Library for scientific computing such as solving differential equations, optimization or machine learning written in Lean. This library is in an early stage of development and at its current stage is just a proof of concept on how Lean can be used for scientific computing.
Lean is an expressive functional programming language that allows to formalize the mathematics behind these computations. This can offer several benefits:
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Code transformation and optimization guided by formalization of underlining mathematics, like automatic differentiation, algebraic simplification, fine control of used approximations or execution scheduling.
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First class symbolic computation. Any function can be purely symbolic, functions like
gradient,integralorlimitare inherently non-computable. However, they carry meaning what the program should be doing and we provide tools to manipulate them or approximate them with actually computable function. -
Code generation based on formal specification. Many problems any scientific computing or machine learning can be stated very easily e.g. find a minimizer of a function. We then provide tools how to turn such specification into a runnable code satisfying the specification, usually in an appropriate limit of used approximations.
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Catalogization of numerical methods.
In short, mathematics is the ultimate abstraction for numerical computing and Lean can understand mathematics. Hopefully, using Lean will allow us to create really powerful and extensible library for scientific computing.
Manual:
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Working in progress book on scientific computing in Lean.
Presentations:
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Automatic Differentiation in Lean - Lean Together 2024(30min)
Overview and motivation behind automatic differentiation in Lean, examples of forward and reverse mode AD.
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Scientific Computing in Lean - Lean for Scientists and Engineers 2024(2h)
Overview and motivation behind SciLean, working with n-dimensional arrays and symbolic/automatic differentiation.
As we are using Lean programming language, you need Lean's version manager =elan=. Follow its installation instructions.
Getting and building SciLean simply:
git clone https://github.com/lecopivo/SciLean.git
cd SciLean
lake exe cache get
lake build
To run examples:
lake build HarmonicOscillator && .lake/build/bin/HarmonicOscillator
lake build WaveEquation && .lake/build/bin/WaveEquation
Other examples in =examples= directory do not currently work.
To get an idea how SciLean works have a look at explanation of the harmonic oscillator example.