The ATerm format does not restrict terms

describing terms schemas with signatures

Stratego Signatures

a type of terms
Constructor declaration

name and types of arguments:

C : S1 * ... * Sn -> S0

To use terms in Stratego programs, their constructors should be declared in a signature. A signature declares a number of sorts and a number of constructors for these sorts. For each constructor, a signature declares the number and types of its arguments. For example, the following signature declares some typical constructors for constructing abstract syntax trees of expressions in a programming language:

module Expressions-sig
imports Common
  sorts Exp
    Var    : ID -> Exp
    Int    : INT -> Exp
    Plus   : Exp * Exp -> Exp
    Mul    : Exp * Exp -> Exp
    Call   : ID  * List(Exp) -> Exp

Currently, the Stratego compiler only checks the arity of constructor applications against the signature. Still, it is considered good style to also declare the types of constructors in a sensible manner for the purpose of documentation. Also, a later version of the language may introduce type checking.

SDF3 Syntax Definitions

signature derived from syntax definition

for example:

module Expressions
imports Common
sorts Exp
context-free syntax
  Exp.Var  = <<ID>>
  Exp.Int  = <<INT>>
  Exp.Plus = <<Exp> + <Exp>> {left}
  Exp.Mul  = <<Exp> * <Exp>> {left}
  Exp.Call = <<ID>(<{Exp ","}*>)>
context-free priorities
  Exp.Mul > Exp.Plus