ML Prolog short functions

1)datatype 'a inf_list = lcons of 'a * (unit -> 'a inf_list) “Lf.Lx.(f x)” “Lf.Lx.(f (f x))” “Lf.Lx.(f (f (f x)))” “Lf.Lx.(f (f (f (f x))))” “Lf.Lx.(f (f (f (f (f x)))))” … a. Define a function church: string -> string inf_list which generates an infinite list of Church numerals starting from 1. The input to the function church is a string “x”. b. Define a function zip: 'a inf_list * 'b inf_list -> ('a * 'b) inf_list which takes two infinite lists, pairs up the corresponding elements, and produces an output infinite list. 2)Prolog walkway(jarvis, furnas). walkway(furnas, bell). walkway(bell, studentunion). a)Define a predicate path(B1, B2, Path) which, given two buildings B1 and B2, returns in Path the list of buildings on a path from B1 to B2 going only through permissible walkways. b)Making use of the path predicate defined in part (a), define a predicate pathvia(BList, B1, B2, Path), which, given two buildings B1 and B2 and a list of buildings BList, returns in Path the list of buildings on a path from B1 to B2 that goes through all buildings in BList.