diff options
Diffstat (limited to 'contrib/omega/omega.ml')
| -rw-r--r--[-rwxr-xr-x] | contrib/omega/omega.ml | 469 |
1 files changed, 260 insertions, 209 deletions
diff --git a/contrib/omega/omega.ml b/contrib/omega/omega.ml index f0eb1e78..fd774c16 100755..100644 --- a/contrib/omega/omega.ml +++ b/contrib/omega/omega.ml @@ -11,52 +11,75 @@ (* *) (* Pierre Crégut (CNET, Lannion, France) *) (* *) +(* 13/10/2002 : modified to cope with an external numbering of equations *) +(* and hypothesis. Its use for Omega is not more complex and it makes *) +(* things much simpler for the reflexive version where we should limit *) +(* the number of source of numbering. *) (**************************************************************************) -(* $Id: omega.ml,v 1.7.2.2 2005/02/17 18:25:20 herbelin Exp $ *) - -open Util -open Hashtbl open Names -let flat_map f = - let rec flat_map_f = function - | [] -> [] - | x :: l -> f x @ flat_map_f l - in - flat_map_f - -let pp i = print_int i; print_newline (); flush stdout +module type INT = sig + type bigint + val less_than : bigint -> bigint -> bool + val add : bigint -> bigint -> bigint + val sub : bigint -> bigint -> bigint + val mult : bigint -> bigint -> bigint + val euclid : bigint -> bigint -> bigint * bigint + val neg : bigint -> bigint + val zero : bigint + val one : bigint + val to_string : bigint -> string +end let debug = ref false -let filter = List.partition +module MakeOmegaSolver (Int:INT) = struct + +type bigint = Int.bigint +let (<?) = Int.less_than +let (<=?) x y = Int.less_than x y or x = y +let (>?) x y = Int.less_than y x +let (>=?) x y = Int.less_than y x or x = y +let (=?) = (=) +let (+) = Int.add +let (-) = Int.sub +let ( * ) = Int.mult +let (/) x y = fst (Int.euclid x y) +let (mod) x y = snd (Int.euclid x y) +let zero = Int.zero +let one = Int.one +let two = one + one +let negone = Int.neg one +let abs x = if Int.less_than x zero then Int.neg x else x +let string_of_bigint = Int.to_string +let neg = Int.neg + +(* To ensure that polymorphic (<) is not used mistakenly on big integers *) +(* Warning: do not use (=) either on big int *) +let (<) = ((<) : int -> int -> bool) +let (>) = ((>) : int -> int -> bool) +let (<=) = ((<=) : int -> int -> bool) +let (>=) = ((>=) : int -> int -> bool) + +let pp i = print_int i; print_newline (); flush stdout let push v l = l := v :: !l -let rec pgcd x y = if y = 0 then x else pgcd y (x mod y) +let rec pgcd x y = if y =? zero then x else pgcd y (x mod y) let pgcd_l = function | [] -> failwith "pgcd_l" | x :: l -> List.fold_left pgcd x l let floor_div a b = - match a >=0 , b > 0 with + match a >=? zero , b >? zero with | true,true -> a / b | false,false -> a / b - | true, false -> (a-1) / b - 1 - | false,true -> (a+1) / b - 1 + | true, false -> (a-one) / b - one + | false,true -> (a+one) / b - one -let new_id = - let cpt = ref 0 in fun () -> incr cpt; ! cpt - -let new_var = - let cpt = ref 0 in fun () -> incr cpt; Nameops.make_ident "WW" (Some !cpt) - -let new_var_num = - let cpt = ref 1000 in (fun () -> incr cpt; !cpt) - -type coeff = {c: int ; v: int} +type coeff = {c: bigint ; v: int} type linear = coeff list @@ -70,60 +93,63 @@ type afine = { (* the variables and their coefficient *) body: coeff list; (* a constant *) - constant: int } + constant: bigint } + +type state_action = { + st_new_eq : afine; + st_def : afine; + st_orig : afine; + st_coef : bigint; + st_var : int } type