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The M-Expression in the post is rather limited in what it can do; if anyone is looking for a system for use in practical mathematical modelling, during my PhD research I created a system for expressing ODE / DAE models in Haskell, and a solver which uses symbolic/numeric techniques (including symbolic differentiation) to solve them.

My RealExpression definition (I also define BoolExpression) is here https://github.com/A1kmm/modml-core/blob/master/ModML/Core/B...

Code to symbolically differentiate a RealExpression is here https://github.com/A1kmm/modml-solver/blob/master/ModML/Solv...

Documented here: Chapters 9 & 10 of https://researchspace.auckland.ac.nz/bitstream/handle/2292/8... [3.3 MB PDF]

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