem of finding a satisfying assignment to a Boolean formula expressed in CNF in which each disjunction contains at most k ...
This is because the syntax directs that any variable cannot be a function of subsequently introduced variables. A less trivial example from mathematical analysis regards the concepts of uniform and pointwise continuity, whose definitions differ only by an exchange in the positions of two quantifiers. A function f from R to R is called
The detailed semantics of "the" ternary operator as well as its syntax differs significantly from language to language. A top level distinction from one language to another is whether the expressions permit side effects (as in most procedural languages) and whether the language provides short-circuit evaluation semantics, whereby only the selected expression is evaluated (most standard ...
The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), [2] and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of ...