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...

properties in the most abstract setting of an abstract rewriting system. The usual rules of elementary arithmetic form an abstract rewriting system. For example...

(abstract rewriting), an element of a rewrite system which cannot be further rewritten in logic: Normal form (natural deduction) Algebraic normal form Canonical...

and theoretical computer science, an abstract rewriting system (also (abstract) reduction system or abstract rewrite system; abbreviated ARS) is a formalism...

logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems...

The Abstract Rewriting Machine (ARM) is a virtual machine which implements term rewriting for minimal term rewriting systems. Minimal term rewriting systems...

In computer science, Backus–Naur form (BNF, pronounced /ˌbækəs ˈnaʊər/), also known as Backus normal form, is a notation system for defining the syntax...

a normal form. A lambda term is in beta normal form if no beta reduction is possible; lambda calculus is a particular case of an abstract rewriting system...

a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of...

Normalizing (abstract rewriting), an abstract rewriting system in which every object has at least one normal form Normalization property (abstract rewriting), a...

language theory, a noncontracting 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,...

termination, confluence, local confluence and normal forms). Newman's lemma: If an abstract rewriting system is terminating and locally confluent, then...

normal form; the latter is impossible in a terminating rewriting system. In the lambda calculus an expression is divergent if it has no normal form....

calculus, equivalence is decidable by comparison of normal forms. The word problem for an abstract rewriting system (ARS) is quite succinct: given objects x...

lemma which states that if an (abstract) rewriting system is strongly normalizing and weakly confluent, then the rewriting system is confluent. So, if we...

which both b and c can be reduced. Viewing the lambda calculus as an abstract rewriting system, the Church–Rosser theorem states that the reduction rules...

that adding a fexpr device to lambda calculus — a device that suppresses rewriting of operands — produces a formal system with a trivial equational theory...

eventually terminates, then by the Church–Rosser theorem it will produce a β-normal form. Variable names are not needed if using a universal lambda function,...

the rewriting of any ground term leads to the same normal form. It is said to be terminating if the rewriting of any ground term will lead to a normal form...

In rewriting, a reduction strategy or rewriting strategy is a relation specifying a rewrite for each object or term, compatible with a given reduction...

Rubio, A. (2006). "Higher-Order Orderings for Normal Rewriting". In Frank Pfenning (ed.). Term Rewriting and Applications, 17th Int. Conf., RTA-06. LNCS...

in polynomial space and unlimited time. Given the formula in the form of an abstract syntax tree, the problem can be solved easily by a set of mutually...

semantics, normalisation by evaluation (NBE) is a method of obtaining the normal form of terms in the λ-calculus by appealing to their denotational semantics...

that have simpler forms, known as normal forms. Some common normal forms include conjunctive normal form and disjunctive normal form. Any propositional...

{\displaystyle S} . A term rewriting system is said to be orthogonal if it is left-linear and is non-ambiguous. Orthogonal term rewriting systems are confluent...

ε-production has an equivalent grammar in Chomsky normal form, and a grammar in Greibach normal form. "Equivalent" here means that the two grammars generate...

ISBN 978-0-804-78802-1. Rogan, Eugene L. (2011). The War for Palestine: Rewriting the History of 1948. Cambridge University Press. ISBN 9780521794763. Rouhana...

describe a scenario in which it has become normal for people to be exploited through data and other forms of technology. It draws parallels to colonialism...

also important differences exist (e.g. fixed point combinator Y has normal form in combinatory logic but not in λ {\displaystyle \lambda } -calculus)...

called the direct sum of two normal subgroups with trivial intersection if it is generated by the subgroups. In abstract algebra, this method of construction...