action = - | DIVIDE_AND_APPROX of afine * afine * int * int - | NOT_EXACT_DIVIDE of afine * int + | DIVIDE_AND_APPROX of afine * afine * bigint * bigint + | NOT_EXACT_DIVIDE of afine * bigint | FORGET_C of int - | EXACT_DIVIDE of afine * int - | SUM of int * (int * afine) * (int * afine) - | STATE of afine * afine * afine * int * int + | EXACT_DIVIDE of afine * bigint + | SUM of int * (bigint * afine) * (bigint * afine) + | STATE of state_action | HYP of afine | FORGET of int * int | FORGET_I of int * int | CONTRADICTION of afine * afine | NEGATE_CONTRADICT of afine * afine * bool - | MERGE_EQ of int * afine * int - | CONSTANT_NOT_NUL of int * int + | MERGE_EQ of int * afine * int + | CONSTANT_NOT_NUL of int * bigint | CONSTANT_NUL of int - | CONSTANT_NEG of int * int + | CONSTANT_NEG of int * bigint | SPLIT_INEQ of afine * (int * action list) * (int * action list) - | WEAKEN of int * int + | WEAKEN of int * bigint exception UNSOLVABLE exception NO_CONTRADICTION -let intern_id,unintern_id = - let cpt = ref 0 in - let table = create 7 and co_table = create 7 in - (fun (name : identifier) -> - try find table name with Not_found -> - let idx = !cpt in - add table name idx; add co_table idx name; incr cpt; idx), - (fun idx -> - try find co_table idx with Not_found -> - let v = new_var () in add table v idx; add co_table idx v; v) - -let display_eq (l,e) = +let display_eq print_var (l,e) = let _ = List.fold_left (fun not_first f -> print_string - (if f.c < 0 then "- " else if not_first then "+ " else ""); + (if f.c <? zero then "- " else if not_first then "+ " else ""); let c = abs f.c in - if c = 1 then - Printf.printf "%s " (string_of_id (unintern_id f.v)) + if c =? one then + Printf.printf "%s " (print_var f.v) else - Printf.printf "%d %s " c (string_of_id (unintern_id f.v)); + Printf.printf "%s %s " (string_of_bigint c) (print_var f.v); true) false l in - if e > 0 then - Printf.printf "+ %d " e - else if e < 0 then - Printf.printf "- %d " (abs e) + if e >? zero then + Printf.printf "+ %s " (string_of_bigint e) + else if e <? zero then + Printf.printf "- %s " (string_of_bigint (abs e)) + +let rec trace_length l = + let action_length accu = function + | SPLIT_INEQ (_,(_,l1),(_,l2)) -> + accu + one + trace_length l1 + trace_length l2 + | _ -> accu + one in + List.fold_left action_length zero l let operator_of_eq = function | EQUA -> "=" | DISE -> "!=" | INEQ -> ">=" @@ -131,49 +157,51 @@ let operator_of_eq = function let kind_of = function | EQUA -> "equation" | DISE -> "disequation" | INEQ -> "inequation" -let display_system l = +let display_system print_var l = List.iter (fun { kind=b; body=e; constant=c; id=id} -> - print_int id; print_string ": "; - display_eq (e,c); print_string (operator_of_eq b); - print_string "0\n") + Printf.printf "E%d: " id; + display_eq print_var (e,c); + Printf.printf "%s 0\n" (operator_of_eq b)) l; print_string "------------------------\n\n" -let display_inequations l = - List.iter (fun e -> display_eq e;print_string ">= 0\n") l; +let display_inequations print_var l = + List.iter (fun e -> display_eq print_var e;print_string ">= 0\n") l; print_string "------------------------\n\n" -let rec display_action = function +let sbi = string_of_bigint + +let rec display_action print_var = function | act :: l -> begin match act with | DIVIDE_AND_APPROX (e1,e2,k,d) -> Printf.printf - "Inequation E%d is divided by %d and the constant coefficient is \ - rounded by substracting %d.