Foo, Shmoo

“We do not realize what tremendous power the structure of an habitual language has. It is not an exaggeration to say that it enslaves us through the mechanism of s[emantic] r[eactions] and that the structure which a language exhibits, and impresses upon us unconsciously, is automatically projected upon the world around us.”
—Korzybski (1930) in Science & Sanity p. 90

I’m trying to train myself to choose nouns as names for my functions, in the hope that doing so will help to free me from the procedural mindset, which was pervasive when I learned to program. In those days, coding concentrated more or less exclusively on the manipulation of state and only rarely on the construction of definitions. In saying this, I’m distinguishing procedures, which legitimately deal in state, from functions, which don’t. Transitive verbs: print, init, reverse(vt), … make good names for procedures.

Many of APL’s primitive monadic functions have nouns as names: floor, reciprocal, reverse(n), shape, …

Except this doesn’t quite work. Each of these names seems to need an “of” when applied to an argument, where the of seems to bind to the word that follows it:

   ⌊÷blah   ⍝ "floor of reciprocal of blah"

I’ve seen dyadic iota documented as index-of, though this grates a bit as “index of” isn’t a noun phrase in English. In fact, as far as I know, all of the romance languages would parse Richard of York as Richard (of York), where (of York) is a noun phrase in the genitive case: York’s Richard; Ricardus Eboracum. Nobody seems to parse it (Richard of) York.

So much for that idea for a blog post; ho hum; back to real work.

Then Nick Nickolov found a Wikipedia entry that suggested: “Some languages, such as the Cariban languages, can be said to have a possessed case, used to indicate the other party (the thing possessed) in a possession relationship”. So the (Richard of) parsing would work in one of the Cariban languages and isn’t therefore a property of any deep structure of language, per se.

Now when I see ceiling, I can still think of it as a noun, but in the possessed case. To emphasise this, for the rest of this posting, I’ll write my function names with a back-tick inflection to represent the case: reverse` meaning reverse-of.

   ⌊÷blah   ⍝ floor` reciprocal` blah

… and when reading my code, I can vocalise the ending with a slight [əv] or [ə] sound as in “Land’v plenty”, “Bagguh chips, please”, “Floor’v reciprocal’v blah”.

But what about dyadic functions? Glad you asked. The left argument of a function (arrays are naturally nouns) can be seen as a noun acting as determiner, technically a noun adjunct: coffee table, bicycle thief, cube root, noun adjunct, … Thus: 2-residue`, N-take`, zilde-reshape`, ⎕AV-index`…

Practising this discipline has been quite illuminating: it has pushed me towards left argument currying. I now mentally parse ¯2⌽V as (¯2⌽)V the ((neg-two)-rotation`) V, where neg qualifies two, which in turn qualifies rotation`.

But surely 2+3 is just a symmetrical expression with respect to its arguments? Well yes, but we could also parse it as follows: Starting from the monadic successor` function 1∘+, the curried dyadic version 1+ would be the one-successor` and so 2+3 is the two-successor` three.

Now, how should we incorporate operators and their operands into this scheme? “The reverse` each` V“, where each` is functioning as a determiner?

PS: Choosing nouns for the names of functions shouldn’t be confused with J’s excellent taxonomy of language components using parts of speech, in which functions are labelled “verbs”.

PPS: Functions reverse`, successor`, shape`, … could also be seen as properties of their argument. A number N has many properties: its successor, its square-root, its floor, ceiling, prime-factorisation vector, … This is beginning to sound a bit like OO…

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