How to prove your calculus is decidable: practical applications of second-order algebraic theories and computation

M Hamana - Proceedings of the ACM on Programming Languages, 2017 - dl.acm.org
We present a general methodology of proving the decidability of equational theory of
programming language concepts in the framework of second-order algebraic theories. We …

Multiversal polymorphic algebraic theories: syntax, semantics, translations, and equational logic

M Fiore, M Hamana - 2013 28th Annual ACM/IEEE Symposium …, 2013 - ieeexplore.ieee.org
We formalise and study the notion of polymorphic algebraic theory, as understood in the
mathematical vernacular as a theory presented by equations between polymorphically …

How to prove decidability of equational theories with second-order computation analyser SOL

M Hamana - Journal of Functional Programming, 2019 - cambridge.org
We present a general methodology of proving the decidability of equational theory of
programming language concepts in the framework of second-order algebraic theories. We …

Initial algebra semantics for cyclic sharing tree structures

M Hamana - Logical Methods in Computer Science, 2010 - lmcs.episciences.org
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 …

Higher-order semantic labelling for inductive datatype systems

M Hamana - Proceedings of the 9th ACM SIGPLAN International …, 2007 - dl.acm.org
We give a novel transformation for proving termination of higher-order rewrite systems in the
format of Inductive Data Type Systems (IDTSs) by Blanqui, Jouannaud and Okada. The …

[HTML][HTML] Polymorphic computation systems: Theory and practice of confluence with call-by-value

M Hamana, T Abe, K Kikuchi - Science of Computer Programming, 2020 - Elsevier
We present a new framework of polymorphic computation rules that can accommodate a
distinction between values and non-values. It is suitable for analysing fundamental calculi of …

Higher-order (non-) modularity

C Appel, V van Oostrom… - Proceedings of the 21st …, 2010 - drops.dagstuhl.de
We show that, contrary to the situation in first-order term rewriting, almost none of the usual
properties of rewriting are modular for higher-order rewriting, irrespective of the higher-order …

Polymorphic rewrite rules: Confluence, type inference, and instance validation

M Hamana - International Symposium on Functional and Logic …, 2018 - Springer
We present a new framework of polymorphic rewrite rules having predicates to restrict their
instances. It is suitable for formulating and analysing fundamental calculi of programming …

Polymorphic abstract syntax via Grothendieck construction

M Hamana - Foundations of Software Science and Computational …, 2011 - Springer
Abstract syntax with variable binding is known to be characterised as an initial algebra in a
presheaf category. This paper extends it to the case of polymorphic typed abstract syntax …

Complete algebraic semantics for second-order rewriting systems based on abstract syntax with variable binding

M Hamana - Mathematical Structures in Computer Science, 2022 - cambridge.org
By using algebraic structures in a presheaf category over finite sets, following Fiore, Plotkin
and Turi, we develop sound and complete models of second-order rewriting systems called …