It’s good to come back. Okay, let me follow on the progress.
I’d take note for a subsection of chapter 2.2.3. This section is about ‘Nested Mappings’. (sicp book)
This section talks about the useful methods to cope with nested lists.
In the book it demonstrates an example to generate the list of numbers that conform the specific rules shown below. The result required is \(i\), \(j\) and their sum, and the argument given is \(n\).
- \(1 \leq i \lt j \leq n\)
- \(i + j\) is a prime
The book gives a full code to construct such a program, besides, I am going to translate it into Haskell, both to deepen my impress and to have fun in Haskell :)
primeSumPairs :: Integer -> [(Integer, Integer, Integer)]
primeSumPairs n =
map makePairSum $ filter isPrimeSum [(x, y)|x <-[1..n], y <- [1..(x-1)]]
where
isPrimeSum (a,b) = isPrime $ a + b
makePairSum (a,b) = (a,b,a+b)Wow, due to the powerful syntax of Haskell, those code looks much more elegant!
The function isPrime, picked from a stackoverflow question, is defined before this.
isPrime :: Integer -> Bool
isPrime x = ([] == [y | y <- [2..floor (sqrt $ fromIntegral x)], mod x y == 0])And then the book presented a permutation generator, which was regularly impressive, looks cool yet.
Exercise 2.40 asks to write a procedure uniq-pairs that takes an argument n and return a sequence of \((i, j)\) for each that satisfies \(1 \leq i \lt j \leq n\).
This was quite easy, as implied in the code above,
uniqPairs :: Integer -> [(Integer, Integer)]
uniqPairs n = [(x, y)|x <-[1..n], y <- [1..(x-1)]]Exercise 2.41 asks for a very simple procedure. Given n and s, the procedure could return all possible lists of pairs of (elements for each takes values from 1 to n that sums to s). (Well, I like such logical English.)
Right as definition, translate those English into Haskell and we will get the answer, a one-liner.
ex241 :: Integer -> Integer -> [(Integer, Integer, Integer)]
ex241 n s = [(a,b,c) | a <- rng, b <- rng, c <- rng, a + b + c == s]
where rng = [1..n]Quite simple isn’t it?