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Some particularly important equational theories have been widely studied in the literature.
The class of compact semigroups does not form an equational variety.
The system is based on the equational superposition calculus.
Abstract rewriting from the practical perspective of solving problems in equational logic.
An array can be specified by the following equational axiom:
These transformation rules can be viewed as an equational theory or as an operational definition.
Theories with a non-empty set of equations are known as equational theories.
Their equational theory is extended with the following axioms:
The terms of equational logic are built up from variables and constants using function symbols (or operations).
The machine code can be optimized using the equational form of a theory of computation.
Meiosis II is the second part of the meiotic process, also known as equational division.
Most scholars argue about his complexity since traditionally the Chinese had developed mathematics as algebraic and equational.
However, semantic unification attempts to make the two input terms equal modulo some equational theory.
At first glance this is simply a technical difference, replacing quantified laws with equational laws.
Subjects and predicates of an equational (non-verbal) sentence, with some notable exceptions.
In equational sentences, both the subject and predicate are noun phrases:
Equational bases for this subvariety, first given by Spinks are:
Equational sentences often require no verb.
The data part of the toolset is based on abstract equational data types extended with higher-order functions.
The equational form of relation algebra treated here was developed by Alfred Tarski and his students, starting in the 1940s.
An equational theory in a given language consists of equations between terms built up from variables using symbols of that language.
Equational clauses can also be complex:
In fact, every equational law satisfied by conjugation in a group follows from the quandle axioms.
The equational theory of an algebra is the set of all equations satisfied by the algebra.
Here, the symbol "" is used for equational constraints in order to provide a syntactic distinction from defining equations.