A Program Inverter for a Functional Language with Equality and Constructors

Glück, Robert; Kawabe, Masahiko

doi:10.1007/978-3-540-40018-9_17

Cited by 33 publications

(22 citation statements)

References 19 publications

(23 reference statements)

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“…The above shows that it is an example of local (peephole) program inversion [13]. Note that the transformation only works as a program inverter under the function semantics, and not under language recognition.…”

Section: Then T −1 Is An Rtm That Computes the Inverse Function Of [[mentioning

confidence: 94%

On reversible Turing machines and their function universality

Axelsen

Glück

2016

Acta Informatica

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We provide a treatment of the reversible Turing machines (RTMs) under a strict function semantics. Unlike many existing reversible computation models, we distinguish strictly between computing the function λx. f (x) and computing the function λx. (x, f (x)), or other injective embeddings of f . We reinterpret and adapt a number of important foundational reversible computing results under this semantics. Unifying the results in a single model shows that, as expected (and previously claimed), the RTMs are robust and can compute exactly all injective computable functions. Because injectivity entails that the RTMs are not strictly Turing-complete w.r.t. functions, we use an appropriate alternative universality definition, and show how to derive universal RTMs (URTMs) from existing irreversible universal machines. We then proceed to construct a URTM from the ground up. This resulting machine is the first URTM which does not depend on a reversible simulation of an existing universal machine. The new construction has the advantage that the interpretive overhead of the URTM is limited to a (program dependent) constant factor. Another novelty is that the URTM can function as an inverse interpreter at no asymptotic cost. Mathematics Subject Classification 68Q05 · 68Q10 · 03D10Revised and extended version of the conference papers [4,5].

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Section: Then T −1 Is An Rtm That Computes the Inverse Function Of [[mentioning

confidence: 94%

On reversible Turing machines and their function universality

Axelsen

Glück

2016

Acta Informatica

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“…Provided that X and Y are false, the execution of C is repeated. The † A version of the duplication/equality operator [12].…”

Section: Semanticsmentioning

confidence: 99%

A Minimalist's Reversible While Language

Glück

Yokoyama

2017

IEICE Trans. Inf. & Syst.

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SUMMARY The paper presents a small reversible language R-CORE, a structured imperative programming language with symbolic tree-structured data (S-expressions). The language is reduced to the core of a reversible language, with a single command for reversibly updating the store, a single reversible control-flow operator, a limited number of variables, and data with a single atom and a single constructor. Despite its extreme simplicity, the language is reversibly universal, which means that it is as powerful as any reversible language can be, while it is linear-time self-interpretable, and it allows reversible programming with dynamic data structures. The four-line program inverter for R-CORE is among the shortest existing program inverters, which demonstrates the conciseness of the language. The translator to R-CORE, which is used to show the formal properties of the language, is clean and modular, and it may serve as a model for related reversible translation problems. The goal is to provide a language that is sufficiently concise for theoretical investigations. Owing to its simplicity, the language may also be used for educational purposes. key words: reversible programming language, reversible self-interpreter, while language, translation, program inversion

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“…In this work, we focus on the so called deterministic conditional rewrite systems (DCTRSs), which are typical functional programs with local declarations [23]. When the rewrite systems are automatically generated (e.g., by program inversion [2,14,15,17,22,27,26,28] or partial evaluation [1,7,8,35]), they often have a poor syntactic structure that might hide some properties. For instance, the rewriting systems generated by program inversion sometimes have overlapping left-hand sides despite the fact that they actually have the unique normal form property w.r.t.…”

Section: Introductionmentioning

confidence: 99%

Computing More Specific Versions of Conditional Rewriting Systems

Nishida

Vidal

2013

Logic-Based Program Synthesis and Transformation

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Abstract. Rewrite systems obtained by some automated transformation often have a poor syntactic structure even if they have good properties from a semantic point of view. For instance, a rewrite system might have overlapping left-hand sides even if it can only produce at most one constructor normal form (i.e., value). In this paper, we propose a method for computing "more specific" versions of deterministic conditional rewrite systems (i.e., typical functional programs) by replacing a given rule (e.g., an overlapping rule) with a finite set of instances of this rule. In some cases, the technique is able to produce a non-overlapping system from an overlapping one. We have applied the transformation to improve the systems produced by a previous technique for function inversion with encouraging results (all the overlapping systems were successfully transformed to non-overlapping systems).

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A Program Inverter for a Functional Language with Equality and Constructors

Cited by 33 publications

References 19 publications

On reversible Turing machines and their function universality

On reversible Turing machines and their function universality

A Minimalist's Reversible While Language

Computing More Specific Versions of Conditional Rewriting Systems

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