vault backup: 2023-11-13 13:50:53

Algo/B1/Courses/Chapter 7 - High Order (exercises).md

@@ -0,0 +1,92 @@
+## Ex 1.2
+```Ocaml
+# let sum n = 
+	if n < 0 then
+		invalid_arg "n<0"
+	else
+		let rec sumrc n  =
+			if n=0 then
+				0
+			else
+				n + sum(n-1)
+		in sumrc n;;
+val sum : int -> int = <fun>
+
+(*Correction*)
+let sigma f n = 
+	if n<0 then
+		invalid_arg "n<0"
+	else
+		let rec sig = function
+			| 0 -> f0
+			| n -> fn + sig (n-1)
+		in sig n;;
+val sigma: (int -> int) -> int -> int = <fun>
+```
+
+## Ex 2.1
+```
+# let rec map f = function
+	| [] -> []
+	|e::t -> f e::map f t ;;
+val map : ('a -> 'b) -> 'a list -> 'b list = <fun>
+```
+
+## Ex 2.2
+```
+# let rec for_all p = function
+	| [] -> true
+	| e::t -> p e && for_all p t;;
+val for_all: ('a -> bool) -> 'a list -> bool = <fun>
+```
+
+## Ex 2.3
+```
+# let rec exists p = function
+	| [] -> true
+	| e::t -> p e || for_all p t;;
+val exists: ('a -> bool) -> 'a list -> bool = <fun>
+```
+
+## Ex 2.4
+```
+# let rec find p = function
+	| [] -> true
+	| e::t -> if p e then e else find p t;;
+val exists: (bool -> bool) -> bool list -> bool = <fun>
+```
+
+## Ex 2.5
+```Ocaml
+# let rec filter p : function
+	| [] -> []
+	| e::t -> if p e then
+		e::filter p t
+		else filter p t;;
+val filter: ('a -> bool) -> 'a list -> 'a 
+```
+
+## Ex 2.6
+```Ocaml
+let rec partition p l =
+	match l with 
+		| [] -> ([], [])
+		| h==t> let (l1, l2) = partition p t in
+			if p h then (h::l1,l2)
+			else (l1, h::l2);;
+val partition : ('a -> bool) -> 'a list -> 'a list * 'a list = <fun>
+```
+
+## Ex 2.7
+```Ocaml
+# let less2 p k l1 l2 =
+	if k < 0 then invalid_arg "k needs to be positive" else
+		let rec less p k l1 l2 acc = match (l1, l2) with 
+			| ([],[]) -> acc < k
+			| (e::t, e::t2) -> if p e e2 then less p k t t2 (acc + 1)
+				else less p k t t2 acc
+		in less p k l1 l2 0;;
+val less2 : ('a -> 'b -> bool) -> int -> 'a list -> 'b list -> bool = <fun>
+```
+## Ex 3.1
+```Ocaml