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Collapsing Towers of Interpreters

This is the artifact package for the corresponding POPL 2018 paper (PDF).


Given a tower of interpreters, i.e., a sequence of multiple interpreters interpreting one another as input programs, we aim to collapse this tower into a compiler that removes all interpretive overhead and runs in a single pass. In the real world, a use case might be Python code executed by an x86 runtime, on a CPU emulated in a JavaScript VM, running on an ARM CPU. Collapsing such a tower can not only exponentially improve runtime performance, but also enable the use of base-language tools for interpreted programs, e.g., for analysis and verification. In this paper, we lay the foundations in an idealized but realistic setting.

We present a multi-level lambda calculus that features staging constructs and stage polymorphism: based on runtime parameters, an evaluator either executes source code (thereby acting as an interpreter) or generates code (thereby acting as a compiler). We identify stage polymorphism, a programming model from the domain of high-performance program generators, as the key mechanism to make such interpreters compose in a collapsible way.

We present Pink, a meta-circular Lisp-like evaluator on top of this calculus, and demonstrate that we can collapse arbitrarily many levels of self-interpretation, including levels with semantic modifications. We discuss several examples: compiling regular expressions through an interpreter to base code, building program transformers from modified interpreters, and others. We develop these ideas further to include re reflection and reification, culminating in Purple, a reflective language inspired by Brown, Blond, and Black, which realizes a conceptually infinite tower, where every aspect of the semantics can change dynamically. Addressing an open challenge, we show how user programs can be compiled and recompiled under user-modified semantics.


We are concerned with the following challenge: given a sequence of programming languages L_0,...,L_n and interpreters for L_i+1 written in L_i, derive a compiler from L_n to L_0. This compiler should be one-pass, and it should be optimal in the sense that the translation removes all interpretive overhead of the intermediate languages.


We first summarize the contents of the artifact package and provide instructions how to run the test cases and examples. Afterwards, we detail the relation between the paper and the code in this package.


Multi-level core language λ↑↓ in PLT Redex


  • core.rkt defines the multi-level core language λ↑↓ as a PLT Redex model, using a small-step operational semantics.
  • core-exs.rkt defines examples and test cases to exercise the semantics.


Run core-exs.rkt in DrRacket.

Pink in Scala


  • base.scala defines the multi-level core language λ↑↓ as a definitional interpreter in Scala.
  • lisp.scala defines a LISP-like front end.
  • pink.scala defines meta-circular stage-parametric interpreters for Pink.
  • matcher.scala defines a regular expression matcher on top of LISP-like front end & Pink.
  • bench.scala defines a microbenchmark for comparing evaluation and compilation in Pink.


Run sbt run using Scala's SBT.

Modify test-main.scala to run more or fewer tests and benchmarks.

Pink in Scheme

available at namin/pink, here referred to as pink-scheme.


available at namin/lms-black, here referred to as purple.

Relation to the Paper (PDF)

In the following, we detail how sections, figures, and claims from the paper are reflected in the artifact package.

3 Multi-Level Core Language λ↑↓

  • Fig. 1 corresponds to PLT Redex development in core.rkt.
  • Fig. 2 is a subset of the Scala development in base.scala. The alternative Scheme development is at pink-scheme/base.scm.
  • Fig. 3 and other such examples are in the PLT Redex examples in core-exs.rkt.

3.1 A Lisp-Like Front-End

  • This section uses Scheme syntax for illustration. The more extensive matcher is developed in matcher.scala.

3.2 Stage Polymorphism

  • Again the specific example used here in Scheme syntax is for illustration, but the technique of abstracting over the stage with via η-expansion is used extensively, for example in pink.scala.

4 Building and Collapsing Towers

4.1 Correctness and Optimality

  • The testCorrectnessOptimality() method in pink.scala directly follows the examples in this section.

4.2 Deriving Translators from Heterogeneous Towers

4.2.1 Instrumenting Execution

  • The testInstrumentation() method in pink.scala demonstrates the example of this section.
  • The further tests deriving translators in matcher.scala demonstrates how translators and translator generators can be derived.

4.2.2 CPS Transform

  • The object Pink_CPS in pink.scala shows a range of CPS-related transformations.

5 Towards Reflective Towers

5.1 Execute-at-Metalevel

5.1.2 Modifying the Tower Structure

  • The testEM() method in the object Pink in pink.scala demonstrates the example of this section.

5.1.3 Language Extensions in User Code

  • The testEM() method in the object Pink_CPS in pink.scala demonstrates the example of this section.

5.2 Compiling under Persistent Semantic Modifications

  • The object Pink_clambda in pink.scala shows how to implement and exercise clambda in Pink.

6 Purple: Reflection à la Black

  • The example shown as a starting point here is in purple/src/test/.../em.scala.
  • The Purple development source consists of the stage-polymorphic base interpreter functions (eval.scala), the LMS instantiation(stage.scala), and various utilities including a REPL. The REPL is automatically imported with sbt console from the top-level purple directory and can be invoked with ev, e.g. ev("(+ 1 1)").

7 Purple / Black Examples

8 from λ↑↓ to LMS

8.1 Stage Polymorphism with Type Classes

9 A Sketch of Purple's Implementation

10 Benchmarks

  • The benchmarks for Pink are collected in bench.scala and ran as part of sbt run. The benchmarks for Purple are collected in purple/src/test/.../bench.scala and ran with sbt test:run from the the top-level purple directory. The benchmark for the original Black is in black/examples/bench.blk -- the number of iterations is only 10'000 instead of 100'000 and it is scaled appropriately when reporting the results. The Black microbenchmark is run in Chez Scheme from the top-level Black directory by (load "init.scm") (load "examples/bench.blk"). The Black microbenchmark requires adding the primitive real-time function from Chez Scheme to Black, which is done in a branch bench.
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