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Within Spoofax, the programs are represented as Abstract Syntax Trees (ASTs). This is an in-memory representation that uses ATerms (Annotated Term Format). ATerms provide a common set of contructs to represent abstract trees, comparable to XML or algebraic data types in functional programming languages. It is based on the ATerms of Van den Brand et al.1, and has both textual and binary representations.

As an example, this is one possible representation of the expression 4 + f(5 * x) as a term:

Plus(Int("4"), Call("f", [Mul(Int("5"), Var("x"))]))

A term t is constructed from the following elements:

  • Constructor application: C(t1, .., tN)
  • Tuple: (t1, .., tN)
  • List: [t1, .., tN]
  • String: "foobar"
  • Integer: 42
  • Real: 13.37
  • Annotations: t{t1, .., tN}

Constructor Application

A constructor is an identifier. It must be an alphanumeric string starting with a letter, or it can be double-quoted string.

A constructor application c(t1, .., tN) creates a term by applying the constructor c to the list of zero or more term t1, .., tN. For example, the term Plus(Int("4"), Var("x")) uses the constructors Plus, Int, and Var to create a nested term from the strings "4" and "x".

A tuple is just a special case of a constructor application where there is no constructor.


A list is a term of the form [t1, .., tN]. That is, a list of zero or more terms written between square brackets. While all applications of a specific constructor typically have the same number of subterms but of varying types, lists can have a variable number of subterms typically of the same type.

An example of a list with two terms is shown in:

Call("f"), [Int("5"), Var("x")]


An integer literal is a whole number. For example, 1, 12345.

A real literal is a number that includes a decimal dot ., and optionally an exponent. Examples include: 12.2, .4, 14.0000001, 0.1e12, 13.37E15.

A string literal is a sequence of characters written between double quotes. For example, "foobar".


While the term elements above are used to create the structural part of terms, a term can also be annotated with a list of terms. These annotations typically carry additional semantic information about the term. A term t annotated with a list t1, .., tN has the form t{t1, .., tN}. The contents of an annotation is up to the application.

Example where the constructor application of Lt is annotated with a term describing the type of the expression Type("bool"):


  1. Mark G. J. van den Brand, H. A. de Jong, Paul Klint, and Pieter A. Olivier. Efficient annotated terms. Software: Practice and Experience, 30(3):259–291, 2000. URL:;2-Y, doi:10.1002/(SICI)1097-024X(200003)30:3%3C259::AID-SPE298%3E3.0.CO;2-Y

Last update: September 15, 2023
Created: September 15, 2023