Breaking through the normalization barrier: a self-interpreter for f-omega

Brown, Marianne; Palsberg, Jens

doi:10.1145/2837614.2837623

Cited by 12 publications

(21 citation statements)

References 27 publications

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“…Nevertheless these representations were only partially typed. The finally tagless approach to embedded representations [29] kicked off a series of papers on typed selfrepresentation [4,5,18,19,20,21,81,107] which eventually succeeded at providing elegant solutions.…”

Section: Reasoning In the Lambda Calculus About Syntaxmentioning

confidence: 99%

Incorporating quotation and evaluation into Church's type theory

Farmer

2018

Information and Computation

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cttqe is a version of Church's type theory that includes quotation and evaluation operators that are similar to quote and eval in the Lisp programming language. With quotation and evaluation it is possible to reason in cttqe about the interplay of the syntax and semantics of expressions and, as a result, to formalize syntax-based mathematical algorithms. We present the syntax and semantics of cttqe as well as a proof system for cttqe. The proof system is shown to be sound for all formulas and complete for formulas that do not contain evaluations. We give several examples that illustrate the usefulness of having quotation and evaluation in cttqe.

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Section: Reasoning In the Lambda Calculus About Syntaxmentioning

confidence: 99%

Incorporating quotation and evaluation into Church's type theory

Farmer

2018

Information and Computation

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“…A line of recent work considers self-representation and self-interpretation of typed languages such as F ω Palsberg 2016, 2017;Rendel et al 2009].…”

Section: Related Workmentioning

confidence: 99%

Collapsing towers of interpreters

Amin

Rompf

2017

Proc. ACM Program. Lang.

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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 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.

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“…Like the STLC representation in Figure 10, we use a typed Mogensen-Scott encoding, though there are several important differences. Following previous work on typed self-representation [7,8,31], we use Parametric Higher-Order Abstract Syntax (PHOAS) [12,40] to give our representation more expressiveness. The type PExp is parametric in V, which determines the type of free variables in a representation.…”

Section: Our Representation Schemementioning

confidence: 99%

Typed self-evaluation via intensional type functions

Brown

Palsberg

2017

Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages

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Many popular languages have a self-interpreter, that is, an interpreter for the language written in itself. So far, work on polymorphically-typed self-interpreters has concentrated on self-recognizers that merely recover a program from its representation. A larger and until now unsolved challenge is to implement a polymorphicallytyped self-evaluator that evaluates the represented program and produces a representation of the result. We present F µi ω , the first λcalculus that supports a polymorphically-typed self-evaluator. Our calculus extends Fω with recursive types and intensional type functions and has decidable type checking. Our key innovation is a novel implementation of type equality proofs that enables us to define a versatile representation of programs. Our results establish a new category of languages that can support polymorphically-typed selfevaluators.

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Breaking through the normalization barrier: a self-interpreter for f-omega

Cited by 12 publications

References 27 publications

Incorporating quotation and evaluation into Church's type theory

Incorporating quotation and evaluation into Church's type theory

Collapsing towers of interpreters

Typed self-evaluation via intensional type functions

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