I need help (everything given)

1. WHILEL uses the same datatype of binary trees as WHILE does. Consider now the following trees in D: (a) >> (c) >>> According to our encoding of datatypes in D, decide for each tree (a)-(d) whether it encodes i a list of numbers; if it does give the corresponding list. ii a list of lists of numbers; if it does give the corresponding list. Note that an empty list can always be considered a list of numbers and a list of lists of numbers. [20 marks) 2. Let prog be the WHILE++-program in Figure 1. Explain what program prog in Figure 1 returns as output for a given input d e D. In other words, state what [prog] WHILE++(d) is for any d e D. (Don't describe the code in the program.) [14 marks) prog read L foreach x in L { while XL Y:= cons nil Y; X:= tl x } } } write Y Figure 1: WHILE++-program prog 1. WHILEL uses the same datatype of binary trees as WHILE does. Consider now the following trees in D: (a) >> (c) >>> According to our encoding of datatypes in D, decide for each tree (a)-(d) whether it encodes i a list of numbers; if it does give the corresponding list. ii a list of lists of numbers; if it does give the corresponding list. Note that an empty list can always be considered a list of numbers and a list of lists of numbers. [20 marks) 2. Let prog be the WHILE++-program in Figure 1. Explain what program prog in Figure 1 returns as output for a given input d e D. In other words, state what [prog] WHILE++(d) is for any d e D. (Don't describe the code in the program.) [14 marks) prog read L foreach x in L { while XL Y:= cons nil Y; X:= tl x } } } write Y Figure 1: WHILE++-program prog