NiLang.jl (逆lang), is a reversible domain-specific language (DSL) that allow a program to go back to the past.

• Requires Julia version >= 1.3,

NiLang features:

• any program written in NiLang is differentiable,
• a reversible language with abstraction and arrays,
• complex values
• reversible logarithmic number system

The main docs can be found here:

There are also some Pluto-based notebooks:

• tutorial
• documentation
• Billiard ball model cellular automata

The strangeness of reversible computing is mainly due to our lack of experience with it.—Henry Baker, 1992

pkg> add NiLang

julia> using NiLang

julia> @i function f(res, y, x)
           for i=1:length(x)
               y += x[i] ^ 2
           end
           res += sqrt(y)
       end

julia> res_out, y_out, x_out = f(0.0, 0.0, [1, 2, 3.0])
(3.7416573867739413, 14.0, [1.0, 2.0, 3.0])

julia> (~f)(res_out, y_out, x_out)  # automatically generated inverse program.
(0.0, 0.0, [1.0, 2.0, 3.0])
        
julia> ∂res, ∂y, ∂x = NiLang.AD.gradient(Val(1), f, (0.0, 0.0, [1, 2, 3.0])) 
    # automatic differentiation, `Val(1)` means the first argument of `f` is the loss.
(1.0, 0.1336306209562122, [0.2672612419124244, 0.5345224838248488, 0.8017837257372732])

The performance of reversible programming automatic differentiation is much better than most traditional frameworks. Here is why, and how it works,

@misc{Liu2020,
    title={Differentiate Everything with a Reversible Programming Language},
    author={Jin-Guo Liu and Taine Zhao},
    year={2020},
    eprint={2003.04617},
    archivePrefix={arXiv},
    primaryClass={cs.PL}
}