Sparcl: a language for partially-invertible computation

Matsuda, Kazutaka; Wang, Meng

doi:10.1145/3409000

Cited by 11 publications

(3 citation statements)

References 66 publications

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“…Another useful string processing algorithm is the encoding and decoding, which is usually used in compressing a string. It is very appropriate to write them as a single bidirectional program in order to make it easier to maintain and optimize the encoding and decoding algorithms at the same time (Matsuda & Wang, 2020). Let us consider the following simple string encoding algorithm which illustrates the idea of Run Length Encoding:…”

Section: String Encoding and Decodingmentioning

confidence: 99%

Contract lenses: Reasoning about bidirectional programs via calculation

ZHANG,

TANG,

XIE

et al. 2023

J. Funct. Prog.

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Bidirectional transformations (BXs) are a mechanism for maintaining consistency between multiple representations of related data. The lens framework, which usually constructs BXs from lens combinators, has become the mainstream approach to BX programming because of its modularity and correctness by construction. However, the involved bidirectional behaviors of lenses make the equational reasoning and optimization of them much harder than unidirectional programs. We propose a novel approach to deriving efficient lenses from clear specifications via program calculation, a correct-by-construction approach to reasoning about functional programs by algebraic laws. To support bidirectional program calculation, we propose contract lenses, which extend conventional lenses with a pair of predicates to enable safe and modular composition of partial lenses. We define several contract-lens combinators capturing common computation patterns including $\textit{fold}, \textit{filter},\textit{map}$ , and $\textit{scan}$ , and develop several bidirectional calculation laws to reason about and optimize contract lenses. We demonstrate the effectiveness of our new calculation framework based on contract lenses with nontrivial examples.

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Section: String Encoding and Decodingmentioning

confidence: 99%

Contract lenses: Reasoning about bidirectional programs via calculation

ZHANG,

TANG,

XIE

et al. 2023

J. Funct. Prog.

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“…The major changes include a description of our Agda implementation in Section 4 and the arithmetic coding and LZ77 examples in Sections 5.3 and 5.4. Moreover, the related work section (Section 6) is updated to include work published after the preliminary version (Matsuda & Wang, 2020).…”

Section: Introductionmentioning

confidence: 99%

“…A preliminary version of this paper appeared in ICFP20 (Matsuda & Wang, 2020) with the same title. The major changes include a description of our Agda implementation in Section 4 and the arithmetic coding and LZ77 examples in Sections 5.3 and 5.4.…”

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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Sparcl: a language for partially-invertible computation

Cited by 11 publications

References 66 publications

Contract lenses: Reasoning about bidirectional programs via calculation

Contract lenses: Reasoning about bidirectional programs via calculation

Sparcl: A language for partially invertible computation

Reconciling Partial and Local Invertibility

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