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Yup yup. I'm on the trail of just this using a purely functional Forth-like language called Joy. Your hunch is correct, you're intuiting the "Categorical" (as

Yup yup. I'm on the trail of just this using a purely functional Forth-like language called Joy. Your hunch is correct, you're intuiting the "Categorical" (as in Category Theory) nature of "point-free" format: http://conal.net/papers/compiling-to-categories/ http://conal.net/papers/compiling-to-categories/ > It is well-known that the simply typed lambda-calculus is modeled by any cartesian closed category (CCC). This correspondence suggests giving typed functional programs a variety of interpretations, each corresponding to a different category. ... This paper describes such an implementation and demonstrates its use for a variety of interpretations including hardware circuits, automatic differentiation, incremental computation, and interval analysis. ... The general technique appears to provide a compelling alternative to deeply embedded domain-specific languages.

ssivark 6y ago
That Conal Elliot paper is being my current level, and I don’t see the relation to the comment about composability in Forth. Is there a simplified explanation somewhere? (Preferable less mathematical and more verbal, but I’ll take what I can get) Thanks.
- carapace 6y ago
  I don't know if it's written up anywhere like that, sorry. The very brief section on mathematical purity of Joy in the Wikipedia article describes it but in (IMO) an unhelpful way: https://en.wikipedia.org/wiki/Joy_(programming_language)#Mathematical_purity https://en.wikipedia.org/wiki/Joy_(programming_language)#Mat... > In Joy, the meaning function is a homomorphism from the syntactic monoid onto the semantic monoid. That is, the syntactic relation of concatenation of symbols maps directly onto the semantic relation of composition of functions. It is a homomorphism rather than an isomorphism, because it is onto but not one-to-one; that is, no symbol has more than one meaning, but some sequences of symbols have the same meaning (e.g. "dup +" and "2 *"). > Joy is a concatenative programming language: "The concatenation of two programs denotes the composition of the functions denoted by the two programs".[2] [2] "Mathematical foundations of Joy" by Manfred von Thun https://web.archive.org/web/20111007025556/http://www.latrobe.edu.au/phimvt/joy/j02maf.html https://web.archive.org/web/20111007025556/http://www.latrob...

ssivark 6y ago

That Conal Elliot paper is being my current level, and I don’t see the relation to the comment about composability in Forth. Is there a simplified explanation somewhere? (Preferable less mathematical and more verbal, but I’ll take what I can get) Thanks.

carapace 6y ago
I don't know if it's written up anywhere like that, sorry. The very brief section on mathematical purity of Joy in the Wikipedia article describes it but in (IMO) an unhelpful way: https://en.wikipedia.org/wiki/Joy_(programming_language)#Mathematical_purity https://en.wikipedia.org/wiki/Joy_(programming_language)#Mat... > In Joy, the meaning function is a homomorphism from the syntactic monoid onto the semantic monoid. That is, the syntactic relation of concatenation of symbols maps directly onto the semantic relation of composition of functions. It is a homomorphism rather than an isomorphism, because it is onto but not one-to-one; that is, no symbol has more than one meaning, but some sequences of symbols have the same meaning (e.g. "dup +" and "2 *"). > Joy is a concatenative programming language: "The concatenation of two programs denotes the composition of the functions denoted by the two programs".[2] [2] "Mathematical foundations of Joy" by Manfred von Thun https://web.archive.org/web/20111007025556/http://www.latrobe.edu.au/phimvt/joy/j02maf.html https://web.archive.org/web/20111007025556/http://www.latrob...