\n" e1.id k d + "Inequation E%d is divided by %s and the constant coefficient is \ + rounded by substracting %s.\n" e1.id (sbi k) (sbi d) | NOT_EXACT_DIVIDE (e,k) -> Printf.printf "Constant in equation E%d is not divisible by the pgcd \ - %d of its other coefficients.\n" e.id k + %s of its other coefficients.\n" e.id (sbi k) | EXACT_DIVIDE (e,k) -> Printf.printf "Equation E%d is divided by the pgcd \ - %d of its coefficients.\n" e.id k + %s of its coefficients.\n" e.id (sbi k) | WEAKEN (e,k) -> Printf.printf "To ensure a solution in the dark shadow \ - the equation E%d is weakened by %d.\n" e k + the equation E%d is weakened by %s.\n" e (sbi k) | SUM (e,(c1,e1),(c2,e2)) -> Printf.printf - "We state %s E%d = %d %s E%d + %d %s E%d.\n" - (kind_of e1.kind) e c1 (kind_of e1.kind) e1.id c2 + "We state %s E%d = %s %s E%d + %s %s E%d.\n" + (kind_of e1.kind) e (sbi c1) (kind_of e1.kind) e1.id (sbi c2) (kind_of e2.kind) e2.id - | STATE (e,_,_,x,_) -> - Printf.printf "We define a new equation %d :" e.id; - display_eq (e.body,e.constant); - print_string (operator_of_eq e.kind); print_string " 0\n" + | STATE { st_new_eq = e } -> + Printf.printf "We define a new equation E%d: " e.id; + display_eq print_var (e.body,e.constant); + print_string (operator_of_eq e.kind); print_string " 0" | HYP e -> - Printf.printf "We define %d :" e.id; - display_eq (e.body,e.constant); + Printf.printf "We define E%d: " e.id; + display_eq print_var (e.body,e.constant); print_string (operator_of_eq e.kind); print_string " 0\n" | FORGET_C e -> Printf.printf "E%d is trivially satisfiable.\n" e | FORGET (e1,e2) -> Printf.printf "E%d subsumes E%d.\n" e1 e2 @@ -182,33 +210,34 @@ let rec display_action = function Printf.printf "E%d and E%d can be merged into E%d.\n" e1.id e2 e | CONTRADICTION (e1,e2) -> Printf.printf - "equations E%d and E%d implie a contradiction on their \ + "Equations E%d and E%d imply a contradiction on their \ constant factors.\n" e1.id e2.id | NEGATE_CONTRADICT(e1,e2,b) -> Printf.printf - "Eqations E%d and E%d state that their body is at the same time + "Equations E%d and E%d state that their body is at the same time equal and different\n" e1.id e2.id | CONSTANT_NOT_NUL (e,k) -> - Printf.printf "equation E%d states %d=0.\n" e k + Printf.printf "Equation E%d states %s = 0.\n" e (sbi k) | CONSTANT_NEG(e,k) -> - Printf.printf "equation E%d states %d >= 0.\n" e k + Printf.printf "Equation E%d states %s >= 0.\n" e (sbi k) | CONSTANT_NUL e -> - Printf.printf "inequation E%d states 0 != 0.\n" e + Printf.printf "Inequation E%d states 0 != 0.\n" e | SPLIT_INEQ (e,(e1,l1),(e2,l2)) -> - Printf.printf "equation E%d is split in E%d and E%d\n\n" e.id e1 e2; - display_action l1; + Printf.printf "Equation E%d is split in E%d and E%d\n\n" e.id e1 e2; + display_action print_var l1; print_newline (); - display_action l2; + display_action print_var l2; print_newline () - end; display_action l + end; display_action print_var l | [] -> flush stdout -(*""*) +let default_print_var v = Printf.sprintf "X%d" v (* For debugging *) +(*""*) let add_event, history, clear_history = let accu = ref [] in - (fun (v : action) -> if !debug then display_action [v]; push v accu), + (fun (v:action) -> if !debug then display_action default_print_var [v]; push v accu), (fun () -> !accu), (fun () -> accu := []) @@ -218,7 +247,7 @@ let nf ((b : bool),(e,(x : int))) = (b,(nf_linear e,x)) let map_eq_linear f = let rec loop = function - | x :: l -> let c = f x.c in if c=0 then loop l else {v=x.v; c=c} :: loop l + | x :: l -> let c = f x.c in if c=?zero then loop l else {v=x.v; c=c} :: loop l | [] -> [] in loop @@ -227,28 +256,28 @@ let map_eq_afine f e = { id = e.id; kind = e.kind; body = map_eq_linear f e.body; constant = f e.constant } -let negate_eq = map_eq_afine (fun x -> -x) +let negate_eq = map_eq_afine (fun x -> neg x) let rec sum p0 p1 = match (p0,p1) with | ([], l) -> l | (l, []) -> l | (((x1::l1) as l1'), ((x2::l2) as l2')) -> if x1.v = x2.v then let c = x1.c + x2.c in - if c = 0 then sum l1 l2 else {v=x1.v;c=c} :: sum l1 l2 + if c =? zero then sum l1 l2 else {v=x1.v;c=c} :: sum l1 l2 else if x1.v > x2.v then x1 :: sum l1 l2' else x2 :: sum l1' l2 -let sum_afine eq1 eq2 = - { kind = eq1.kind; id = new_id (); +let sum_afine new_eq_id eq1 eq2 = + { kind = eq1.kind; id = new_eq_id (); body = sum eq1.body eq2.body; constant = eq1.constant + eq2.constant } exception FACTOR1 let rec chop_factor_1 = function | x :: l -> - if abs x.c = 1 then x,l else let (c',l') = chop_factor_1 l in (c',x::l') + if abs x.c =? one then x,l else let (c',l') = chop_factor_1 l in (c',x::l') | [] -> raise FACTOR1 exception CHOPVAR @@ -261,24 +290,24 @@ let normalize ({id=id; kind=eq_flag; body=e; constant =x} as eq) = if e = [] then begin match eq_flag with | EQUA -> - if x =0 then [] else begin + if x =? zero then [] else begin add_event (CONSTANT_NOT_NUL(id,x)); raise UNSOLVABLE end | DISE -> - if x <> 0 then [] else begin + if x <> zero then [] else begin add_event (CONSTANT_NUL id); raise UNSOLVABLE end | INEQ -> - if x >= 0 then [] else begin + if x >=? zero then [] else begin add_event (CONSTANT_NEG(id,x)); raise UNSOLVABLE end end else let gcd = pgcd_l (List.map (fun f -> abs f.c) e) in - if eq_flag=EQUA & x mod gcd <> 0 then begin + if eq_flag=EQUA & x mod gcd <> zero then begin add_event (NOT_EXACT_DIVIDE (eq,gcd)); raise UNSOLVABLE - end else if eq_flag=DISE & x mod gcd <> 0 then begin + end else if eq_flag=DISE & x mod gcd <> zero then begin add_event (FORGET_C eq.id); [] - end else if gcd <> 1 then begin + end else if gcd <> one then begin let c = floor_div x gcd in let d = x - c * gcd in let new_eq = {id=id; kind=eq_flag; constant=c; @@ -288,97 +317,107 @@ let normalize ({id=id; kind=eq_flag; body=e; constant =x} as eq) = [new_eq] end else [eq] -let eliminate_with_in {v=v;c=c_unite} eq2 +let eliminate_with_in new_eq_id {v=v;c=c_unite} eq2 ({body=e1; constant=c1} as eq1) = try let (f,_) = chop_var v e1 in - let coeff = if c_unite=1 then -f.c else if c_unite= -1 then f.c + let coeff = if c_unite=?one then neg f.c else if c_unite=? negone then f.c else failwith "eliminate_with_in" in - let res = sum_afine eq1 (map_eq_afine (fun c -> c * coeff) eq2) in - add_event (SUM (res.id,(1,eq1),(coeff,eq2))); res + let res = sum_afine new_eq_id eq1 (map_eq_afine (fun c -> c * coeff) eq2) in + add_event (SUM (res.id,(one,eq1),(coeff,eq2))); res with CHOPVAR -> eq1 -let omega_mod a b = a - b * floor_div (2 * a + b) (2 * b) -let banerjee_step original l1 l2 = +let omega_mod a b = a - b * floor_div (two * a + b) (two * b) +let banerjee_step (new_eq_id,new_var_id,print_var) original l1 l2 = let e = original.body in - let sigma = new_var_num () in + let sigma = new_var_id () in let smallest,var = try - List.fold_left (fun (v,p) c -> if v > (abs c.c) then abs c.c,c.v else (v,p)) + List.fold_left (fun (v,p) c -> if v >? (abs