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Sure, will do my best! I'm not familiar with program verification / Isabelle, however if you take a look at the source code for the optim family of functions, you'll see that the last line of the function calls `.External2()`, which is similar to `.Call()|`. Both these functions allow R to call compiled C code, which means some of the work being done in these functions happens in this C code.
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There are two ways you can generally see the source code for packages. The simplest is to look for the github repository for the package (assuming it exists). For dplyr, it's here. Easiest way to find these is to google search "r github" plus the name of the package. Usually it'll be one of the first results. The github repo would also usually be linked on the package's CRAN page. However, be aware that this may be a development version of the package and not the same version that is currently released on CRAN (e.g. dplyr on CRAN is version 1.0.10, but on github it is listed as version 1.0.99.9000, which will probably become version 1.1.0 when it is released onto CRAN).
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