arXiv subjects

Kazutaka Matsuda

Publications and source records attributed to Kazutaka Matsuda.

4 recordsLinked to original sources

arXiv2026

Lenses for Partially-Specified States (Extended Version)

A bidirectional transformation is a pair of transformations satisfying certain well-behavedness properties: one maps source data into view data, and the other translates changes on the view back to the source. However, when multiple views share a source, an update on one view may affect the others, making it hard to maintain correspondence while preserving the user's update, especially when multiple views are changed at once. Ensuring these properties within a compositional framework is even more challenging. In this paper, we propose partial-state lenses, which allow source and view states to be partially specified to precisely represent the user's update intentions. These intentions are partially ordered, providing clear semantics for merging intentions of updates coming from multiple views and a refined notion of update preservation compatible with this merging. We formalize partial-state lenses, together with partial-specifiedness-aware well-behavedness that supports compositional reasoning and ensures update preservation. In addition, we demonstrate the utility of the proposed system through examples.

cs.PL↗

arXiv2021

Synbit: Synthesizing Bidirectional Programs using Unidirectional Sketches

We propose a technique for synthesizing bidirectional programs from the corresponding unidirectional code plus a few input/output examples. The core ideas are: (1) constructing a sketch using the given unidirectional program as a specification, and (2) filling the sketch in a modular fashion by exploiting the properties of bidirectional programs. These ideas are enabled by our choice of programming language, HOBiT, which is specifically designed to maintain the unidirectional program structure in bidirectional programming, and keep the parts that control bidirectional behavior modular. To evaluate our approach, we implemented it in a tool called Synbit and used it to generate bidirectional programs for intricate microbenchmarks, as well as for a few larger, more realistic problems. We also compared Synbit to a state-of-the-art unidirectional synthesis tool on the task of synthesizing backward computations.

cs.PL↗

arXiv2020

Modular Inference of Linear Types for Multiplicity-Annotated Arrows

Bernardy et al. [2018] proposed a linear type system $λ^q_\to$ as a core type system of Linear Haskell. In the system, linearity is represented by annotated arrow types $A \to_m B$, where $m$ denotes the multiplicity of the argument. Thanks to this representation, existing non-linear code typechecks as it is, and newly written linear code can be used with existing non-linear code in many cases. However, little is known about the type inference of $λ^q_\to$. Although the Linear Haskell implementation is equipped with type inference, its algorithm has not been formalized, and the implementation often fails to infer principal types, especially for higher-order functions. In this paper, based on OutsideIn(X) [Vytiniotis et al., 2011], we propose an inference system for a rank 1 qualified-typed variant of $λ^q_\to$, which infers principal types. A technical challenge in this new setting is to deal with ambiguous types inferred by naive qualified typing. We address this ambiguity issue through quantifier elimination and demonstrate the effectiveness of the approach with examples.

cs.PL↗

arXiv2016

The Algebra of Recursive Graph Transformation Language UnCAL: Complete Axiomatisation and Iteration Categorical Semantics

The aim of this paper is to provide mathematical foundations of a graph transformation language, called UnCAL, using categorical semantics of type theory and fixed points. About twenty years ago, Buneman et al. developed a graph database query language UnQL on the top of a functional meta-language UnCAL for describing and manipulating graphs. Recently, the functional programming community has shown renewed interest in UnCAL, because it provides an efficient graph transformation language which is useful for various applications, such as bidirectional computation. In order to make UnCAL more flexible and fruitful for further extensions and applications, in this paper, we give a more conceptual understanding of UnCAL using categorical semantics. Our general interest of this paper is to clarify what is the algebra of UnCAL. Thus, we give an equational axiomatisation and categorical semantics of UnCAL, both of which are new. We show that the axiomatisation is complete for the original bisimulation semantics of UnCAL. Moreover, we provide a clean characterisation of the computation mechanism of UnCAL called "structural recursion on graphs" using our categorical semantics. We show a concrete model of UnCAL given by the lambdaG-calculus, which shows an interesting connection to lazy functional programming.

cs.LO↗