Solutions to Exercises for October 12, 2018

The previous version was

x = mod length data Y
   where
     { data = [1..10] Y = 5 }

containing the following errors:

1. data is a keyword and is therefore not allowed as variable name.
2. In the last line we are using braces ({ and }) to disregard the layout rule. But then items need to be separated by semicolons (;).
3. Y is not allowed as variable name (since it is uppercase).
4. Missing parentheses around length data, since it is supposed to be the first argument of mod.

nth corresponds to the Prelude function !!, that is, we have

nth xs i = xs !! i

whenever i is between 0 and the length of xs.

Just to get some intuition: for integer lists of the shape [0..k], fromTo satisfies the property

fromTo [0..k] i j = [i..j]

for all 0 <= i <= j <= k.

allTrue corresponds to the Prelude function and, that is, we have

allTrue bs = and bs

for all lists of boolean values bs.