Typed self-evaluation via intensional type functions

Brown, Marianne; Palsberg, Jens

doi:10.1145/3009837.3009853

Cited by 8 publications

(5 citation statements)

References 31 publications

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“…Most closely related to this work is our previous work [Brown and Palsberg 2017] that defined typed self-representations and three typed self-evaluators. Each of those self-evaluators implements a particular evaluation strategy for the calculus itself.…”

Section: Related Workmentioning

confidence: 99%

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Jones-optimal partial evaluation by specialization-safe normalization

Brown

Palsberg

2017

Proc. ACM Program. Lang.

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We present partial evaluation by specialization-safe normalization, a novel partial evaluation technique that is Jones-optimal, that can be self-applied to achieve the Futamura projections and that can be type-checked to ensure it always generates code with the correct type. Jones-optimality is the gold-standard for nontrivial partial evaluation and guarantees that a specializer can remove an entire layer of interpretation. We achieve Jones-optimality by using a novel affine-variable static analysis that directs specialization-safe normalization to always decrease a program's runtime.We demonstrate the robustness of our approach by showing Jones-optimality in a variety of settings. We have formally proved that our partial evaluator is Jones-optimal for call-by-value reduction, and we have experimentally shown that it is Jones-optimal for call-by-value, normal-order, and memoized normal-order. Each of our experiments tests Jones-optimality with three different self-interpreters.We implemented our partial evaluator in F µi ω , a recent language for typed self-applicable meta-programming. It is the first Jones-optimal and self-applicable partial evaluator whose type guarantees that it always generates type-correct code.

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Section: Related Workmentioning

confidence: 99%

“…It is type-safe and type checking is decidable. For more details, we refer the interested reader to Brown and Palsberg [Brown and Palsberg 2017].…”

Section: Typed Self-applicable Partial Evaluation For Fmentioning

confidence: 99%

Jones-optimal partial evaluation by specialization-safe normalization

Brown

Palsberg

2017

Proc. ACM Program. Lang.

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“…It is well-known that we cannot encode the Y combinator in the polymorphic lambda calculus, but that we can encode it if we have recursive types [14,Section 20.3]. 6 We need the following types:…”

Section: Recursive Term Bindingsmentioning

confidence: 99%

“…There are other implementations of System F ω with recursive types. Brown and Palsberg [6] use isorecursive types, and includes an indexed fixpoint operator as well as a typecase operator. However, the index for the fixpoint must be of kind * , whereas ours may be of any kind.…”

Section: Encoding Recursive Datatypesmentioning

confidence: 99%

Unraveling Recursion: Compiling an IR with Recursion to System F

Jones¹,

Gkoumas²,

Kireev³

et al. 2019

Lecture Notes in Computer Science

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Lambda calculi are often used as intermediate representations for compilers. However, they require extensions to handle higherlevel features of programming languages. In this paper we show how to construct an IR based on System F µ ω which supports recursive functions and datatypes, and describe how to compile it to System F µ ω . Our IR was developed for commercial use at the IOHK company, where it is used as part of a compilation pipeline for smart contracts running on a blockchain.

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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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Typed self-evaluation via intensional type functions

Cited by 8 publications

References 31 publications

Jones-optimal partial evaluation by specialization-safe normalization

Jones-optimal partial evaluation by specialization-safe normalization

Unraveling Recursion: Compiling an IR with Recursion to System F

Incorporating quotation and evaluation into Church's type theory

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