s

hw11.ml

@@ -0,0 +1,5 @@
+let rec merge (l1,l2) = 
+	match (l1,l2) with
+		| ([], _) -> l2
+		| (_, []) -> l1
+		| (h1::t1, h2::t2) -> h1::h2::merge(t1,t2)

hw12.ml

@@ -0,0 +1,3 @@
+sigma(a,b,f) =
+	if a>b-1 then 0
+	else f(b) + sigma(a,b-1,f)

hw14.ml

@@ -0,0 +1,15 @@
+t = ZERO | SUCC of nat
+
+let rec natadd (a,b) =
+	match(a,b) with
+		| (ZERO,ZERO) -> ZERO
+		| (ZERO, b) -> b
+		| (a, ZERO) -> a
+		| (SUCC a', SUCC b') -> SUCC(natadd(a,b'))
+
+let rec natmul(a,b)=
+	match(a,b) with
+		| (ZERO,ZERO)->ZERO
+		| (ZERO,b)->ZERO
+		| (a,ZERO)->ZERO
+		| (SUCC a', SUCC b') -> natadd(natmul(a,b'),a)

hw22.ml

@@ -0,0 +1,35 @@
+
+ world*)
+
+type crazy2 = NIL | ZERO of  crazy2 | ONE of crazy2 | MONE of crazy2
+
+let is_even n = (n mod 2 = 0)
+
+let pow base exponent =
+	if exponent <0 then invalid_arg "exponent cannot be negative" else
+	let rec aux accumulator base = function
+		| 0 -> accumulator
+		| 1 -> base * accumulator
+		| e when is_even e -> aux accumulator (base * base) (e/2)
+		| e-> aux(base * accumulator)(base*base)((e-1)/2) in
+	aux 1 base exponent
+(*
+let _ = print_endline(string_of_int(pow 2 5))
+*)
+let rec find_depth l = 
+	match l with
+		| NIL -> 0
+		| MONE(l') -> 1 + find_depth l'
+		| ONE(l') -> 1+ find_depth l'
+		| ZERO(l') -> 1+find_depth l'
+(*
+let _ = print_endline(string_of_int(find_depth(ZERO(ONE(MONE NIL)))))
+*)
+
+let rec crazy2val x =
+	let sam = find_depth x in
+	match x with
+		| NIL -> 0
+		| MONE(x') -> (pow 2 (sam-1))*(-1)+crazy2val(x')
+		| ONE(x') -> (pow 2 (sam-1))*1 + crazy2val(x')
+		| ZERO(x') -> crazy2val(x')

hw23.ml

@@ -0,0 +1,48 @@
+
+
+type crazy2 = NIL | ZERO of  crazy2 | ONE of crazy2 | MONE of crazy2
+
+let is_even n = (n mod 2 = 0)
+
+let pow base exponent =
+	if exponent <0 then invalid_arg "exponent cannot be negative" else
+	let rec aux accumulator base = function
+		| 0 -> accumulator
+		| 1 -> base * accumulator
+		| e when is_even e -> aux accumulator (base * base) (e/2)
+		| e-> aux(base * accumulator)(base*base)((e-1)/2) in
+	aux 1 base exponent
+(*
+let _ = print_endline(string_of_int(pow 2 5))
+*)
+let rec find_depth l = 
+	match l with
+		| NIL -> 0
+		| MONE(l') -> 1 + find_depth l'
+		| ONE(l') -> 1+ find_depth l'
+		| ZERO(l') -> 1+find_depth l'
+(*
+let _ = print_endline(string_of_int(find_depth(ZERO(ONE(MONE NIL)))))
+*)
+
+let rec crazy2val x =
+	let sam = find_depth x in
+	match x with
+		| NIL -> 0
+		| MONE(x') -> (pow 2 (sam-1))*(-1)+crazy2val(x')
+		| ONE(x') -> (pow 2 (sam-1))*1 + crazy2val(x')
+		| ZERO(x') -> crazy2val(x')
+(*
+let _ = print_endline(string_of_int(crazy2val(MONE(ONE(MONE(ZERO(NIL)))))))*)
+
+let rec decode (x, l) =
+	if (x = 0) then l else 
+	if (x mod 2 = 0) then decode ((x/2), ZERO(l))
+	else decode ((x/2), ONE(l))	
+
+
+let crazy2add (x,y) =
+	let sam = crazy2val x in
+	let sam2 = crazy2val y in
+	let sam3 = sam+sam2 in
+	decode (sam3, NIL)