# Help with recursive type for automatic differentiation (Taylor Numbers) as in a Haskell example

**URL:** <https://discourse.julialang.org/t/help-with-recursive-type-for-automatic-differentiation-taylor-numbers-as-in-a-haskell-example/30804>\
**Category:** General Usage\
**Tags:** question\
**Created:** [November 6, 2019, 7:43pm UTC](https://discourse.julialang.org/t/help-with-recursive-type-for-automatic-differentiation-taylor-numbers-as-in-a-haskell-example/30804 "2019-11-06T19:43:29Z")\
**Posts on this page:** 1\
**Showing post:** 11

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**Author:** ![chakravala](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chakravala/32/6832_2.png) [@chakravala](https://discourse.julialang.org/u/chakravala)\
**Post date:** [November 6, 2019, 9:58pm UTC](https://discourse.julialang.org/t/help-with-recursive-type-for-automatic-differentiation-taylor-numbers-as-in-a-haskell-example/30804/11 "2019-11-06T21:58:11Z")

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As described in some of my other posts, I have also implemented higher order recursive dual numbers:

> [@\[ANN\] Grassmann.jl : Differential geometric algebra](https://discourse.julialang.org/t/ann-grassmann-jl-differential-geometric-algebra/21125/17):
>
> With v0.3.1 of [Grassmann.jl](https://github.com/chakravala/Grassmann.jl) it is now fairly stable to work with higher-order generalizations of derivations. Using the tangent(V,D,#) space it is possible to explore the higher order Leibniz derivations. Based on the definitions of differential geometric algebra, a higher order derivation is ∂i^(D+1)==0: julia\> using Reduce, Grassmann; @mixedbasis tangent(ℝ^2,3,2); julia\> x = :x\*v1 + ∂1v1 + ∂1\*∂1v1 + ∂1\*∂1\*∂1v1 0.0 + xv₁ + (1 + (1 + 1∂₁)∂₁)∂₁v₁ julia\> x^2 x ^ 2 + (2x + (2x + 1 + (2 \* (x …

> **[GitHub - chakravala/Grassmann.jl: ⟨Grassmann-Clifford-Hodge⟩ multilinear...](https://github.com/chakravala/Grassmann.jl#differential-forms-and-leibniz-tangent-algebra)**
>
> ⟨Grassmann-Clifford-Hodge⟩ multilinear differential geometric algebra - GitHub - chakravala/Grassmann.jl: ⟨Grassmann-Clifford-Hodge⟩ multilinear differential geometric algebra

It’s not fully optimized for automatic differentiation yet, but has the general functionality for doing dual quaternions and other geometries.

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