4 ms·

I thought it was more of an accident? The story I know goes that Church used hats over variables, and then he switched over to lambda prefixes for ease of print

by kmill 6y ago

I thought it was more of an accident? The story I know goes that Church used hats over variables, and then he switched over to lambda prefixes for ease of printing.

crdrost 6y ago
I have often thought that if I were to teach a class on functional programming, I would use JavaScript’s fat arrow notation to introduce lambda calculus. Less succinct with all the extra parentheses that occur in function calls but I think it’s easy enough to explain.
- kmill 6y ago
  Pretty much the same idea, but in math contexts I tend to use the \mapsto arrow (↦), since mathematicians are more familiar with this than lambda calculus. (The fat arrow seems like an interesting alternative in programming contexts, but I worry that it might be confused with implication.) The function that swaps the arguments to a two-argument function: f ↦ ((x, y) ↦ f(y, x))
  - MayeulC 6y ago
    Interesting. The mathematical notation I learned in school was: f:x↦2x+3, So I guess this would translate to f:(x,y)↦(y,x). Alternatively, the f(x,y) = (y,x) notation would work (sort of, you tend to explicitly write out the base vector 𝑒ₖ for both notations: f(x,y) = f(x𝑒₁+y𝑒₂) = y𝑒₁+x𝑒₂ ) https://en.wikipedia.org/wiki/Function_(mathematics)#Arrow_notation https://en.wikipedia.org/wiki/Function_(mathematics)#Arrow_n...
    - kmill 6y ago
      That's close but not quite how I meant for the notation to be interpreted: f is an argument to an anonymous function. Maybe clearer is swap = f ↦ ((x, y) ↦ f(y, x)) The rule this satisfies is swap(f)(x, y) = f(y, x) and the type for swap is swap : (X × Y → Z) → (Y × X → Z) for some types/sets X, Y, and Z. (Also, note that tuples might not be anything like a vector space. For example, for String × [Int], you wouldn't usually write ("hi", [2,3]) as "hi"𝑒₁ + [2,3]𝑒₂ since there's not really a good commutative addition operation for strings or lists.)

by kmill 6y ago

I thought it was more of an accident? The story I know goes that Church used hats over variables, and then he switched over to lambda prefixes for ease of printing.

crdrost 6y ago

I have often thought that if I were to teach a class on functional programming, I would use JavaScript’s fat arrow notation to introduce lambda calculus. Less succinct with all the extra parentheses that occur in function calls but I think it’s easy enough to explain.

kmill 6y ago
Pretty much the same idea, but in math contexts I tend to use the \mapsto arrow (↦), since mathematicians are more familiar with this than lambda calculus. (The fat arrow seems like an interesting alternative in programming contexts, but I worry that it might be confused with implication.) The function that swaps the arguments to a two-argument function: f ↦ ((x, y) ↦ f(y, x))
- MayeulC 6y ago
  Interesting. The mathematical notation I learned in school was: f:x↦2x+3, So I guess this would translate to f:(x,y)↦(y,x). Alternatively, the f(x,y) = (y,x) notation would work (sort of, you tend to explicitly write out the base vector 𝑒ₖ for both notations: f(x,y) = f(x𝑒₁+y𝑒₂) = y𝑒₁+x𝑒₂ ) https://en.wikipedia.org/wiki/Function_(mathematics)#Arrow_notation https://en.wikipedia.org/wiki/Function_(mathematics)#Arrow_n...
  - kmill 6y ago
    That's close but not quite how I meant for the notation to be interpreted: f is an argument to an anonymous function. Maybe clearer is swap = f ↦ ((x, y) ↦ f(y, x)) The rule this satisfies is swap(f)(x, y) = f(y, x) and the type for swap is swap : (X × Y → Z) → (Y × X → Z) for some types/sets X, Y, and Z. (Also, note that tuples might not be anything like a vector space. For example, for String × [Int], you wouldn't usually write ("hi", [2,3]) as "hi"𝑒₁ + [2,3]𝑒₂ since there's not really a good commutative addition operation for strings or lists.)