4 ms·

I find that his mentioning of "monadic" and "dyadic" instead of "unary" and "binary" interesting, why did he mention those?

nprescott 7y ago
As far as I know, this is a peculiarity of APL resulting from Iverson's stance on the language as a "tool for thought"[0]. The best explanation I've heard is that "binary" is most apt to number systems (or matrices!) - but a "verb" in APL is not binary, it is dyadic. The language of verbs and nouns is a similar reflection of the ideas that APL is primarily a _language_ (like English, more so than Fortran) to express mathematics succinctly (with a minimum of ambiguity or syntax). This is (to me) even more apparent in his next language, J; where he sought to "correct" deficiencies in APL and further expanded the "language" to include things like "gerunds"[1] more explicitly, which are nominally (as defined in an English dictionary): > a noun formed from a verb, denoting an action or state Which may be summarized somewhat unsatisfactorily as: "Because Ken said so". [0]: https://www.jsoftware.com/papers/tot.htm https://www.jsoftware.com/papers/tot.htm [1]: https://code.jsoftware.com/wiki/Vocabulary/GerundsAndAtomicRepresentation https://code.jsoftware.com/wiki/Vocabulary/GerundsAndAtomicR...
- mjn 7y ago
  It's not totally APL-specific terminology, although it's uncommon in other areas of computer science. You can find it (predating APL) in areas like mathematical logic, where a predicate over two terms is sometimes called a "dyadic predicate". I'm guessing Iverson was familiar with that usage and extended it to APL. I wouldn't read too much into it though. It's mostly just Latin vs. Greek roots (unary, binary, ternary are Latin; monadic, dyadic, triadic are Greek).
TheRealDevonMcC 7y ago
It's also likely that his usage preceded the more common one prevalent now.

4 ms·

I find that his mentioning of "monadic" and "dyadic" instead of "unary" and "binary" interesting, why did he mention those?

by coldpresent 7y ago

nprescott 7y ago
As far as I know, this is a peculiarity of APL resulting from Iverson's stance on the language as a "tool for thought"[0]. The best explanation I've heard is that "binary" is most apt to number systems (or matrices!) - but a "verb" in APL is not binary, it is dyadic. The language of verbs and nouns is a similar reflection of the ideas that APL is primarily a _language_ (like English, more so than Fortran) to express mathematics succinctly (with a minimum of ambiguity or syntax). This is (to me) even more apparent in his next language, J; where he sought to "correct" deficiencies in APL and further expanded the "language" to include things like "gerunds"[1] more explicitly, which are nominally (as defined in an English dictionary): > a noun formed from a verb, denoting an action or state Which may be summarized somewhat unsatisfactorily as: "Because Ken said so". [0]: https://www.jsoftware.com/papers/tot.htm https://www.jsoftware.com/papers/tot.htm [1]: https://code.jsoftware.com/wiki/Vocabulary/GerundsAndAtomicRepresentation https://code.jsoftware.com/wiki/Vocabulary/GerundsAndAtomicR...
- mjn 7y ago
  It's not totally APL-specific terminology, although it's uncommon in other areas of computer science. You can find it (predating APL) in areas like mathematical logic, where a predicate over two terms is sometimes called a "dyadic predicate". I'm guessing Iverson was familiar with that usage and extended it to APL. I wouldn't read too much into it though. It's mostly just Latin vs. Greek roots (unary, binary, ternary are Latin; monadic, dyadic, triadic are Greek).
TheRealDevonMcC 7y ago
It's also likely that his usage preceded the more common one prevalent now.