module HW8 where

import Hugs.Prelude

{-######################################

QUESTION 10.12

BEFORE:

------

comp2::(a->b)->(b->b->c)->(a->a->c)

comp2 f g = (\x y ->g (f x (f y))

total::(Int->Int)->(Int->Int)

total func = \n-> sum(map func [0..n])

######################################-}

comp2 :: (a -> b) -> (b -> b -> c) -> (a -> aa -> c)

comp2 f = \g x y -> g (f x) (f y)

total::(Int->Int)->(Int->Int)

total = \func n-> sum (map func [0 .. n])

{-######################################

QUESTION 10.13

(filter (>0). map (+1)) [-3,-2,-1,0,1,2,3] gives [1,2,3,4]

(map (+1). filter (> -1)) [-3,-2,-1,0,1,2,3] also gives [1,2,3,4]

######################################-}

{-

ANSWER

sec1 ==> (+1)

sec2 ==> (> -1)

-}

{-######################################

QUESTION 10.33

f.(g.h) ?= (f.g).h

knowing that

(f.g) x = f (g x)

######################################-}

{-

f.(g.h) x ==> f ((g.h) x) ==> f( g( h x) )

(f.g).h x ==> (f.g) (h x) ==> f( g( h x) )

-}

{-######################################

QUESTION 10.34

knowing that

(f.g) x = f (g x)

and by the definition of

id::a->a

id x=x

######################################-}

{-

(id.f) x ==> id (f x) ==> f x

-}

{-######################################-}

{-######################################-}