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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 11th 2014
    • (edited May 11th 2014)

    Roux Cody kindly alerted me of the fact that analog of synthetic mathematics under “computational trinitarianism” in programming theory is that of domain specific embedded programming languages. To record this neat insight I have now created a minimum entry on the latter and cross-linked a bit.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeMay 12th 2014
    • (edited May 12th 2014)

    A domain specific programming language is one designed for a specialized kind (“domain”) of applications. A domain specific embedded programming language (DSEL) is a domain specific language realized “inside” a general-purpose high level (typed) programming language.

    To me this looks ambivalent as toward weather the domain specific thing will implement something synthetic or something analytic. Somebody can have a philosophy that a moment when creating a specific domain specific extension/module, is an opportunity to have synthetic point of view in mind as a method, but it is also the opportunity to build analytically. It looks to me that there is nothing inherently synthetic about embedding domain specific extensions. It is just a moment of choice. Having already some basic language behind makes ambitious projects of extension more feasible than building something from the scratch – indeed if one does not have one, you have to do various side basic things so it looks like you are not yet ready for cleanly seeing the axiom-like structures. But if one abstracts the auxiliary pieces than there is no essential difference. So, it is more like practically a good ground for synthetic approach then something what is abstractly, inherently and essentially such.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 12th 2014
    • (edited May 12th 2014)

    That’s probably true when strictly speaking. On the other hand, the same kind of ambiguity applies to “synthetic” itself. But the way Hudak 89 explains DSELs work in Haskell is exactly what mathematically you’d want to call synthetic. So even if you maybe can argue that people could abuse the terminology, it seems they do not.

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