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General Tech Learning Aids/Tools 2 years ago
Posted on 16 Aug 2022, this text provides information on Learning Aids/Tools related to General Tech. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
Turn Your Knowledge into Earnings.
I am always interested in learning new languages, a fact that keeps me on my toes and makes me (I believe) a better programmer. My attempts at conquering Haskell come and go - twice so far - and I decided it was time to try again. 3rd time's the charm, right?
Nope. I re-read my old notes... and get disappointed :-(
The problem that made me lose faith last time, was an easy one: permutations of integers. i.e. from a list of integers, to a list of lists - a list of their permutations:
[int] -> [[int]]
This is in fact a generic problem, so replacing 'int' above with 'a', would still apply.
From my notes:
I code it first on my own, I succeed. Hurrah!
I send my solution to a good friend of mine - Haskell guru, it usually helps to learn from gurus - and he sends me this, which I am told, "expresses the true power of the language, the use of generic facilities to code your needs". All for it, I recently drank the kool-aid, let's go:
permute :: [a] -> [[a]] permute = foldr (concatMap.ins) [[]] where ins x [] = [[x]] ins x (y:ys) = (x:y:ys):[ y:res | res <- ins x ys]
Hmm. Let's break this down:
bash$ cat b.hs ins x [] = [[x]] ins x (y:ys) = (x:y:ys):[ y:res | res <- ins x ys] bash$ ghci Prelude> :load b.hs [1 of 1] Compiling Main ( b.hs, interpreted ) Ok, modules loaded: Main. *Main> ins 1 [2,3] [[1,2,3],[2,1,3],[2,3,1]]
OK, so far, so good. Took me a minute to understand the second line of "ins", but OK: It places the 1st arg in all possible positions in the list. Cool.
Now, to understand the foldr and concatMap. in "Real world Haskell", the DOT was explained...
(f . g) x
...as just another syntax for...
f (g x)
And in the code the guru sent, DOT was used from a foldr, with the "ins" function as the fold "collapse":
*Main> let g=concatMap . ins *Main> g 1 [[2,3]] [[1,2,3],[2,1,3],[2,3,1]]
OK, since I want to understand how the DOT is used by the guru, I try the equivalent expression according to the DOT definition, (f . g) x = f (g x) ...
*Main> concatMap REPLY 0 views 0 likes 0 shares Facebook Twitter Linked In WhatsApp
(f . g) x = f (g x)
This is true. You concluded from that that
(f . g) x y = f (g x y)
must also be true, but that is not the case. In fact, the following is true:
(f . g) x y = f (g x) y
which is not the same.
Why is this true? Well (f . g) x y is the same as ((f . g) x) y and since we know that (f . g) x = f (g x) we can reduce that to (f (g x)) y, which is again the same as f (g x) y.
(f . g) x y
((f . g) x) y
(f (g x)) y
f (g x) y
So (concatMap . ins) 1 [[2,3]] is equivalent to concatMap (ins 1) [[2,3]]. There is no magic going on here.
(concatMap . ins) 1 [[2,3]]
concatMap (ins 1) [[2,3]]
Another way to approach this is via the types:
. has the type (b -> c) -> (a -> b) -> a -> c, concatMap has the type (x -> [y]) -> [x] -> [y], ins has the type t -> [t] -> [[t]]. So if we use concatMap as the b -> c argument and ins as the a -> b argument, then a becomes t, b becomes [t] -> [[t]] and c becomes [[t]] -> [[t]] (with x = [t] and y = [t]).
.
(b -> c) -> (a -> b) -> a -> c
concatMap
(x -> [y]) -> [x] -> [y]
ins
t -> [t] -> [[t]]
b -> c
a -> b
a
t
b
[t] -> [[t]]
c
[[t]] -> [[t]]
x
[t]
y
So the type of concatMap . ins is t -> [[t]] -> [[t]], which means a function taking a whatever and a list of lists (of whatevers) and returning a list of lists (of the same type).
concatMap . ins
t -> [[t]] -> [[t]]
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