They write: The LFortran compiler has made great strides over the last few years. In 2020, it was missing a lot of features and only supported a very small subset of Fortran. Now it now supports a much wider range of language features and can be used to compile a reasonable amount of Fortran code. It can even compile to WebAssembly out of the box!
However, there are still some barriers that make using LFortran a little rough. The project is currently considered to be in alpha phase and the developers state that issues compiling real-world code are expected. While it can successfully compile some projects, such as MINPACK, the full Fortran specification is not yet supported and so many larger projects still cannot be compiled.
The LFortran developers are targeting full support for Fortran 2018, and its standout feature is an interactive Jupyter-like Fortran REPL. With a few more years of development, I expect that LFortran will be an excellent choice for compiling Fortran code for WebAssembly.
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Check out the LFortran demo at https://dev.lfortran.org. While extremely impressive, note that the first thing I tried was changing x * 2 to x * 3 and saw that such a change is currently not supported by the code generator.