Normal form may refer to: * Normal form (databases) * Normal form (game theory) *

Canonical form In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an obje ...

Normal form (dynamical systems) In mathematics, the normal form of a dynamical system is a simplified form that can be useful in determining the system's behavior. Normal forms are often used for determining local bifurcations in a system. All systems exhibiting a certain type ...

Hesse normal form The Hesse normal form named after Otto Hesse, is an equation used in analytic geometry, and describes a line in \mathbb^2 or a plane in Euclidean space \mathbb^3 or a hyperplane in higher dimensions.John Vince: ''Geometry for Computer Graphics''. S ...

* Normal form in music *

Jordan normal form In linear algebra, a Jordan normal form, also known as a Jordan canonical form (JCF), is an upper triangular matrix of a particular form called a Jordan matrix representing a linear operator on a finite-dimensional vector space with respect to som ...

in formal language theory: *

Chomsky normal form In formal language theory, a context-free grammar, ''G'', is said to be in Chomsky normal form (first described by Noam Chomsky) if all of its production rules are of the form: : ''A'' → ''BC'', or : ''A'' → ''a'', or : ''S'' → ...

Greibach normal form In formal language theory, a context-free grammar is in Greibach normal form (GNF) if the right-hand sides of all production rules start with a terminal symbol, optionally followed by some variables. A non-strict form allows one exception to this fo ...

Kuroda normal form In formal language theory, a context-sensitive grammar is in Kuroda normal form if all production rules are of the form: :''AB'' → ''CD'' or :''A'' → ''BC'' or :''A'' → ''B'' or :''A'' → ''a'' where A, B, C and D are nonterminal symbols an ...

Normal form (abstract rewriting) In abstract rewriting, an object is in normal form if it cannot be rewritten any further, i.e. it is irreducible. Depending on the rewriting system, an object may rewrite to several normal forms or none at all. Many properties of rewriting systems ...

, an element of a rewrite system which cannot be further rewritten in logic: *

Normal form (natural deduction) An inference of natural deduction is a normal form, according to Dag Prawitz Dag Prawitz (born 1936, Stockholm) is a Swedish philosopher and logician. He is best known for his work on proof theory and the foundations of natural deduction. Pr ...

Algebraic normal form In Boolean algebra, the algebraic normal form (ANF), ring sum normal form (RSNF or RNF), '' Zhegalkin normal form'', or '' Reed–Muller expansion'' is a way of writing logical formulas in one of three subforms: * The entire formula is purely tr ...

Canonical normal form In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form ( CDNF) or minterm canonical form and its dual canonical conjunctive normal form ( CCNF) or maxterm canonical form. Other canonical forms include ...

Clausal normal form In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs. As a can ...

Conjunctive normal form In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs. As a can ...

Disjunctive normal form In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or (in philosophical logic) a ''cluster c ...

Negation normal form In mathematical logic, a formula is in negation normal form (NNF) if the negation operator (\lnot, ) is only applied to variables and the only other allowed Boolean operators are conjunction (\land, ) and disjunction (\lor, ). Negation normal for ...

Prenex normal form A formula of the predicate calculus is in prenex normal form (PNF) if it is written as a string of quantifiers and bound variables, called the prefix, followed by a quantifier-free part, called the matrix. Together with the normal forms in propos ...

Skolem normal form In mathematical logic, a formula of first-order logic is in Skolem normal form if it is in prenex normal form with only universal first-order quantifiers. Every first-order formula may be converted into Skolem normal form while not changing its ...

in lambda calculus: *

Beta normal form In the lambda calculus, a term is in beta normal form if no ''beta reduction'' is possible. A term is in beta-eta normal form if neither a beta reduction nor an ''eta reduction'' is possible. A term is in head normal form if there is no ''beta-red ...

See also