## /Prelude-v21.1.0/List/foldLeft.dhall

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foldLeft is like List/fold except that the accumulation starts from the left

If you treat the list [ x, y, z ] as cons (cons (cons nil x) y) z, then foldLeft just replaces each cons and nil with something else

### Examples

foldLeft
Natural
[ 2, 3, 5 ]
Text
(λ(x : Text) → λ(y : Natural) → x ++ Natural/show y)
"0"
≡ "0235"
( λ(nil : Text) →
foldLeft
Natural
[ 2, 3, 5 ]
Text
(λ(x : Text) → λ(y : Natural) → x ++ Natural/show y)
nil
)
≡ (λ(nil : Text) → nil ++ "2" ++ "3" ++ "5")
( λ(cons : Text → Natural → Text) →
λ(nil : Text) →
foldLeft Natural [ 2, 3, 5 ] Text cons nil
)
≡ ( λ(cons : Text → Natural → Text) →
λ(nil : Text) →
cons (cons (cons nil 2) 3) 5
)

### Source

{-|
`foldLeft` is like `List/fold` except that the accumulation starts from the left

If you treat the list `[ x, y, z ]` as `cons (cons (cons nil x) y) z`, then
`foldLeft` just replaces each `cons` and `nil` with something else
-}
let foldLeft
: ∀(a : Type) →
List a →
∀(list : Type) →
∀(cons : list → a → list) →
∀(nil : list) →
list
= λ(a : Type) →
λ(xs : List a) →
λ(list : Type) →
λ(cons : listalist) →
λ(nil : list) →
List/fold
a
xs
(listlist)
(λ(x : a) → λ(f : listlist) → λ(l : list) → f (cons l x))
(λ(l : list) → l)
nil

let example0 =
assert
: foldLeft
Natural
[ 2, 3, 5 ]
Text
(λ(x : Text) → λ(y : Natural) → x ++ Natural/show y)
"0"
≡ "0235"

let example1 =
assert
: ( λ(nil : Text) →
foldLeft
Natural
[ 2, 3, 5 ]
Text
(λ(x : Text) → λ(y : Natural) → x ++ Natural/show y)
nil
)
≡ (λ(nil : Text) → nil ++ "2" ++ "3" ++ "5")

let example2 =
assert
: ( λ(cons : Text → Natural → Text) →
λ(nil : Text) →
foldLeft Natural [ 2, 3, 5 ] Text cons nil
)
≡ ( λ(cons : Text → Natural → Text) →
λ(nil : Text) →
cons (cons (cons nil 2) 3) 5
)

in foldLeft