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Scope Graphs, as introduced in the previous section can be queried. Scope graph queries always start in a particular scope, and traverse the scope graph in order to find declarations under a particular relation. The syntax for queries is as follows:

query $QueryTarget
   filter $LabelRE and $DataWF
      min $LabelOrder* and $DataLeq
       in $Scope |-> $Result

The $Scope parameter is a term with type scope. In this scope, the query starts. All other query arguments are explained in the following subsections.

Query Targets

The query target is the 'thing' that is looked for in the query. This can be one of:

  • $Relation: A relation identifier. In this case, the query will return data that is declared under that relation.
  • (): the end of path query target. In this case, the query will return all paths that match the appropriate filters.
() as relation

The () query target can be thought of as a regular relation if one assumes #1 |-()-> #1 to exist for every scope #1 in the scope graph.


Query results can be filtered using two different filters. First, a regular expression on labels ($LabelRE) defines a filter on the paths that the query resolution algorithm will explore. This regular expression can be build from the following components:

  • $Label: Matches paths that travers a single edge with the label $Label. Requires the label to be declared in a signature section, as explained in the section on edges.
  • e: epsilon. Matches the empty path. Queries using this filter will only return declarations in the scope where the query started.
  • 0: empty set. Matches no path.
  • $LabelRE $LabelRE: concatenation. Matches paths that can be split in two segments p1 and p2, such that p1 matches the first regular expression, and p2 matches the second.
  • $LabelRE | $LabelRE: disjunction. Matches paths that match either the first or the second regular expression.
  • $LabelRE & $LabelRE: conjunction. Matches paths that match both the first and the second regular expression.
  • ~$LabelRE: negation. Matches all paths that do not match the inner regular expression.
  • $LabelRE*: closure. Matches paths that can be split into zero or more segments that each match the inner regular expression.
  • $LabelRE+: one or more. Matches paths that can be split into one or more segments that each match the inner regular expression. Equivalent to $LabelRE $LabelRE*
  • $LabelRE?: zero or one. Matches paths that are matched by the inner regular expression, or empty paths. Equivalent to $LabelRE | e.

Additionally, regular expression can be grouped by brackets.

Second, data well-formedness filters ($DataWF) can be applied. These filters restrict which datums are included in the query result. They are expressed as anonymous lambda rules:

{ $Pattern :- $Constraint }

This rule is instantiated for every declaration that is reachable according to the path well-formedness expression. When the instantiated body constraint holds, the declaration is included in the query answer.

Lambda Instantiation

Lambda constraint instantiation is similar to rule instantiation. For more information on rule instantiation, see the section about rule definitions.

Entailment semantics

Data well-formedness conditions are treated as entailment/implied conditions. Hence, they are not allowed to extend or refine the outer context. For more information on this evaluation mode, see the documentation of the try construct.

The type of the predicate that is expected depends on the kind of relation that is used. For predicative relations, all arguments in the relation are provided to the data well-formedness constraint. However, for functional relations, the 'output value' (i.e. the value that the relation maps to) is not provided to the filter.

When multiple arguments are provided to a data-wellformedness predicate (when there are multiple 'input' arguments to the queried relation), these arguments must be wrapped in a tuple.

When the end-of-path query target () is used, the data-wellformedness constraint expects a single scope as argument.

Example of filters

A simple query for variables illustrates both filters. Suppose the relation var is in scope with type string -> TYPE. Then a rule (with type ascriptions) that looks up a variable definition can be defined as follows.

resolveVar(s : scope, name : string) = R :-
  query var
    filter P* I?
       and { name' : string :- name' == name }
    in s |-> R.
In this example, the path well-formedness expression P* I? indicates that any number of P edges may be traversed, and then, optionally, a single I edge. This resolution policy excludes e.g. transitive imports, and the traversal of P edges in an imported module.

The anonymous data well-formedness condition states that a declaration with name name' may only be included in the query result if name' is equal to name from the enclosing scope. Suppose that resolveVar is instantiated for name |-> "x", and declarations with name "x" and "y" are in scope. Now the anonymous inner rule is instantiated for both "x" and "y". For "x", the constraint "x" == "x" is generated, which can be solved successfully. For "y" however, the constraint "y" == "x" is generated, which cannot be solved successfully. Hence, only the declaration for "x" is included in the eventual query answer.

There are three shorthands for common data well-formedness predicates:

  • true, which is equivalent to { _ :- true }. This shorthand will thus include all encountered declaration in the query result.
  • false, which is equivalent to { _ :- false }. This shorthand will include no declarations in the query answer.
  • eq($Term), is equivalent to { x :- x == $Term } and hence will include all declarations that are equal to $Term.

