How can I solve this following function in haskell?-CodePudding

I've Seen this following exercise in a book and there was no sample solution for that. I'm very new to functions of higher orders and i'm not sure how should i implement this function.I thought maybe you can give me some ideas.

I should implement a function foldleft :: (a -> b -> a) -> a -> [b] -> a, by that for every is valid that: f :: a -> b -> a and a0 :: a,b₁, …, b_k :: b,k∈N and foldleft f a₀ [b₁, …, b_k] = f (f … (f a₀ b₁) ⋯ b_k−1)b_k ,

so for example:

foldleft( ) 5 [1, 4, 3] = ( ) (( ) (( ) 5 1) 4) 3 = ((5   1)   4)   3

and in particular, it should apply : foldleft f a [] = a

CodePudding user response：

Start by breaking it into two cases:

foldleft f a0 [] = ...
foldleft f a0 (b1:b2_through_bk) = ...

Then look at the equations in your specification, and see which, if any, of them can help you start filling in the ...s.

CodePudding user response：

You can do pattern matching on the two data constructors of a list: the empty list, and the "cons" (:), so:

foldleft :: (a -> b -> a) -> a -> [b] -> a
foldleft f z [] = …
foldleft f z (x:xs) = …

for the second clause you will need to apply f on a and the head of the list, and then use this as initial accumulator when recursing on the tail of the list.