Speak now
Please Wait Image Converting Into Text...
Embark on a journey of knowledge! Take the quiz and earn valuable credits.
Challenge yourself and boost your learning! Start the quiz now to earn credits.
Unlock your potential! Begin the quiz, answer questions, and accumulate credits along the way.
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]]
No matter what stage you're at in your education or career, TuteeHub will help you reach the next level that you're aiming for. Simply,Choose a subject/topic and get started in self-paced practice sessions to improve your knowledge and scores.
General Tech 9 Answers
General Tech 7 Answers
General Tech 3 Answers
General Tech 2 Answers
Ready to take your education and career to the next level? Register today and join our growing community of learners and professionals.