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  • $\begingroup$ "What matters semantically is what is done, not how (and how fast) it is done" -- it bears mention that non-functional criteria exist in practice. There are many functionally equivalent target programs but we may prefer some over others for some reason (efficiency, size, better memory alignment, ...). That is to say, the view of a compiler as a function as you define is more limited than we want it to be (it also often skips over side effects, e.g. I/O). It serves the explanatory purpose you want to to, though. $\endgroup$ Commented Aug 23, 2015 at 13:19
  • $\begingroup$ @Raphael Regarding full employment theorem, I had that in mind (in my comment on C), but I did not know the name, and postponed finding a reference. Thanks for doing it. --- The semantics I talk about is that of the compiler, not that of the target program. The target program is preserved syntactically and operationally, not just semantically. Or did I misunderstand your remark. I edited to make things more precise in my text. $\endgroup$ Commented Aug 23, 2015 at 13:49
  • $\begingroup$ @Raphael Since you did not delete your comment, does it mean that I misunderstood it, or did not answer it properly? How is it that the view of the compiler (not of the compiled program) as a function is too limited, from a semantic point of view. Of course, as a function, it could take other arguments than just the compiled program, such as optimization directives) but this is a detail that would not change the discussion. $\endgroup$ Commented Aug 23, 2015 at 14:56
  • $\begingroup$ I think my comment stands as a pointer towards "there's more than this model". What you write is not wrong, but it's not everything. Theoretically, this seems obvious: "the" compiler function is not per se well-defined since there are infinitely many possible target programs, all semantically equivalent. Which to pick is a very important part of designing compilers. $\endgroup$ Commented Aug 23, 2015 at 14:59
  • $\begingroup$ @Raphael There is only this model. You are misreading my text: I am saying "a computable function", because others are possible. The compiler is implementing one specific compiling function "curly $\mathcal C$", which is a function from S syntax to T syntax, defining a precise set of syntactic pairs of programs (italic letters). These pairs are supposed to compute the same function "curly $\mathcal P$", but the second component cannot be replaced by another one with the same property. I am intentionally ignoring the semantics of programs to keep things comparable in the translation processes. $\endgroup$ Commented Aug 23, 2015 at 15:51