Normalization by Evaluation with Typed Abstract Syntax

Danvy, Olivier; Rhiger, Morten; Rose, Kristoffer H.

doi:10.7146/brics.v8i16.20473

Cited by 5 publications

(7 citation statements)

References 13 publications

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“…The development is akin to Filinski's proof that type-directed partial evaluation implements a normalization function [16]. A corollary of Filinski's work is that type-directed partial evaluation is type preserving, a result we have also established using the typed embedded language described in this work [6,7].…”

Section: Related Workmentioning

confidence: 91%

“…They have been used to design embedded languages [17,25,27] and to prove properties of programs [6,7]. An experiment with run-time code generation for the rewrite engine of the logical framework MetaPRL [20] also confirms the utility of phantom types in a two-stage language [38,39].…”

Section: Discussionmentioning

confidence: 99%

“…For example, phantom types are instrumental for embedding COM objects and for embedding SQL queries into Haskell [17,25,27]. They also provide a key for using Haskell's type inferencer as a theorem prover to show that normalization functions as embodied in type-directed partial evaluation preserve types and yield normal forms [6,7]. These applications of phantom types show that embedded type systems provide a powerful tool for both designing embedded programming languages and reasoning about program correctness.…”

Section: Introductionmentioning

confidence: 99%

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A Foundation for Embedded Languages

Rhiger¹

2002

BRICS

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Recent work on embedding object languages into Haskell use "phantom types" (i.e., parameterized types whose parameter does not occur on the right-hand side of the type definition) to ensure that the embedded object-language terms are simply typed. But is it a safe assumption that only simply-typed terms can be represented in Haskell using phantom types? And conversely, can all simply-typed terms be represented in Haskell under the restrictions imposed by phantom types? In this article we investigate the conditions under which these assumptions are true: We show that these questions can be answered affirmatively for an idealized Haskell-like language and discuss to which extent Haskell can be used as a meta-language.

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Section: Related Workmentioning

confidence: 91%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Foundation for Embedded Languages

Rhiger¹

2002

BRICS

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“…Typedirected partial evaluation, which we present next, has been investigated both practically [5,15,17,18,29,31,38] and foundationally [24,25,47].…”

Section: Background: Reduction-based Vs Reduction-free Normalizationmentioning

confidence: 99%

Memoization in Type-Directed Partial Evaluation

Balat¹,

Danvy²

2002

BRICS

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We use a code generator-type-directed partial evaluation-to verify conversions between isomorphic types, or more precisely to verify that a composite function is the identity function at some complicated type. A typed functional language such as ML provides a natural support to express the functions and type-directed partial evaluation provides a convenient setting to obtain the normal form of their composition. However, off-the-shelf type-directed partial evaluation turns out to yield gigantic normal forms.We identify that this gigantism is due to redundancies, and that these redundancies originate in the handling of sums, which uses delimited continuations. We successfully eliminate these redundancies by extending type-directed partial evaluation with memoization capabilities. The result only works for pure functional programs, but it provides an unexpected use of code generation and it yields orders-of-magnitude improvements both in time and in space for type isomorphisms. *

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“…An approach to constructing a higher-order typeful program representation is presented by Danvy et al [10] that makes use of the notion of phantom types available in Haskell. With this approach, it is shown that an implementation of the normalization function for the simply typed λ-calculus preserves types and always yields βη-long normal form.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Implementing typeful program transformations

Chen

2003

Proceedings of the 2003 ACM SIGPLAN Workshop on Partial Evaluation and Semantics-Based Program Manipulation

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Abstract. The notion of program transformation is ubiquitous in programming language studies on interpreters, compilers, partial evaluators, etc. In order to implement a program transformation, we need to choose a representation in the meta language, that is, the programming language in which we construct programs, for representing object programs, that is, the programs in the object language on which the program transformation is to be performed. In practice, most representations chosen for typed object programs are typeless in the sense that the type of an object program cannot be reflected in the type of its representation. This is unsatisfactory as such typeless representations make it impossible to capture in the type system of the meta language various invariants in a program transformation that are related to the types of object programs. In this paper, we propose an approach to implementing program transformations that makes use of a first-order typeful program representation, where the type of an object program as well as the types of the free variables in the object program can be reflected in the type of the representation of the object program. We introduce some programming techniques needed to handle this typeful program representation, and then present an implementation of a CPS transform function where the relation between the type of an object program and that of its CPS transform is captured in the type system of DML. In a broader context, we claim to have taken a solid step along the line of research on constructing certifying compilers.

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Normalization by Evaluation with Typed Abstract Syntax

Cited by 5 publications

References 13 publications

A Foundation for Embedded Languages

A Foundation for Embedded Languages

Memoization in Type-Directed Partial Evaluation

Implementing typeful program transformations

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