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This parser function can be used to detect whether a template parameter is defined, even if it has been set to a false value. For example, to check whether the first positional parameter has been passed to a template (note that the strings "+" and "-" can be any two different non-whitespace strings):
Some programming languages, e.g., Ada, have short-circuit Boolean operators. These operators use a lazy evaluation, that is, if the value of the expression can be determined from the left hand Boolean expression then they do not evaluate the right hand Boolean expression.
Parameter 1 selects the if-type as "eq", "expr", "exist" or "error" (for #iferror), or empty "||" for a simple if-there (for #if). The template can be repeatedly nested 6 or 7 levels, one inside the other, because the outer-most is completed before running either the then/else inner levels.
Different sets of allowed Boolean functions lead to different problem versions. As an example, R(¬x,a,b) is a generalized clause, and R(¬x,a,b) ∧ R(b,y,c) ∧ R(c,d,¬z) is a generalized conjunctive normal form. This formula is used below, with R being the ternary operator that is TRUE just when exactly one of its arguments is.
In computational complexity theory, the language TQBF is a formal language consisting of the true quantified Boolean formulas.A (fully) quantified Boolean formula is a formula in quantified propositional logic (also known as Second-order propositional logic) where every variable is quantified (or bound), using either existential or universal quantifiers, at the beginning of the sentence.
An atomic formula is a formula that contains no logical connectives nor quantifiers, or equivalently a formula that has no strict subformulas. The precise form of atomic formulas depends on the formal system under consideration; for propositional logic, for example, the atomic formulas are the propositional variables.
A propositional formula may also be called a propositional expression, a sentence, [1] or a sentential formula. A propositional formula is constructed from simple propositions, such as "five is greater than three" or propositional variables such as p and q, using connectives or logical operators such as NOT, AND, OR, or IMPLIES; for example:
It is assumed that the value of a function f defined on [,] is known at + equally spaced points: < < <.There are two classes of Newton–Cotes quadrature: they are called "closed" when = and =, i.e. they use the function values at the interval endpoints, and "open" when > and <, i.e. they do not use the function values at the endpoints.