theoretical computer science Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumsc ...

and

formal language theory In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of sy ...

, a ranked alphabet is a pair of an ordinary alphabet ''F'' and a function ''Arity'': ''F''→

\mathbb

. Each letter in ''F'' has its

arity Arity () is the number of arguments or operands taken by a function, operation or relation in logic, mathematics, and computer science. In mathematics, arity may also be named ''rank'', but this word can have many other meanings in mathematics. In ...

so it can be used to build terms. Nullary elements (of zero arity) are also called constants. Terms built with unary symbols and constants can be considered as strings. Higher arities lead to proper

trees In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are ...

. For instance, in the term :

f(a,g(a),f(a,b,c))

, ''a,b,c'' are constants, ''g'' is unary, and ''f'' is ternary. Contrariwise, :

f(a,f(a))

cannot be a valid term, as the symbol ''f'' appears once as binary, and once as unary, which is illicit, as ''Arity'' must be a function.

References

* {{Comp-sci-theory-stub Trees (data structures) Automata (computation) Formal languages Theoretical computer science