6 papers
Optimizing Optimizations, Declaratively: Optimizing the Higher-Order Functions in Mathematical Optimization with egglog
Hiromi Ishii
We present two applications of egglog to mathematical optimization in JijModeling 2, a mathematical modeller whose internal representation is based on simply typed -calculus. Fi…
Pure Borrow: Linear Haskell Meets Rust-Style Borrowing
Yusuke Matsushita, Hiromi Ishii
A promising approach to unifying functional and imperative programming paradigms is to localize mutation using linear or affine types. Haskell, a purely functional language, was re…
Automatic Differentiation With Higher Infinitesimals, or Computational Smooth Infinitesimal Analysis in Weil Algebra
Hiromi Ishii
We propose an algorithm to compute the -ring structure of arbitrary Weil algebra. It allows us to do some analysis with higher infinitesimals numerically and symbolically…
Functional Pearl: Witness Me -- Constructive Arguments Must Be Guided with Concrete Witness
Hiromi Ishii
Beloved Curry--Howard correspondence tells that types are intuitionistic propositions, and in constructive math, a proof of proposition can be seen as some kind of a construction,…
A Succinct Multivariate Lazy Multivariate Tower AD for Weil Algebra Computation
Hiromi Ishii
We propose a functional implementation of \emph{Multivariate Tower Automatic Differentiation}. Our implementation is intended to be used in implementing -structure comput…
A Purely Functional Computer Algebra System Embedded in Haskell
Hiromi Ishii
We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is…