Semi-inversion of Conditional Constructor Term Rewriting Systems

Kirkeby, Maja Hanne; Glück, Robert

doi:10.1007/978-3-030-45260-5_15

Cited by 4 publications

(6 citation statements)

References 18 publications

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“…The goal of this work was to provide a design space for the experimental evaluation and comparison of different well-behaved rule inverters, including those using heuristic approaches [7]. It will be interesting to investigate Romanenko's inversion method [15] as well as related global approaches [2,4,5] and program analyses such as mode and binding-time analyses.…”

Section: Discussionmentioning

confidence: 99%

“…This means that with our tool, we produced all four possible partial inversions (including the special case of full inversion) of the Ackermann function in the course of the three experiments. Using our tool, we also reproduced all of the examples in [6,7].…”

Section: Second Experimentsmentioning

confidence: 99%

“…In this paper, we report on a tool implementation of an inversion framework [6] and on some computer experiments within the framework. The implementation includes four well-behaved rule inverters ranging from trivial to full, partial and semi-inverters, several of which have been studied in the literature [7,12,13]. The generic inversion algorithm used by the tool was proven to produce the correct result for all well-behaved rule inverters [6].…”

Section: Introductionmentioning

confidence: 99%

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An Inversion Tool for Conditional Term Rewriting Systems - A Case Study of Ackermann Inversion

Mikkelsen

Glück

Kirkeby

2021

Electron. Proc. Theor. Comput. Sci.

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We report on an inversion tool for a class of oriented conditional constructor term rewriting systems. Four well-behaved rule inverters ranging from trivial to full, partial and semi-inverters are included. Conditional term rewriting systems are theoretically well founded and can model functional and nonfunctional rewrite relations. We illustrate the inversion by experiments with full and partial inversions of the Ackermann function. The case study demonstrates, among others, that polyvariant inversion and input-output set propagation can reduce the search space of the generated inverse systems.

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Section: Discussionmentioning

confidence: 99%

Section: Second Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An Inversion Tool for Conditional Term Rewriting Systems - A Case Study of Ackermann Inversion

Mikkelsen

Glück

Kirkeby

2021

Electron. Proc. Theor. Comput. Sci.

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“…Specifically, such function arguments must be names of top-level functions; neither closures nor partial applications is supported. The Inversion Framework (Kirkeby & Glück, 2020) unifies the partial and semi inversion methods based on the authors' reformulation (Kirkeby & Glück, 2019) of semi inversion for conditional constructor term rewriting systems (Terese, 2003). The PINS system allows users to specify control structures as they sometimes differ from the original program (Srivastava et al, 2011).…”

Section: Program Inversion and Invertible/reversible Computationmentioning

confidence: 99%

“…Like most program transformations, program inversion may fail, and often for reasons that are not obvious to users. Indeed, the method by Nishida et al (2005) fails for subs, and for some other methods (Almendros-Jiménez & Vidal, 2006;Kirkeby & Glück, 2019, 2020, success depends on the (heuristic) processing order of the expressions.…”

Section: Introductionmentioning

confidence: 99%

Sparcl: A language for partially invertible computation

MATSUDA,

WANG

2024

J. Funct. Prog.

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Invertibility is a fundamental concept in computer science, with various manifestations in software development (serializer/deserializer, parser/printer, redo/undo, compressor/decompressor, and so on). Full invertibility necessarily requires bijectivity, but the direct approach of composing bijective functions to develop invertible programs is too restrictive to be useful. In this paper, we take a different approach by focusing on partially invertible functions—functions that become invertible if some of their arguments are fixed. The simplest example of such is addition, which becomes invertible when fixing one of the operands. More involved examples include entropy-based compression methods (e.g., Huffman coding), which carry the occurrence frequency of input symbols (in certain formats such as Huffman tree), and fixing this frequency information makes the compression methods invertible. We develop a language Sparcl for programming such functions in a natural way, where partial invertibility is the norm and bijectivity is a special case, hence gaining significant expressiveness without compromising correctness. The challenge in designing such a language is to allow ordinary programming (the “partially” part) to interact with the invertible part freely, and yet guarantee invertibility by construction. The language Sparcl is linear-typed and has a type constructor to distinguish data that are subject to invertible computation and those that are not. We present the syntax, type system, and semantics of the language and prove that Sparcl correctly guarantees invertibility for its programs. We demonstrate the expressiveness of Sparcl with examples including tree rebuilding from preorder and inorder traversals, Huffman coding, arithmetic coding, and LZ77 compression.

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Reconciling Partial and Local Invertibility

Ågren Thuné,

Matsuda,

Wang

2024

Lecture Notes in Computer Science

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Invertible programming languages specify transformations to be run in two directions, such as compression/decompression or encryption/decryption. Two key concepts in invertible programming languages are partial invertibility and local invertibility. Partial invertibility lets invertible code be parameterized by the results of non-invertible code, whereas local invertibility requires all code to be invertible. The former allows for more flexible programming, while the latter has connections to domains such as low-energy computing and quantum computing. We find that existing approaches lack a satisfying treatment of partial invertibility, leaving the connection to local invertibility unclear.In this paper, we identify four core constructs for partially invertible programming, and show how to give them a locally invertible interpretation. We show the expressiveness of the constructs by designing the functional invertible language Kalpis, and show how to give them a locally invertible semantics using the novel arrow combinator language $$\textsc {rrArr}$$ R R A R R —the key idea is viewing partial invertibility as an invertible effect. By formalizing the two systems and giving Kalpis semantics by translation to $$\textsc {rrArr}$$ R R A R R , we reconcile partial and local invertibility, solving an open problem in the field. All formal developments are mechanized in Agda.

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Semi-inversion of Conditional Constructor Term Rewriting Systems

Cited by 4 publications

References 18 publications

An Inversion Tool for Conditional Term Rewriting Systems - A Case Study of Ackermann Inversion

An Inversion Tool for Conditional Term Rewriting Systems - A Case Study of Ackermann Inversion

Sparcl: A language for partially invertible computation

Reconciling Partial and Local Invertibility

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