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dec2bin: Write a predicate dec2bin(N, L) that takes a positive integer N and returns a list L that is the binary representation of N. For instance: dec2bin(1,L) should succeed with L=[1] and dec2bin(2,L) should succeed with L=[1,0] dec2bin(26,L) should succeed with L=[1,1,0,1,0] eval: Consider expression trees represented as a Prolog data structure, as discussed in class (Sep 20). Write a predicate eval(E, V) that takes an expression tree E and returns in V the value of the expression. For instance: eval(plus(num(4), num(2)), V) succeeds with V=6 eval(star(plus(num(4), num(2)),minus(num(3), num(1))), V) succeeds with V=12 You may assume that the first argument is always a valid expression tree. comp: This question also deals with expression trees. Write a predicate traverse(E, L) that takes an expression tree E and returns in L the list of stack machine instructions that evaluate E. The relevant instructions for this exercise are: ildc(n) which pushes a given integer n on the stack; iadd, isub, imul and idiv that add, subtract, multiply or divide the top two elements of the stack. For instance: comp(plus(num(4), num(2)), C) succeeds with C=[ildc(4), ildc(2), iadd] comp(minus(num(4), num(2)), C) succeeds with C=[ildc(4), ildc(2), isub] comp(star(plus(num(4), num(2)),minus(num(3), num(1))), C) succeeds with C=[ildc(4), ildc(2), iadd, ildc(3), ildc(1), isub, imul] You may assume that the first argument is always a valid expression tree.