c.c) then abs c.c,c.v else (v,p)) (abs (List.hd e).c, (List.hd e).v) (List.tl e) - with Failure "tl" -> display_system [original] ; failwith "TL" in - let m = smallest + 1 in + with Failure "tl" -> display_system print_var [original] ; failwith "TL" in + let m = smallest + one in let new_eq = { constant = omega_mod original.constant m; - body = {c= -m;v=sigma} :: + body = {c= neg m;v=sigma} :: map_eq_linear (fun a -> omega_mod a m) original.body; - id = new_id (); kind = EQUA } in + id = new_eq_id (); kind = EQUA } in let definition = - { constant = - floor_div (2 * original.constant + m) (2 * m); - body = map_eq_linear (fun a -> - floor_div (2 * a + m) (2 * m)) + { constant = neg (floor_div (two * original.constant + m) (two * m)); + body = map_eq_linear (fun a -> neg (floor_div (two * a + m) (two * m))) original.body; - id = new_id (); kind = EQUA } in - add_event (STATE (new_eq,definition,original,m,sigma)); + id = new_eq_id (); kind = EQUA } in + add_event (STATE {st_new_eq = new_eq; st_def = definition; + st_orig = original; st_coef = m; st_var = sigma}); let new_eq = List.hd (normalize new_eq) in let eliminated_var, def = chop_var var new_eq.body in let other_equations = - flat_map (fun e -> normalize (eliminate_with_in eliminated_var new_eq e)) - l1 in + Util.list_map_append + (fun e -> + normalize (eliminate_with_in new_eq_id eliminated_var new_eq e)) l1 in let inequations = - flat_map (fun e -> normalize (eliminate_with_in eliminated_var new_eq e)) - l2 in - let original' = eliminate_with_in eliminated_var new_eq original in + Util.list_map_append + (fun e -> + normalize (eliminate_with_in new_eq_id eliminated_var new_eq e)) l2 in + let original' = eliminate_with_in new_eq_id eliminated_var new_eq original in let mod_original = map_eq_afine (fun c -> c / m) original' in add_event (EXACT_DIVIDE (original',m)); List.hd (normalize mod_original),other_equations,inequations -let rec eliminate_one_equation (e,other,ineqs) = - if !debug then display_system (e::other); +let rec eliminate_one_equation ((new_eq_id,new_var_id,print_var) as new_ids) (e,other,ineqs) = + if !debug then display_system print_var (e::other); try let v,def = chop_factor_1 e.body in - (flat_map (fun e' -> normalize (eliminate_with_in v e e')) other, - flat_map (fun e' -> normalize (eliminate_with_in v e e')) ineqs) - with FACTOR1 -> eliminate_one_equation (banerjee_step e other ineqs) - -let rec banerjee (sys_eq,sys_ineq) = + (Util.list_map_append + (fun e' -> normalize (eliminate_with_in new_eq_id v e e')) other, + Util.list_map_append + (fun e' -> normalize (eliminate_with_in new_eq_id v e e')) ineqs) + with FACTOR1 -> + eliminate_one_equation new_ids (banerjee_step new_ids e other ineqs) + +let rec banerjee ((_,_,print_var) as new_ids) (sys_eq,sys_ineq) = let rec fst_eq_1 = function (eq::l) -> - if List.exists (fun x -> abs x.c = 1) eq.body then eq,l + if List.exists (fun x -> abs x.c =? one) eq.body then eq,l else let (eq',l') = fst_eq_1 l in (eq',eq::l') | [] -> raise Not_found in match sys_eq with - [] -> if !debug then display_system sys_ineq; sys_ineq + [] -> if !debug then display_system print_var sys_ineq; sys_ineq | (e1::rest) -> let eq,other = try fst_eq_1 sys_eq with Not_found -> (e1,rest) in if eq.body = [] then - if eq.constant = 0 then begin - add_event (FORGET_C eq.id); banerjee (other,sys_ineq) + if eq.constant =? zero then begin + add_event (FORGET_C eq.id); banerjee new_ids (other,sys_ineq) end else begin add_event (CONSTANT_NOT_NUL(eq.id,eq.constant)); raise UNSOLVABLE end - else banerjee (eliminate_one_equation (eq,other,sys_ineq)) + else + banerjee new_ids + (eliminate_one_equation new_ids (eq,other,sys_ineq)) + type kind = INVERTED | NORMAL -let redundancy_elimination system = + +let redundancy_elimination new_eq_id system = let normal = function - ({body=f::_} as e) when f.c < 0 -> negate_eq e, INVERTED + ({body=f::_} as e) when f.c <? zero -> negate_eq e, INVERTED | e -> e,NORMAL in - let table = create 7 in + let table = Hashtbl.create 7 in List.iter (fun e -> let ({body=ne} as nx) ,kind = normal e in if ne = [] then - if nx.constant < 0 then begin + if nx.constant <? zero then begin add_event (CONSTANT_NEG(nx.id,nx.constant)); raise UNSOLVABLE end else add_event (FORGET_C nx.id) else try - let (optnormal,optinvert) = find table ne in + let (optnormal,optinvert) = Hashtbl.find table ne in let final = if kind = NORMAL then begin match optnormal with Some v -> let kept = - if v.constant < nx.constant + if v.constant <? nx.constant then begin add_event (FORGET (v.id,nx.id));v end else begin add_event (FORGET (nx.id,v.id));nx end in (Some(kept),optinvert) @@ -386,32 +425,32 @@ let redundancy_elimination system = end else begin match optinvert with Some v -> - let kept = - if v.constant > nx.constant + let _kept = + if v.constant >? nx.constant then begin add_event (FORGET_I (v.id,nx.id));v end else begin add_event (FORGET_I (nx.id,v.id));nx end in - (optnormal,Some(if v.constant > nx.constant then v else nx)) + (optnormal,Some(if v.constant >? nx.constant then v else nx)) | None -> optnormal,Some nx end in begin match final with (Some high, Some low) -> - if high.constant < low.constant then begin + if high.constant <? low.constant then begin add_event(CONTRADICTION (high,negate_eq low)); raise UNSOLVABLE end | _ -> () end; - remove table ne; - add table ne final + Hashtbl.remove table ne; + Hashtbl.add table ne final with Not_found -> - add table ne + Hashtbl.add table ne (if kind = NORMAL then (Some nx,None) else (None,Some nx))) system; let accu_eq = ref [] in let accu_ineq = ref [] in - iter + Hashtbl.iter (fun p0 p1 -> match (p0,p1) with - | (e, (Some x, Some y)) when x.constant = y.constant -> - let id=new_id () in + | (e, (Some x, Some y)) when x.constant =? y.constant -> + let id=new_eq_id () in add_event (MERGE_EQ(id,x,y.id)); push {id=id; kind=EQUA; body=x.body; constant=x.constant} accu_eq | (e, (optnorm,optinvert)) -> @@ -425,17 +464,17 @@ let redundancy_elimination system = exception SOLVED_SYSTEM let select_variable system = - let table = create 7 in + let table = Hashtbl.create 7 in let push v c= - try let r = find table v in r := max !r (abs c) - with Not_found -> add table v (ref (abs c)) in + try let r = Hashtbl.find table v in r := max !r (abs c) + with Not_found -> Hashtbl.add table v (ref (abs c)) in List.iter (fun {body=l} -> List.iter (fun f -> push f.v f.c) l) system; - let vmin,cmin = ref (-1), ref 0 in + let vmin,cmin = ref (-1), ref zero in let var_cpt = ref 0 in - iter + Hashtbl.iter (fun v ({contents = c}) -> incr var_cpt; - if c < !cmin or !vmin = (-1) then begin vmin := v; cmin := c end) + if c <? !cmin or !vmin = (-1) then begin vmin := v; cmin := c end) table; if !var_cpt < 1 then raise SOLVED_SYSTEM; !vmin @@ -444,25 +483,25 @@ let classify v system = List.fold_left (fun (not_occ,below,over) eq -> try let f,eq' = chop_var