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Artifact for OOPSLA'18 Submission 'Scopes as Types'

Artifact Description

This is the artifact accompanying the OOPSLA'18 submission 'Scopes as Types'. This artifact consists of the following:

  • The paper draft in scopes-as-types.pdf, which is updated to match the artifact. Note that the paper submitted as part of the HotCRP submission, is the original draft, which may deviate in places from this artifact.

  • An implementation of the Statix language, embedded in the Spoofax language workbench. A test suite of unit tests for Statix is included in the artifact.

  • Language implementations for the three case studies in the paper. Each implementation includes a static semantics definition in Statix, some example programs, and a test suite to test the static semantics. The implementations provide source code editors with syntax highlighting and type checking. The result of type checking is simply yes or no at the moment, and no detailed error messages are shown in the editors.

Getting Started

This section explains how to get the artifact running and what can be inspected. The artifact consists of a Spoofax Eclipse workspace with language implementation projects for the case studies presented in the paper. The static semantics of these languages are defined in Statix, the constraint language defined in the paper. First we explain how to get Spoofax, and build the language projects. Then we explain the structure of the language projects, and what can be inspected and tested.

Getting Spoofax and Building the Language Projects

The case studies are implemented in the Spoofax language workbench, which supports Statix is one of its meta-languages.

  • Download the appropriate Spoofax 2.5.0 release for your platform from It is recommended to use a version with an included JRE, since they do not require a compatible local Java installation.

  • Install and run Spoofax by unpacking the archive, and starting eclipse or eclipse.exe. When Spoofax is started, it will ask for a workspace; select the artifact root directory. Workspaces can be changed using the File > Switch Workspace menu, if necessary.

  • After start-up, wait until the task Building workspace... is not shown in the bottom right status bar anymore.

  • Build all language projects using the Project > Build All menu. After a successful language build, the console shows something like:

    Reloading language project eclipse:///lang.sysf

    Individual languages can be rebuilt by selecting the project in the Package Explorer, and selecting Project > Build from the menu.

Inspecting the Language Projects

The workspace contains three language projects, for the three case studies: the Simply Typed Lambda Calculus with Structural Records in lang.stlcrec, System F in lang.sysf, and Featherweight Generic Java in lang.fgj. Each project contains a Statix specification of the static semantics, some example programs, and a test suite.

  • The Statix specification of a language is found in the file trans/statics.stx. The file can be opened in an editor by double-clicking.

  • Example programs can be found in the example folder of a language project. Double-clicking opens an editor and starts type checking for the file, using the language's Statix specification. If the file contains errors, a red marker appears at the top of the editor. Depending on the size of the program, type checking can take some time. Only after type checking is done will the error marker be updated. When done, the console shows a status line similar to:

    Solved 415 constraints (103 delays) with 0 failed and 0 remaining constraint(s).

    If the number of failed or remaining constraints is not zero, the program did not successfully type check.

  • Every language project has an accompanying test project, which contains a test suite for the static semantics of the language. Test files have a .spt extension, and can be opened and inspected in an editor by double-clicking. Failing tests are marked with a red marker. If a file contains many tests, it may take a while before the tests are finished and the success and failures are correctly marked. Use the console or the progress window to check if the tests are still running.

  • All tests in a project or directory can be run by selecting the project or directory in the Package Explorer, and selecting the Spoofax (meta) > Run all selected tests menu. A test runner will appear, listing all tests, showing progress and which tests success or failure. Running all tests (especially for FGJ) takes quite a while. For faster results, open individual files, or run fewer tests by selecting subdirectories of the test project.

The statix.test project contains unit tests for Statix itself.

Claims Supported by the Artifact

This artifact supports the following claims from the paper:

"We show that viewing scopes as types enables us to model the internal structure of types in a range of non-simple type systems (including structural records and generic classes) using the generic representation of scopes. Further, we show that relations between such types can be expressed in terms of generalized scope graph queries. We extend scope graphs with scoped relations and queries."

The specifications of all three languages model non-syntactic aspects of types, such as record and class structure, or type variables and lazy substitution, using the scope graph model.

