What is a primitive? (opens in new tab)

(mlochbaum.github.io)

30 pointschrispsn4y ago18 comments

18 comments

Author here if you have any questions. The main reason to write this document is people used to APL wondering why BQN leaves out certain primitives (answer: I don't think they're really primitives), but probably more HNers would wonder why it has so many that ASCII isn't even fit to keep them all (the full list is at https://mlochbaum.github.io/BQN/doc/primitive.html). Just as well; hopefully I've addressed both concerns!

myWindoonn4y ago

I think that you're after the universal morphisms in a computational category. Curien called them "categorical combinators" and gave a listing in https://core.ac.uk/download/pdf/82017242.pdf

mlochbaum4y ago

I doubt it? Universal constructions give a nice definition for a few operations but I doubt they have the power to pull out all primitives, that is, select out of all the well-defined things you could do the ones that are natural or useful. Can Indices[0] be constructed as a universal morphism? Is defining it in this way simpler than an algorithmic definition, which can be quite short? One of the properties of primitives I list is that they tend to have short definitions, so constructive definition is already a sort of filter that prefers primitives. Universal morphisms might be another, even a more useful, filter, but probably not a perfect filter.

Although, if you're here... there's a more focused question that's been bothering me because I feel it should appear in category theory but can't locate it. There's an operation I call Under that I partially introduce at [1] and define at [2]. The idea is that given functions F and G, where G manipulates things in some overall framework like arrays, F⌾G is a function so that F⌾G x is as similar as possible to x while satisfying (G F⌾G x) = G x. Maybe it's a sort of pullback along a functor G. Does that look familiar?

[0] https://mlochbaum.github.io/BQN/doc/replicate.html

[1] https://mlochbaum.github.io/BQN/tutorial/variable.html#modif...

[2] https://mlochbaum.github.io/BQN/spec/inferred.html#under

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neolog4y ago

What tool did you use to make those diagrams?

mlochbaum4y ago

BQN! The entire BQN website is generated with a markdown processor[0] that handles the parts of Github-flavored markdown I use and adds features like highlighting and the ability to drop into BQN to generate html or svg. Github doesn't display markdown source nicely, but you can scroll down to the <!--GEN line in [1] to see how this diagram is made (plus definitions at [2]).

[0] https://github.com/mlochbaum/BQN/blob/master/md.bqn

[1] https://raw.githubusercontent.com/mlochbaum/BQN/master/comme...

[2] https://github.com/mlochbaum/BQN/blob/master/svg.bqn

moonchild4y ago

Along vaguely related lines is https://gist.github.com/chrispsn/b1020918a83a28ab8b4442d8aff...

mlochbaum4y ago

The relationship is interesting. Chris is trying to find a minimal set of functions good enough to derive the rest (a worthwhile goal, and it mentions at the bottom that I did something similar in BQN). Part of my current thinking about primitives is that it's not important how many there are, more that each represents a coherent simple concept. But primitives that are too similar can cause problems for memory and maybe intuition.

moonchild4y ago

What is your opinion of the j. primitive in j?

1 more reply

armchairhacker4y ago

When I write programming languages, I usually define primitives as "any value without children". Strings, numbers, booleans, are primitives. Collections and records are not.

Some edge cases: literal ranges would be primitives, because their ast is represented (in Haskell) as "Range Int Int". Ranges which take values wouldn't be primitives, because their ast is represented as "Range expr expr"

mlochbaum4y ago

BQN uses the term "atom" for such values[0]. They include numbers, characters, and functions, as well as namespaces—really "atom" just means "non-array". These are the values that can't be split apart by array operations, but they might still be made up of multiple things, for example a function train[1].

In contrast, primitives are the starting point for programming, particularly tacit programming ("point-free" in Haskell). While the two names have a similar meaning, I think it fits a little better to call values that are indivisible from a particular perspective "atoms" and the ones that are meant to really be fundamental "primitives".

[0] https://mlochbaum.github.io/BQN/doc/types.html

[1] https://mlochbaum.github.io/BQN/doc/train.html

gigjbfjv4y ago

Are you saying that you consider strings in Haskell to be a primitive?

armchairhacker4y ago

No, Haskell is weird since a string is [Char]. If it was it’s own value, yes.

The languages i’ve written are pretty basic. e.g. the data types might be

- Number - String - True, false, null - Array of values - Record of fields (key + value) - Variant of options (key + value)

So the distinction is clearer.

1 more reply

smitty1e4y ago

Is BQN a near-incrementing of the letters in APL?

Is it pronounced "bacon"?

mlochbaum4y ago

Yes, as you can verify pretty easily in BQN: https://mlochbaum.github.io/BQN/try.html#code=IkJRTiItIkFQTC.... I explained at https://news.ycombinator.com/item?id=24172488.

Like APL versus "apple", the normal pronunciation is to spell it out B-Q-N, but it may be pronounced "bacon" if one wishes to establish a double-entendre. So a BQN user is a BQNator, pronounced like https://en.wikipedia.org/wiki/Baconator.

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18 comments

mlochbaum4y ago

myWindoonn4y ago

I think that you're after the universal morphisms in a computational category. Curien called them "categorical combinators" and gave a listing in https://core.ac.uk/download/pdf/82017242.pdf

mlochbaum4y ago

[0] https://mlochbaum.github.io/BQN/doc/replicate.html

[1] https://mlochbaum.github.io/BQN/tutorial/variable.html#modif...

[2] https://mlochbaum.github.io/BQN/spec/inferred.html#under

1 more reply

neolog4y ago

What tool did you use to make those diagrams?

mlochbaum4y ago

[0] https://github.com/mlochbaum/BQN/blob/master/md.bqn

[1] https://raw.githubusercontent.com/mlochbaum/BQN/master/comme...

[2] https://github.com/mlochbaum/BQN/blob/master/svg.bqn

moonchild4y ago

Along vaguely related lines is https://gist.github.com/chrispsn/b1020918a83a28ab8b4442d8aff...

mlochbaum4y ago

moonchild4y ago

What is your opinion of the j. primitive in j?

1 more reply

armchairhacker4y ago

When I write programming languages, I usually define primitives as "any value without children". Strings, numbers, booleans, are primitives. Collections and records are not.

mlochbaum4y ago

[0] https://mlochbaum.github.io/BQN/doc/types.html

[1] https://mlochbaum.github.io/BQN/doc/train.html

gigjbfjv4y ago

Are you saying that you consider strings in Haskell to be a primitive?

armchairhacker4y ago

No, Haskell is weird since a string is [Char]. If it was it’s own value, yes.

The languages i’ve written are pretty basic. e.g. the data types might be

- Number - String - True, false, null - Array of values - Record of fields (key + value) - Variant of options (key + value)

So the distinction is clearer.

1 more reply

smitty1e4y ago

Is BQN a near-incrementing of the letters in APL?

Is it pronounced "bacon"?

mlochbaum4y ago

Yes, as you can verify pretty easily in BQN: https://mlochbaum.github.io/BQN/try.html#code=IkJRTiItIkFQTC.... I explained at https://news.ycombinator.com/item?id=24172488.

j / k navigate · click thread line to collapse