v eq.body in - if f.c >= 0 then (not_occ,((f.c,eq) :: below),over) - else (not_occ,below,((-f.c,eq) :: over)) + if f.c >=? zero then (not_occ,((f.c,eq) :: below),over) + else (not_occ,below,((neg f.c,eq) :: over)) with CHOPVAR -> (eq::not_occ,below,over)) ([],[],[]) system -let product dark_shadow low high = +let product new_eq_id dark_shadow low high = List.fold_left (fun accu (a,eq1) -> List.fold_left (fun accu (b,eq2) -> let eq = - sum_afine (map_eq_afine (fun c -> c * b) eq1) + sum_afine new_eq_id (map_eq_afine (fun c -> c * b) eq1) (map_eq_afine (fun c -> c * a) eq2) in add_event(SUM(eq.id,(b,eq1),(a,eq2))); match normalize eq with | [eq] -> let final_eq = if dark_shadow then - let delta = (a - 1) * (b - 1) in + let delta = (a - one) * (b - one) in add_event(WEAKEN(eq.id,delta)); {id = eq.id; kind=INEQ; body = eq.body; constant = eq.constant - delta} @@ -473,33 +512,34 @@ let product dark_shadow low high = accu high) [] low -let fourier_motzkin dark_shadow system = +let fourier_motzkin (new_eq_id,_,print_var) dark_shadow system = let v = select_variable system in let (ineq_out, ineq_low,ineq_high) = classify v system in - let expanded = ineq_out @ product dark_shadow ineq_low ineq_high in - if !debug then display_system expanded; expanded + let expanded = ineq_out @ product new_eq_id dark_shadow ineq_low ineq_high in + if !debug then display_system print_var expanded; expanded -let simplify dark_shadow system = +let simplify ((new_eq_id,new_var_id,print_var) as new_ids) dark_shadow system = if List.exists (fun e -> e.kind = DISE) system then failwith "disequation in simplify"; clear_history (); List.iter (fun e -> add_event (HYP e)) system; - let system = flat_map normalize system in - let eqs,ineqs = filter (fun e -> e.kind=EQUA) system in - let simp_eq,simp_ineq = redundancy_elimination ineqs in + let system = Util.list_map_append normalize system in + let eqs,ineqs = List.partition (fun e -> e.kind=EQUA) system in + let simp_eq,simp_ineq = redundancy_elimination new_eq_id ineqs in let system = (eqs @ simp_eq,simp_ineq) in let rec loop1a system = - let sys_ineq = banerjee system in + let sys_ineq = banerjee new_ids system in loop1b sys_ineq and loop1b sys_ineq = - let simp_eq,simp_ineq = redundancy_elimination sys_ineq in + let simp_eq,simp_ineq = redundancy_elimination new_eq_id sys_ineq in if simp_eq = [] then simp_ineq else loop1a (simp_eq,simp_ineq) in let rec loop2 system = try - let expanded = fourier_motzkin dark_shadow system in + let expanded = fourier_motzkin new_ids dark_shadow system in loop2 (loop1b expanded) - with SOLVED_SYSTEM -> if !debug then display_system system; system + with SOLVED_SYSTEM -> + if !debug then display_system print_var system; system in loop2 (loop1a system) @@ -520,11 +560,9 @@ let rec depend relie_on accu = function depend (e1.id::e2.id::relie_on) (act::accu) l else depend relie_on accu l - | STATE (e,_,o,_,_) -> - if List.mem e.id relie_on then - depend (o.id::relie_on) (act::accu) l - else - depend relie_on accu l + | STATE {st_new_eq=e;st_orig=o} -> + if List.mem e.id relie_on then depend (o.id::relie_on) (act::accu) l + else depend relie_on accu l | HYP e -> if List.mem e.id relie_on then depend relie_on (act::accu) l else depend relie_on accu l @@ -548,59 +586,68 @@ let rec depend relie_on accu = function end | [] -> relie_on, accu -let solve system = - try let _ = simplify false system in failwith "no contradiction" - with