"reducing a list by +" means adding up the elements of the list
reduce(+, 0, [1,2,3,4])
==> 1+2+3+4
==> 10
0 is called the unit ; it is the value when the list is empty
reduce(+,0,[]) ==> 0
reduce(*,1,[3,7,5]) ==> 105
›
unit for *
recall append creates a new list by following the elements of the first list by those of
append([4,5,7],[6,4,1]) ==> [4,5,7,6,4,1]
[[1,2], [3,4,5], [6,7]]
==> [1,2,3,4,5,6,7]
Use reduce. What is the unit for append ?
[ ]
reduce(append, [], LoL)
›
list of lists
mappend(f, range(1,N)) ==>
reduce(append, [], [f(1),f(2),º,f(N)])
result of map(f, range(1,N))
We want
f(1) = [1]
f(2) = [1,2]
f(3) = [1,2,3]
:
:
f(N) = [1,2,3,º,N]
f(i) = range(1,i)
mappend combines map & append
mappend(f,L)
= reduce(append, [], map(f,L))
Example (synthesis)
Make a list
Overall Solution
map would have given
[[1], [1,2], [1,2,3], º [1,2,3,ºN]]
