Blog articles/Mathematics

Haskell and mathematics. See also the Haskell math community.

Haskell for mathematics

General

• Eleven Reasons to use Haskell as a Mathematician
• Haskell for Maths: commutative algebra, combinatorics, number theory, and group theory libraries
• Learn Maths with Haskell
• Prototyping thought
• Why Haskell?

Calculus and Differential Geometry

• Practical Synthetic Differential Geometry
• Non-standard analysis, automatic differentiation, Haskell

Algebraic Topology and Geometry

• Algebraic Topology in Haskell
• More Low Cost Geometric Algebra
• Geometric Algebra for Free!

Geometry

• Haskell, PDF and penrose tilings

Group Theory

• Computational Group Theory in Haskell
• Carry bits and group cohomology

Set Theory

• Powerset oneliner
• Countable Ordinals in Haskell

Ring Theory

• Polynomials

Number Theory

• GCD and Higher Order Functions

Cryptography and Coding Theory

• Feistel Ciphers and DES in Haskell
• Arithmetic coding in Haskell
• Two-dimensional spatial hashing with space-filling curves

Logic

• Laws of Form: An Opinion

Numerics

• The Division Bell
  • Part One
  • Part Two
  • Part Three
  • Part Four (Conclusion)
  • The Divisive Aftermath

• Overloading Haskell numbers
  • Part 1: symbolic expressions
  • Part 2: Forward Automatic Differentiation
  • Part 3: Fixed Precision
  • Dynamic epsilons in Haskell with a bit of type hackery

Theorem Proving

• Quick and Dirty Theorem Prover

Quantum Computing

• The Essence of Quantum Computing
• Monads for vector spaces, probability and quantum mechanics pt. I
• Monads, Vector Spaces and Quantum Mechanics pt. II
• Independence, entanglement and decoherence with the quantum monad
• The Shor Quantum Error Correcting Code (and a Monad for Heat)
• The Frame Of Reference Monad

Mathematics of Haskell

Category Theoretic

• Category Theory and the Category of Haskell programs:
  • Category Theory and the category of Haskell programs
  • Part 2

• Why isn't ListT list a monad?
• Reverse Engineering Machines with the Yoneda Lemma
• Variable substitution gives a...
• Games, Strategies and the Self-Composition of the List Monad.

Lambda and Combinator Calculi

• Programs are Proofs: Models and Types in Lambda Calculus
• Don't need the Y combinator

Other Formal Logics

• From Löb's Theorem to Spreadsheet Evaluation

Miscellaneous

• ML, Haskell and Coq
• Infinitesimal Types
• Djinn, Coq, Monad and a bit of Haskell