One of the most important definition element in CASM-IR are functions. They can be specified by using a global symbol and a proper relation type definition. Functions are defined with the following Extended Backus–Naur Form (EBNF) grammar:
Function ::= Global "=" Relation
Listing given below defines a nullary function @f with relation $f : Integer → Integer$,
a unary function @g with relation $g : Integer → String$, and
a binary function @h with relation $h : Boolean ∗ Rational → Decimal$.
@f = < -> i > @g = < i -> s > @h = < b , q -> z >