Please help me with these exericises in Haskell.

1. The function church takes an integer n as its argument and returns a function which composes any unary function n times.

For example:

*Main> :t church

church :: Int -> (c -> c) -> c -> c

*Main> (church 4) tail "ABCDEFGH"

"EFGH"

Write church using foldr.

2. Write a function trees which takes a list of leaf values as its argument and returns a list of all binary trees with the given leaves.

For example, *Main> :t trees

trees :: (Ord t) => [t] -> [Btree t]

*Main> (trees "ABCDE") !! 114

Fork (Leaf E) (Fork (Fork (Leaf A) (Fork (Leaf C) (Leaf B))) (Leaf D))

*Main> length (trees [0..4])

1680

3. A DNA molecule is a sequence of four bases which are conventionally represented using the characters A, G, C, and T. Genomes represented by DNA molecules are subject to four different types of point mutations:

insertions - A base is inserted between two adjacent points in a genome.

deletions - A point is deleted from a genome.

substitutions - A base at a point is replaced with another base.

transpositions - The bases at two adjacent points are exchanged.

Give definitions for Haskell functions insertions, deletions, substitutions and transpositions which take a genome represented as a string and return a list of all genomes produced by single point point mutations of the specifed kind.

For example:

*Main> insertions "GC"

["AGC","GAC","GCA","GGC","GGC","GCG","CGC","GCC","GCC", "TGC","GTC","GCT"]

*Main> deletions "AGCT"

["GCT","ACT","AGT","AGC"]

*Main> substitutions "ACT"

["ACT","AAT","ACA","GCT","AGT","ACG","CCT","ACT","ACC", "TCT","ATT","ACT"]

*Main> transpositions "GATC"

["AGTC","GTAC","GACT"]