## Summing the elements of a list

Summing the elements of a list, in various ways

Authors: Claude Marché

Topics: List Data Structure

Tools: Why3

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```theory SumList

use export int.Int
use export real.RealInfix
use export list.List

type or_integer_float = Integer int | Real real

(* sum integers in a list *)
function add_int (e: list or_integer_float) : int =
match e with
| Nil -> 0
| Cons (Integer n) t -> n + add_int t
| Cons _ t -> add_int t
end

(* sum reals in a list *)
function add_real (e: list or_integer_float) : real =
match e with
| Nil -> 0.0
| Cons (Real x) t -> x +. add_real t
| Cons _ t -> add_real t
end

end

use import SumList

let rec sum (l: list or_integer_float) : (int, real) =
variant { l }
returns { si, sf -> si = add_int l /\ sf = add_real l }
match l with
| Nil -> (0, 0.0)
| Cons h t ->
let (a,b) = sum t in
match h with
| Integer n -> (n + a,b)
| Real x -> (a,x +. b)
end
end

let main () =
let l =
Cons (Integer 5) (Cons (Real 3.3) (Cons (Integer 8)
(Cons (Real 1.4) (Cons (Integer 9) Nil))))
in
let (s,f) = sum l in
assert { s = 22 };
assert { f = 4.7 }

end

use import SumList
use import ref.Ref

exception Break

let sum (l: list or_integer_float) : (int, real) =
returns { si, sf -> si = add_int l /\ sf = add_real l }
let si = ref 0 in
let sf = ref 0.0 in
let ll = ref l in
try
while True do
}
variant { !ll }
match !ll with
| Nil -> raise Break
| Cons (Integer n) t ->
si := !si + n; ll := t
| Cons (Real x) t ->
sf := !sf +. x; ll := t
end
done;
absurd
with Break -> (!si, !sf)
end

let main () =
let l =
Cons (Integer 5) (Cons (Real 3.3) (Cons (Integer 8)
(Cons (Real 1.4) (Cons (Integer 9) Nil))))
in
let (s,f) = sum l in
assert { s = 22 };
assert { f = 4.7 }

end
```