Skip to content

Language Concepts

In this section, a brief description of the main concepts of the Statix language is provided.


The data model that underlies all Statix specifications is algebraic data. Besides several built-in primitives, such as integer and string literals, users can build composite terms using term constructors, tuples and lists. Statix is a sorted logic, in the sense that all runtime data should adhere to a multi-sorted signature.


Key to the Statix design philosophy is to view a type-checking problem as a constraint problem. When solving the constraint problem, a minimal model is inferred from the constraints. This model represents a principal typing for the original program. In order to express such constraint problems, a versatile set of built-in constraints is provided by the Statix language. For more information on constraints, see the Basic Constraints section.


Besides using built-in constraints, users can define their own constraints using constraint handling rules. Rules consist of a head and a body. The head specifies the arguments to the constraint, and (optionally) a guard, which indicates when to apply the rule. The body is a regular constraint, which, when proven, asserts that the constraint holds. More detailed information about user-defined constraints can be found in the Rules section.

Scope Graphs

Since Statix is especially designed for type-checking, and type-checking is heavily intertwined with name binding, special support for name binding is integrated in the language. Name binding is modelled using scope graphs, in which scopes are represented as nodes, visibility is modelled using labelled edges between nodes, and declarations using special terminal nodes that are associated with a particular datum. References are modelled using scope graph queries. For more information on scope graph construction and querying, see sections Scope Graph Constraints and Queries, respectively.

Last update: April 19, 2024
Created: April 19, 2024