"We extend the scope graph model with scoped relations to model the association of types with declarations and explicit substitutions in the instantiation of parametrized types. We generalize name resolution in scope graph from resolution from references to declarations to general queries for scoped relations. This enables flexible definition of queries for reachable or visible declarations and other properties, such as the visible record fields in the definition of subtyping of structural record types."

This extended model and a resolution algorithm are implemented as part of the Statix implementation. Many tests for different resolution scenarios are included in the statix.test project, in the scopegraphs directory.

"We introduce Statix, a declarative, language for specifying type systems. The language provides simple guarded rules for definition of user-defined constraints with unification and scope graph construction and resolution as built-in theories. We provide a declarative and an operational semantics of Statix."

The Statix language, including a type checker and a solver, are implemented and included as a part of Spoofax. The tests in statix.test document and test the behavior of the solver for different Statix programs.

"We simplify the resolution calculus and algorithm of Néron et al. [2015a] and Van Antwerpen et al. [2016] by not including imports as a primitive. We demonstrate how imports (and other name- and type-dependent name resolution schemas) can be encoded using the scopes as types approach. We discuss how these patterns depend on resolution in incomplete scope graphs, and how the algorithm guarantees soundness of resolution in incomplete graphs. We further generalize resolution by namespace/query-specific parameterization with visibility policies instead of global policies."

The case study specifications implement binding patterns -- such as class inheritance -- using the simplified model that is a part of Statix. In earlier work, these patterns were implemented using the import mechanism. Global resolution policies, for example how to resolve methods or variables in FGJ, are provided in the Statix language for convenience, but every query can redefine every parameter of the resolution calculus.

Statix provides integrated support for guaranteeing that resolution in incomplete graphs is safe, following the principles discussed in the paper Section 5.2. Specific tests for this behavior can be found in the statix.test project, in scopegraphs/relations.spt; search for tests with incomplete in the name.

"We have evaluated the Statix language in three case studies: the simply-typed lambda calculus with records [Pierce 2002] (STLC-REC), System F [Girard 1972; Reynolds 1974], and Featherweight Generic Java [Igarashi et al. 2001]."

The artifact contains type checkers for the case study languages. These type checkers are not (yet) meant to be efficient, nor to provide good error messages. For now, the type checkers merely check whether programs type check or not. The test suites give us trust in the correctness of the given specifications.

The following claims from the paper are not supported by this artifact:

"We extend the visual notation of scope graph diagrams with scoped relations, which provides a useful language for explaining patterns of names and types in programming languages. We also extend the visual notation with unresolved (constraint) nodes for illustrating the resolution process."

The visual notation that the paper introduces and demonstrates is not a part of Statix or of its output.

Case study languages

We briefly summarize the case study languages that we have implemented. Each of the specifications were developed with a focus on object language feature coverage, correctness, and clarity of specification.


This case study implements an extension of the simply-typed lambda-calculus with records. The language contains the following constructs:

  • numbers and addition (1 + 2);

  • functions and identifiers (fun (x : num) { x }), as well as function application (f 1 where f is a function-typed expression);

  • type ascription expressions (1 + 2 : num);

  • let expressions (e.g., let x = 1 in x);

  • records ({x = 1}) and record types ({x : num}) with structural subtyping;

  • record extension expressions ({x = 1} with r where r is a record-typed expression); and

  • type let binders and type identifier references (type r = {x : num} in fun(y : r) { y.x }).

Syntax, Semantics, and Example Files

The syntax of the language is given in lang.stlcrec/syntax/STLCrec.sdf3.

The Statix semantics is given in lang.stlcrec/trans/statics.stx.

For object language tests, consult the files in lang.stlcrec.test/.

About the Semantics

Section 3.1 of the paper contains example illustrations of scope graphs for STLCrec programs. Here we highlight some of the core features of the semantics and its use of scopes as types:

  • Record field names and function parameter names reside in separate namespaces, Fld and Var respectively. Each namespace has its own name resolution policy (see their name-resolution signatures in lang.stlcrec/trans/statics.stx).

  • There are two notions of type in the language:

    1. Type expressions (TypeExp): syntactic type representations in object language programs.
    2. Types (Type): semantic type representations used in the type system specification.
  • typeOfTypeExp translates type expressions (TypeExp) into types (Type).

  • Record types (REC) are given by a scope in the scope graph.

