Initial Algebra Semantics for Cyclic Sharing Tree Structures

Terms are a concise representation of tree structures. Since they can be naturally defined by an inductive type, they offer data structures in functional programming and mechanised reasoning with useful principles such as structural induction and structural recursion. However, for graphs or "tree-like" structures - trees involving cycles and sharing - it remains unclear what kind of inductive structures exists and how we can faithfully assign a term representation of them. In this paper we propose a simple term syntax for cyclic sharing structures that admits structural induction and recursion principles. We show that the obtained syntax is directly usable in the functional language Haskell and the proof assistant Agda, as well as ordinary data structures such as lists and trees. To achieve this goal, we use a categorical approach to initial algebra semantics in a presheaf category. That approach follows the line of Fiore, Plotkin and Turi's models of abstract syntax with variable binding

Lensing magnification effects on the cosmic shear statistics

Gravitational lensing causes a correlation between a population of foreground large-scale structures and the observed number density of the background distant galaxies as a consequence of the flux magnification and the lensing area distortion. This correlation has not been taken into account in calculations of the theoretical predictions of the cosmic shear statistics but may cause a systematic error in a cosmic shear measurement. We examine its impact on the cosmic shear statistics using the semi-analytic approach. We find that the lensing magnification has no practical influence on the cosmic shear variance. Exploring possible shapes of redshift distribution of source galaxies, we find that the relative amplitude of the effect on the convergence skewness is 3% at mostComment: 7 pages, 1 figure, accepted for publication in MNRA

Iteration Algebras for UnQL Graphs and Completeness for Bisimulation

This paper shows an application of Bloom and Esik's iteration algebras to model graph data in a graph database query language. 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. However, no mathematical semantics of UnQL/UnCAL graphs has been developed. In this paper, we give an equational axiomatisation and algebraic semantics of UnCAL graphs. The main result of this paper is to prove that completeness of our equational axioms for UnCAL for the original bisimulation of UnCAL graphs via iteration algebras. Another benefit of algebraic semantics is a clean characterisation of structural recursion on graphs using free iteration algebra.Comment: In Proceedings FICS 2015, arXiv:1509.0282

Performing Shakespeare in Contemporary Japan: The Yamanote Jijosha’s The Tempest

In considering the Yamanote Jijosha’s The Tempest, this paper explores the significance of performing Shakespeare in contemporary Japan. The company’s The Tempest reveals to contemporary Japanese audiences the ambiguity of Shakespeare’s text by experimenting with the postdramatic and a new acting style. While critically pursuing the meaning and possibility of theatre and performing arts today, this version of The Tempest powerfully presents a critical view of the blindness and dumbness of contemporary Japan, as well as the world represented in the play

Cyclic Datatypes modulo Bisimulation based on Second-Order Algebraic Theories

Cyclic data structures, such as cyclic lists, in functional programming are tricky to handle because of their cyclicity. This paper presents an investigation of categorical, algebraic, and computational foundations of cyclic datatypes. Our framework of cyclic datatypes is based on second-order algebraic theories of Fiore et al., which give a uniform setting for syntax, types, and computation rules for describing and reasoning about cyclic datatypes. We extract the "fold" computation rules from the categorical semantics based on iteration categories of Bloom and Esik. Thereby, the rules are correct by construction. We prove strong normalisation using the General Schema criterion for second-order computation rules. Rather than the fixed point law, we particularly choose Bekic law for computation, which is a key to obtaining strong normalisation. We also prove the property of "Church-Rosser modulo bisimulation" for the computation rules. Combining these results, we have a remarkable decidability result of the equational theory of cyclic data and fold.Comment: 38 page