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Migrate to Statix from NaBL2


All sorts and constructors must be explicitly defined in Statix in sorts and constructors signatures. Sorts in Statix are mostly similar to terms in NaBL2. Notable differences:

  • There is no catch-all sort term in Statix.
  • There are no sort variables in Statix.
  • List sorts in Statix are written as list(X) for some sort X.

Statix signatures for language syntax can be generated from SDF3 definitions with the signature generator.


Name resolution in NaBL2 heavily relies on occurrences and their unique identity. In Statix, the notion of a stand-alone reference is replaced by the notion of a query. Therefore, the use of occurrences is now discouraged in favour of regular terms, relations, and and predicates for the different namespaces.



  name resolution
    labels P
    well-formedness P*
    order D < P


   [[ Def(x, T) ^ (s) ]] :=
     Var{x} <- s,
     Var{x} : T.

   [[ Var(x) ^ (s) : T ]] :=
     Var{x} -> s,
     Var{x} |-> d,
     d : T.

    var : string * TYPE

    labels P


  declareVar : scope * string * TYPE

  declareVar(s, x, T) :-
    !var[x, T] in s.

  resolveVar : scope * string -> TYPE

  resolveVar(s, x) = T :-
    query var
      filter P* and { x' :- x' == x}
      min $ < P and true
      in s |-> [(_, (x, T))],
    @x.ref := x'.


   stmtOk : scope * Stmt

   stmtOk(s, Def(x, T)) :-
     declareVar(s, x, T);

   typeOfExp : scope * Exp -> TYPE

   typeOfExp(s, Var(x)) = T :-
     T == resolveVar(s, x).

Things to note:

  • Each namespace gets its own relation, and set of predicates to declare and resolve in that namespace (declareXXX and resolveXXX).
  • The regular expression and order on labels is not global anymore, but part of the query in the resolveXXX rules.
  • If a declaration should have a type associated with it, it is now part of the relation. The fact that it appears after the arrow -> indicates that each declaration has a single type. As a result, declareXXX combines the constraints XXX{...} <- s, XXX{...} : T. Similarly, resolveXXX combines the constraints XXX{...} -> s, XXX{...} |-> d, d : T.
  • The end-of-path label, called D in NaBL2, now has a special symbol $, instead of the reserved name.


NaBL2 functions can be translated to Statix predicates in a straight-forward manner. Note that if the function was used overloaded,it is necessary to defined different predicates for the different argument types.



    plusType : (Type * Type) -> Type {
      (IntTy()  , IntTy()  ) -> IntTy(),
      (StrTy()  , _        ) -> StrTy(),
      (ListTy(a), a        ) -> ListTy(a),
      (ListTy(a), ListTy(a)) -> ListTy(a)
plusType : Type * Type -> Type

plusType(IntTy()  , IntTy()  ) = IntTy().
plusType(StrTy()  , _        ) = StrTy().
plusType(ListTy(a), a        ) = ListTy(a).
plusType(ListTy(a), ListTy(a)) = ListTy(a).


Relations as they exist in NaBL2 are not supported in Statix.

An example of a subtyping relation in NaBl2 would translate as follows:


    reflexive, transitive, anti-symmetric sub : Type * Type {
      FunT(-sub, +sub),


  [[ Class(x, superX, _) ^ (s) ]] :=
    ... more constraints ...,
    ClassT(x) <sub! ClassT(superX).

  [[ Def(x, T, e) ^ (s) ]] :=
    [[ e ^ (s) : T' ]],
    T1 <sub? T2.

  subType : TYPE * TYPE

  subType(FunT(T1, T2), FunT(U1, U2)) :-
    subType(U1, T1),
    subType(T2, T1).

  subType(ListT(T), ListT(U)) :-
    subType(T, U).

  subType(ClassT(s1), ClassT(s2)) :-
    ... check connectivity of s1 and s2 in the scope graph ...

In this case implementing the subType rule for ClassT requires changing the encoding of class types. Instead of using names, we use the class scope to identify the class type. This pattern is know as Scopes as Types. Subtyping between class scopes can be checked by checking if one scope is reachable from the other.


NaBL2 constraint generation rules must be translated to Statix predicates and corresponding rules. Predicates in Statix are explcitly typed, and a predicate has to be defined for each sort for which constraint generation rules are defined.

Here are some example rules for expressions in NaBL2:

[[ Let(binds, body) ^ (s) : T ]] :=
  new s_let, s_let -P-> s,
  Map1[[ binds ^ (s, s_let) ]],
  [[ body ^ (s_let) : T ]].

[[ Bind(x, e) ^ (s, s_let) ]] :-
  [[ e ^ (s) : T ]],
  Var{x} <- s_let,
  Var{x} : T.

In Statix these would be encoded as:

typeOfExp : scope * Exp -> TYPE

typeOfExp(s, e@Let(binds, body)) = T :- {s_let}
  new s_let, s_let -P-> s,
  bindsOk(s, binds, s_let),
  T == typeOfExp(s_let, body),
  @e.type := T.

bindOk : scope * Bind * scope
bindsOk maps bindOk(*, list(*))

bindOk(s, Bind(x, e), s_let) :- {T}
  T == typeOfExp(s, e),
  declareVar(s_let, x, T).

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