  • Record extension is modeled as an R-labeled edge in the scope graph; see, e.g., typeOfExp(s, FExtend(e, finits)) in lang.stlcrec/trans/statics.stx.

  • Records with duplicate field names are disallowed via the uniqueness check in fieldInitsOK in lang.stlcrec/trans/statics.stx.

  • Record subtyping is modeled using two queries over the scope graph (see subType(REC(s_sub), REC(s_sup)) in lang.stlcrec/trans/statics.stx):

    1. the query given by allFields finds all visible fields in the super type.
    2. the query given by subFields checks that there is exactly one visible field of a matching (sub-)type for every field in the super type.

System F

This case study implements System F with type let binders. The language contains the following constructs:

  • functions, identifiers, function application, let expressions, type ascription expressions, and type let binders (using the same syntax as STLCrec);

  • type binders (Fun(T) { fun(x : T) { x } }) and forall type quantifiers (T => T -> T);

Syntax, Semantics, and Example Files

The syntax of the language is given in lang.sysf/syntax/SystemF.sdf3.

The Statix semantics is given in lang.sysf/trans/statics.stx.

For object language tests, consult the files in lang.sysf.test/.

About the Semantics

We highlight some of the core features of our semantics for System F and its use of scopes as types:

  • Type parameter names and function parameter names reside in separate namespaces.

  • Forall-types (ALL) are modeled as a scope with two declarations in it: one declaration that records the formal parameter; and one declaration that is associated with the type of the body of the forall-type. In this sense, the ALL type is reminiscent of a two-field record.

  • Type application uses the instWith relation to add a substitution to the scope of an ALL type, and projects the body from the resulting record (see typeOfExp(s, TApp(e, t)) = T in lang.sysf/trans/statics.stx). Projections are evaluated lazily: the PROJ type represents a lazily postponed projection.

  • When we match on a type we first apply strict to it, which normalizes PROJ types by stricting the postponed projection. The type resuling from applying strict is in WHNF: the substitution is pushed inwards in a lazy fashion. The precise definitions of strict and type normalization are given in lang.sysf/trans/statics.stx. Laziness is not built into Statix, so the lazy substitution strategy is encoded rather explicitly in the aforementioned definition of norm. strict and norm are mostly generically defined: the same notions are used to implement generics in FGJ, as described in the paper Section 3.3.

  • When we compare two types (e.g., in typeOfExp(s, App(e1, e2)) in lang.sysf/trans/statics.stx) we use typeEq which implements the following scheme for comparing types:

    1. If either of the types we are comparing is a PROJection, apply strictness.

    2. Numbers and function types are compared in the obvious compositional way.

    3. ALL-types are compared by inventing a fresh place holder value PL and substituting this in each of the quantified types for the two ALL types that we are comparing. We then compare the quantified types by projecting the bodies from the scopes with these substitutions.

Featherweight Generic Java (FGJ)

This case study language implements FGJ. The language contains the same constructs as in the original paper Featherweight Java: a minimal core calculus for Java and GJ by Igarashi, Pierce, and Wadler. Our FGJ language has a few minor differences in syntax and semantics from the original FGJ language:

  • In our variant of FGJ, it is not mandatory that each class has a constructor parameter for each field in the class.

  • In our variant of FGJ, fields can be initialized with arbitrary expressions, whereas original FGJ only allows variable references as the right-hand side of field initialization expressions.

  • Our variant of FGJ does not check that every field is explicitly initialized.

Syntax, Semantics, and Example Files

The syntax of the language is given in lang.fgj/syntax/FGJ.sdf3.

The Statix semantics is given in lang.fgj/trans/statics.stx.

For object language tests, consult the files in lang.fgj.test/.

About the Semantics

Section 3.2 and 3.3 of the paper contains example illustrations of scope graphs for STLCrec programs. Here we highlight some of the core features of the semantics and its use of scopes as types:

  • Inheritance is represented using a dedicated "super" edge in the scope graph.

  • Subtyping is defined in terms of a query over the scope graph: the extendsQ constraint represents a query which checks that we can traverse a sequence of "super" edges in the graph to connect a sub-class with its super-class.

  • Generic type parameter substitution and class type comparison is implemented using similar machinery as summarized for System F above.