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Formal system, an abstract means of generating inferences in a formal language; Formal language, comprising the symbolic "words" or "sentences" of a formal system; Formal grammar, a grammar describing a formal language; Colloquialism, the linguistic style used for informal communication
A formal system (also called a logical calculus, or a logical system) consists of a formal language together with a deductive apparatus (also called a deductive system). The deductive apparatus may consist of a set of transformation rules , which may be interpreted as valid rules of inference, or a set of axioms , or have both.
Formal language, which is a set of well-formed formulas, which are strings of symbols from an alphabet, formed by a formal grammar (consisting of production rules or formation rules). Deductive system , deductive apparatus, or proof system , which has rules of inference that take axioms and infers theorems , both of which are part of the formal ...
The categorical dual definition is a formal definition of a comonad (or cotriple); this can be said quickly in the terms that a comonad for a category is a monad for the opposite category. It is therefore a functor U {\displaystyle U} from C {\displaystyle C} to itself, with a set of axioms for counit and comultiplication that come from ...
Formal verification is the use of software tools to prove properties of a formal specification, or to prove that a formal model of a system implementation satisfies its specification. Once a formal specification has been developed, the specification may be used as the basis for proving properties of the specification, and by inference ...
Formal definitions, first devised in the early 19th century, are given below. Informally, a function f assigns an output f ( x ) to every input x . We say that the function has a limit L at an input p , if f ( x ) gets closer and closer to L as x moves closer and closer to p .
You may have vague recollections of hyperbole from high school English or Language Arts class es.Or, perhaps you’re a seasoned writer looking to add more hyperbole examples to your arsenal.
Lambda calculus definition – Formal definition of the lambda calculus. Let expression – An expression closely related to an abstraction. Minimalism (computing) Rewriting – Transformation of formulæ in formal systems; SECD machine – A virtual machine designed for the lambda calculus; Scott–Curry theorem – A theorem about sets of ...