Programming Language Theory Concept

Arity

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(Syntax & Grammar) According to Practical foundations for programming languages , a syntactic type signature of an Operator, determining the Sort of an operator and the number and the sorts of the arguments expected by the operator.

Example: In the context of Abstract syntax tree (AST)s, if an operator $o$ has an arity $(s_{1}, \dots, s_{n}) s$ for $s, s_{1}, \dots, s_{n} \in 𝒮$ , then $o (a_{1}, \dots, a_{n})$ is of sort $s$ if $a_{i}$ is of sort $s_{i}$ .

Example: In the context of Abstract binding tree (ABT)s, if an operator $o$ has an arity $(v_{1}, \dots, v_{n}) s$ , where $s \in 𝒮$ and $v_{i}$ is $s_{1}, \dots, s_{k} . s$ , then $o ({\vec{x}}_{1} . a_{1}, \dots, {\vec{x}}_{n} . a_{n})$ is of sort $s$ if ${\vec{x}}_{i} . a_{i}$ has the corresponding Valence $v_{i}$ .