Syntactically, the query filter can be omitted entirely, or the data well-formedness predicate can be omitted, even if a path filter is provided. By default, the path filter is ~0, meaning that every path is considered valid, and the data well-formedness predicate is true, meaning that every datum will be returned in the query answer.


For many languages, name resolution involves dealing with shadowing correctly. In Statix queries, it is possible to encode shadowing policies using label orders and data comparison predicates. A declaration shadows another declaration iff its path is 'smaller than' the other path by a prefix order defined over a label comparison relation, and when the declaration data is smaller than or equal to the data of the other declaration according to a data comparison predicate.

Label orders ($LabelOrder) are expressed as less-than relations on labels.

$Label < $Label

Here, a label is either a declared label symbol, or $, which denotes the 'end-of-path' label. This label can be used to express orders on path length. For example, $ < P expresses that paths with fewer P labels are preferred over paths with more P labels.

Strict Partial Order

Label orders must be strict partial orders. That is, they are implicitly transitive, but may not be reflexive or symmetric. Label order specifications that are not strict partial orders will be rejected at specification loading time.

Prefix order

Note that the label order is a prefix order, not a lexicographical full-path order. That is, paths that diverged by traversing different edges with the same label are not ordered by this relation.

In addition to a label ordering relation, a data comparison predicate ($DataLeq) can be provided. This predicate can be written as follows:

{ $Pattern, $Pattern :- $Constraint }

This constraint indicates that the left argument is smaller than the right argument, given that the constraint can be satisfied.

The types of each patterns is similar to the type of the data-wellformedness predicate. When the queried relation is predicative (i.e. has no 'output'), the pattern is a tuple containing arguments of the declaration that is compared. If the queried relation is functional, a tuple with only the 'input' arguments must be provided. When there is only one declaration argument, the tuple may be omitted.

There are several shorthands available for the data comparison constraint:

  • true is equivalent to { _, _ :- true }, and hence ensures that declarations are shadowed based on the label order only.
  • false is equivalent to { _, _ :- false }, and hence ensures that no shadowing is applied, even when paths can be ordered using the label order.
  • $ConstraintName is equivalent to { d1, d2 :- $ConstraintName(d1, d2) }, which means that d1 shadows d2 when $ConstraintName(d1, d2) can be satisfied.
  • { $Pattern, $Pattern } is equivalent to { $Pattern, $Pattern :- true }, which means that the first argument shadows the second if they match the patterns.
Non-linear Patterns

The data comparison shorthand is mostly used with non-linear patterns. For example, to encode that declarations with equal names shadow each other, the data comparison shorthand { x, x } can be used. When using this pattern however, please ensure that variable names are fresh, because the behavior of shadowing names is planned to change in the future.

Partial Order

Data comparison functions orders must be (non-strict) partial orders. That is, they are implicitly transitive and reflexive, but may not be symmetric. However, this is not validated for tractability reasons. Therefore, for any predicate that is not a partial order (other than true), shadowing behavior is undefined.

Syntactically, the shadowing parameters can be omitted altogether, or the data comparison predicate can be omitted, even when an label order is specified. The default value of the label order is an empty relation, while the default value of the data comparison predicate is true. On the one hand, this ensures that no shadowing is applied when no shadowing parameters are provided. On the other hand, when a label order, but no data comparison predicate is provided, all declarations shadow each other based on a path comparison only.

Operationally, the label order and the data comparison constraints are applied conjunctively. For any declaration d and d', if the path to d is smaller than the path to d' according to the label order, and the application of the data comparison constraint to d, d' can be satisfied, d' will be excluded from the query answer.

Result Pattern

When the query resolution is completed, the query result will be unified with the $Result term. This term is a list that contains path-datum entries. Therefore, the type of this term is list((path * R)), where R is a tuple type with the argument types of the relation that is queried. In case the relation is functional, the 'output' type is included in the result. When the relation is unary, the tuple is omitted. When the query target is (), R is the scope type.

For the syntactic structure of the paths, please refer to the section on path terms. Semantically, for any query answer pair (p, d), the path p represents the path followed from the scope in which the query started to the scope in which the declaration of d was found.

Top-level Destination scope

Since path terms are left-recursive, have the source scope at the left side, and the destination scope (i.e. the scope in which the paired datum was declared) on the right, it turns out that the target scope is in the third argument of the top-level constructor. This is convenient, since it allows to access the target scope without destructuring the whole path. (Direct access to the source scope is not really important, since it is already available as an argument to the query constraint). On the other side, it is sometimes perceived as not completely intuitive to have the target scope in the top level constructor.

When multiple results are returned by the query, Statix has no guarantees on the order of their appearence in the list.

Query Sugar


Since Spoofax 2.5.15, the query sugar constructs are deprecated.

Last update: May 31, 2024
Created: May 31, 2024