Composing Bidirectional Programs Monadically

Xia, Li-yao; Orchard, Dominic; Wang, Meng

doi:10.1007/978-3-030-17184-1_6

Cited by 3 publications

(1 citation statement)

References 37 publications

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“…Another approach is to wrap the return type of get and put in the Maybe monad to remove partiality (Matsuda & Wang, 2015a;Ko et al, 2016;Xia et al, 2019). The put direction is a total function of type s → v → Maybe s, and it returns Nothing at run-time when an invalid input is passed to it.…”

Section: Totality With Maybe Monadmentioning

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: Totality With Maybe Monadmentioning

confidence: 99%

Contract lenses: Reasoning about bidirectional programs via calculation

ZHANG,

TANG,

XIE

et al. 2023

J. Funct. Prog.

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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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Reflecting on Random Generation

Goldstein,

Frohlich,

Wang

et al. 2023

Proc. ACM Program. Lang.

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Expert users of property-based testing often labor to craft random generators that encode detailed knowledge about what it means for a test input to be valid and interesting. Fortunately, the fruits of this labor can also be put to other uses. In the bidirectional programming literature, for example, generators have been repurposed as validity checkers, while Python's Hypothesis library uses the same structures for shrinking and mutating test inputs. To unify and generalize these uses and many others, we propose reflective generators, a new foundation for random data generators that can "reflect" on an input value to calculate the random choices that could have been made to produce it. Reflective generators combine ideas from two existing abstractions: free generators and partial monadic profunctors. They can be used to implement and enhance the aforementioned shrinking and mutation algorithms, generalizing them to work for any values that can be produced by the generator, not just ones for which a trace of the generator's execution is available. Beyond shrinking and mutation, reflective generators generalize a published algorithm for example-based generation, and they can also be used as checkers, partial value completers, and other kinds of test data producers.

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Composing Bidirectional Programs Monadically

Cited by 3 publications

References 37 publications

Contract lenses: Reasoning about bidirectional programs via calculation

Contract lenses: Reasoning about bidirectional programs via calculation

Reconciling Partial and Local Invertibility

Reflecting on Random Generation

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