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I have heard the simply typed lambda calculus is the internal language of closed Cartesian categories.

I have a written a compiler from the STLC to CCCs but this involves a lot of ugly tuple shuffling.

Is it possible to get the STLC for free from the definition of a closed Cartesian category?

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  • $\begingroup$ Have you seen Compiling to Categories? $\endgroup$ – jmite Sep 3 '20 at 2:31
  • $\begingroup$ @jmite yeah. I have even written such compilers myself as I mentioned in the question. But one can compile to assembly code as well. I feel like lambda calculus is supposed to have a deeper relationship to cccs than to assembly code. $\endgroup$ – Molossus Spondee Sep 5 '20 at 23:59

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