3 ms·

Can we solve for x and y? All I see is algebra here, is my intuition wrong?

Zhyl 6mo ago
It's more like a recipe (for functions). The first example, I, is an identity function. It takes y and returns y. The second, K, is a constant which takes X and y and returns x. This gets more complicated as you go along. The idea is that you get rid of a lot of the syntax for composition and have it all be implicit by what you put next to each other (given APL programs are usually one long line of a bunch of different symbols all representing functions).
seanhunter 6mo ago
The intuition here is that combinators are higher order functions which take functions and combine them together in various ways. So for a simple example "fix" is a combinator in regular maths where Fix f = {f(x): f(x) = x for all x in the domain of f} So if f is a function or a group action or whatever, the fixed-point set of f is all points x in the domain of f such that f(x)=x. ie the points which are unchanged by x. So if f is a reflection, the points which sit on the axis of reflection. The fixed-point combinator is of particular relevance to this site because it's often called the y combinator.
- travisjungroth 6mo ago
  No one who would ask that question would be able to understand your answer.
  - seanhunter 6mo ago
    Hehe. Sorry. Yes perhaps you’re right. Wasn’t trying to be obtuse but I didn’t express that particularly clearly.
    - Sharlin 6mo ago
      Your explanation was several years worth of math studies beyond what GP was asking.
    - travisjungroth 6mo ago
      Perfectly clearly, just for a different audience.
  - general_reveal 6mo ago
    I’m going to frame this comment.
skydhash 6mo ago
Combinators can be a bit sill for values. The usefulness come when you use them as a meta language for functions.
travisjungroth 6mo ago
More directly than the other comments: No you can’t solve for x and y here and yes your intuition is wrong. These are functions. I don’t know your level of knowledge in math or programming and what that would mean to you. Here’s an example. double(x) -> x*2 So, double(3) = 6. You can’t solve for x because x doesn't have a value. It’s a placeholder for whatever you put in. These combinators are functions that take other functions and return them unmodified. “Unmodified” is a little misleading because it can do things like drop inputs.
- deleted 6mo ago
  [deleted]

Zhyl 6mo ago

It's more like a recipe (for functions). The first example, I, is an identity function. It takes y and returns y. The second, K, is a constant which takes X and y and returns x. This gets more complicated as you go along. The idea is that you get rid of a lot of the syntax for composition and have it all be implicit by what you put next to each other (given APL programs are usually one long line of a bunch of different symbols all representing functions).

seanhunter 6mo ago

The intuition here is that combinators are higher order functions which take functions and combine them together in various ways. So for a simple example "fix" is a combinator in regular maths where Fix f = {f(x): f(x) = x for all x in the domain of f} So if f is a function or a group action or whatever, the fixed-point set of f is all points x in the domain of f such that f(x)=x. ie the points which are unchanged by x. So if f is a reflection, the points which sit on the axis of reflection. The fixed-point combinator is of particular relevance to this site because it's often called the y combinator.

travisjungroth 6mo ago
No one who would ask that question would be able to understand your answer.
- seanhunter 6mo ago
  Hehe. Sorry. Yes perhaps you’re right. Wasn’t trying to be obtuse but I didn’t express that particularly clearly.
  - Sharlin 6mo ago
    Your explanation was several years worth of math studies beyond what GP was asking.
  - travisjungroth 6mo ago
    Perfectly clearly, just for a different audience.
- general_reveal 6mo ago
  I’m going to frame this comment.

skydhash 6mo ago

Combinators can be a bit sill for values. The usefulness come when you use them as a meta language for functions.

travisjungroth 6mo ago

More directly than the other comments: No you can’t solve for x and y here and yes your intuition is wrong. These are functions. I don’t know your level of knowledge in math or programming and what that would mean to you. Here’s an example. double(x) -> x*2 So, double(3) = 6. You can’t solve for x because x doesn't have a value. It’s a placeholder for whatever you put in. These combinators are functions that take other functions and return them unmodified. “Unmodified” is a little misleading because it can do things like drop inputs.

deleted 6mo ago
[deleted]