82 lines
1.4 KiB
Markdown
82 lines
1.4 KiB
Markdown
## Ex 1.2
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```Ocaml
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# let sum n =
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if n < 0 then
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invalid_arg "n<0"
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else
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let rec sumrc n =
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if n=0 then
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0
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else
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n + sum(n-1)
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in sumrc n;;
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val sum : int -> int = <fun>
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(*Correction*)
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let sigma f n =
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if n<0 then
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invalid_arg "n<0"
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else
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let rec sig = function
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| 0 -> f0
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| n -> fn + sig (n-1)
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in sig n;;
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val sigma: (int -> int) -> int -> int = <fun>
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```
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## Ex 2.1
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```
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# let rec map f = function
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| [] -> []
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|e::t -> f e::map f t ;;
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val map : ('a -> 'b) -> 'a list -> 'b list = <fun>
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```
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## Ex 2.2
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```
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# let rec for_all p = function
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| [] -> true
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| e::t -> p e && for_all p t;;
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val for_all: ('a -> bool) -> 'a list -> bool = <fun>
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```
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## Ex 2.3
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```
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# let rec exists p = function
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| [] -> true
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| e::t -> p e || for_all p t;;
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val exists: ('a -> bool) -> 'a list -> bool = <fun>
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```
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## Ex 2.4
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```
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# let rec find p = function
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| [] -> true
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| e::t -> if p e then e else find p t;;
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val exists: (bool -> bool) -> bool list -> bool = <fun>
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```
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## Ex 2.5
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```Ocaml
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# let rec filter p : function
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| [] -> []
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| e::t -> if p e then
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e::filter p t
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else filter p t;;
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val filter: ('a -> bool) -> 'a list -> 'a
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```
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## Ex 2.6
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```Ocaml
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let rec partition p l =
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match l with
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| [] -> ([], [])
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| h==t> let (l1, l2) = partition p t in
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if p h then (h::l1,l2)
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else (l1, h::l2);;
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val partition : ('a -> bool) -> 'a list -> 'a list * 'a list = <fun>
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```
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## Ex 2.7
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```Ocaml
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