 ### Alt-ergo has no input syntax for triggers on existential quantifiers

parent 56135b10
 * marks an incompatible change o fixed Alt-ergo output: no triggers for "exists" quantifier o [IDE] tool "Replay" works o [IDE] does not use Threads anymore, thanks to Call_provers.query_call o VC gen produces explanations in a suitable form for IDE ... ...
 (* Floyd's ``the tortoise and the hare'' algorithm. *) module TortoiseHare use import int.Int (* We consider a function f over an abstract type t *) type t logic f t : t (* Given some x0 in t, we consider the sequence of the repeated calls to f starting from x0. *) logic x int : t axiom xdef: forall n:int. n >= 0 -> x (n+1) = f (x n) logic x0 : t = x 0 (* If t is finite, this sequence will eventually end up on a cycle. Let us simply assume the existence of this cycle, that is x (i + lambda) = x i, for some lambda > 0 and i large enough. *) logic mu : int axiom mu: mu >= 0 logic lambda : int axiom lambda: lambda >= 1 axiom cycle: forall i:int. mu <= i -> x (i + lambda) = x i lemma cycle_gen: forall i:int. mu <= i -> forall k:int. 0 <= k -> x (i + lambda * k) = x i (* The challenge is to prove that the recursive function let rec run x1 x2 = if x1 <> x2 then run (f x1) (f (f x2)) terminates when called on x0 and (f x0). *) logic dist int int : int axiom dist_def1: forall n m: int. 0 <= n <= m -> x (n + dist n m) = x m axiom dist_def2: forall n m: int. 0 <= n <= m -> forall k: int. x (n + k) = x m -> dist n m <= k logic r (x12 : (t, t)) (x'12 : (t, t)) = let x1, x2 = x12 in let x'1, x'2 = x'12 in exists m:int. x1 = x (m+1) and x2 = x (2*m+2) and x'1 = x m and x'2 = x (2*m) and m < mu or (mu <= m and dist (m+1) (2*m+2) < dist m (2*m)) let rec run x1 x2 variant { (x1, x2) } with r = { exists m:int [x m]. x1 = x m and x2 = x (2*m) } if x1 <> x2 then run (f x1) (f (f x2)) { } end (* Local Variables: compile-command: "unset LANG; make -C ../.. examples/programs/tortoise_hare.gui" End: *)
 ... ... @@ -102,8 +102,11 @@ let rec print_fmla info fmt f = match f.f_node with (print_list comma (print_term info)) tl end | Fquant (q, fq) -> let q = match q with Fforall -> "forall" | Fexists -> "exists" in let vl, tl, f = f_open_quant fq in let q, tl = match q with | Fforall -> "forall", tl | Fexists -> "exists", [] (* Alt-ergo has no triggers for exists *) in let forall fmt v = fprintf fmt "%s %a:%a" q print_ident v.vs_name (print_type info) v.vs_ty in ... ... @@ -141,8 +144,7 @@ and print_triggers info fmt tl = | Term _ -> true | Fmla {f_node = Fapp (ps,_)} -> not (ls_equal ps ps_equ) | _ -> false in let tl = List.map (List.filter filter) tl in let tl = List.map (List.filter filter) tl in let tl = List.filter (function [] -> false | _::_ -> true) tl in if tl = [] then () else fprintf fmt "@ [%a]" (print_list alt (print_list comma (print_expr info))) tl ... ...
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