MARCHE Claude committed Oct 13, 2017 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 ``````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 module AddListRec `````` Andrei Paskevich committed Jun 15, 2018 30 ``````use SumList `````` MARCHE Claude committed Oct 13, 2017 31 `````` `````` Andrei Paskevich committed Jun 07, 2018 32 ``````let rec sum (l: list or_integer_float) : (si: int, sf: real) = `````` MARCHE Claude committed Oct 13, 2017 33 `````` variant { l } `````` Andrei Paskevich committed Jun 07, 2018 34 `````` ensures { si = add_int l /\ sf = add_real l } `````` Guillaume Melquiond committed Jan 12, 2018 35 `````` [@vc:sp] `````` MARCHE Claude committed Oct 13, 2017 36 37 38 39 40 41 42 43 44 45 46 `````` 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 () = `````` Guillaume Melquiond committed Jan 12, 2018 47 `````` [@vc:sp] `````` MARCHE Claude committed Oct 13, 2017 48 49 50 51 52 53 54 55 56 57 58 59 60 `````` 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 module AddListImp `````` Andrei Paskevich committed Jun 15, 2018 61 62 ``````use SumList use ref.Ref `````` MARCHE Claude committed Oct 13, 2017 63 `````` `````` Andrei Paskevich committed Jun 07, 2018 64 65 ``````let sum (l: list or_integer_float) : (si: int, sf: real) = ensures { si = add_int l /\ sf = add_real l } `````` Guillaume Melquiond committed Jan 12, 2018 66 `````` [@vc:sp] `````` MARCHE Claude committed Oct 13, 2017 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 `````` let si = ref 0 in let sf = ref 0.0 in let ll = ref l in while True do invariant { !si + add_int !ll = add_int l /\ !sf +. add_real !ll = add_real l } variant { !ll } match !ll with | Nil -> return !si, !sf | Cons (Integer n) t -> si := !si + n; ll := t | Cons (Real x) t -> sf := !sf +. x; ll := t end done; absurd let main () = `````` Guillaume Melquiond committed Jan 12, 2018 86 `````` [@vc:sp] `````` MARCHE Claude committed Oct 13, 2017 87 88 89 90 91 92 93 94 95 `````` 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``````