UNSOLVABLE -> display_action (snd (depend [] [] (history ()))) +(* +let depend relie_on accu trace = + Printf.printf "Longueur de la trace initiale : %d\n" + (trace_length trace + trace_length accu); + let rel',trace' = depend relie_on accu trace in + Printf.printf "Longueur de la trace simplifiée : %d\n" (trace_length trace'); + rel',trace' +*) + +let solve (new_eq_id,new_eq_var,print_var) system = + try let _ = simplify new_eq_id false system in failwith "no contradiction" + with UNSOLVABLE -> display_action print_var (snd (depend [] [] (history ()))) let negation (eqs,ineqs) = - let diseq,_ = filter (fun e -> e.kind = DISE) ineqs in + let diseq,_ = List.partition (fun e -> e.kind = DISE) ineqs in let normal = function - | ({body=f::_} as e) when f.c < 0 -> negate_eq e, INVERTED + | ({body=f::_} as e) when f.c <? zero -> negate_eq e, INVERTED | e -> e,NORMAL in - let table = create 7 in + let table = Hashtbl.create 7 in List.iter (fun e -> let {body=ne;constant=c} ,kind = normal e in - add table (ne,c) (kind,e)) diseq; + Hashtbl.add table (ne,c) (kind,e)) diseq; List.iter (fun e -> - if e.kind <> EQUA then pp 9999; + assert (e.kind = EQUA); let {body=ne;constant=c},kind = normal e in try - let (kind',e') = find table (ne,c) in + let (kind',e') = Hashtbl.find table (ne,c) in add_event (NEGATE_CONTRADICT (e,e',kind=kind')); raise UNSOLVABLE with Not_found -> ()) eqs exception FULL_SOLUTION of action list * int list -let simplify_strong system = +let simplify_strong ((new_eq_id,new_var_id,print_var) as new_ids) system = clear_history (); List.iter (fun e -> add_event (HYP e)) system; (* Initial simplification phase *) let rec loop1a system = negation system; - let sys_ineq = banerjee system in + let sys_ineq = banerjee new_ids system in loop1b sys_ineq and loop1b sys_ineq = - let dise,ine = filter (fun e -> e.kind = DISE) sys_ineq in - let simp_eq,simp_ineq = redundancy_elimination ine in + let dise,ine = List.partition (fun e -> e.kind = DISE) sys_ineq in + let simp_eq,simp_ineq = redundancy_elimination new_eq_id ine in if simp_eq = [] then dise @ simp_ineq else loop1a (simp_eq,dise @ simp_ineq) in let rec loop2 system = try - let expanded = fourier_motzkin false system in + let expanded = fourier_motzkin new_ids false system in loop2 (loop1b expanded) - with SOLVED_SYSTEM -> if !debug then display_system system; system + with SOLVED_SYSTEM -> if !debug then display_system print_var system; system in let rec explode_diseq = function | (de::diseq,ineqs,expl_map) -> - let id1 = new_id () - and id2 = new_id () in + let id1 = new_eq_id () + and id2 = new_eq_id () in let e1 = - {id = id1; kind=INEQ; body = de.body; constant = de.constant - 1} in + {id = id1; kind=INEQ; body = de.body; constant = de.constant -one} in let e2 = - {id = id2; kind=INEQ; body = map_eq_linear (fun x -> -x) de.body; - constant = - de.constant - 1} in + {id = id2; kind=INEQ; body = map_eq_linear neg de.body; + constant = neg de.constant - one} in let new_sys = List.map (fun (what,sys) -> ((de.id,id1,true)::what, e1::sys)) ineqs @ @@ -611,13 +658,13 @@ let simplify_strong system = | ([],ineqs,expl_map) -> ineqs,expl_map in try - let system = flat_map normalize system in - let eqs,ineqs = filter (fun e -> e.kind=EQUA) system in - let dise,ine = filter (fun e -> e.kind = DISE) ineqs in - let simp_eq,simp_ineq = redundancy_elimination ine in + let system = Util.list_map_append normalize system in + let eqs,ineqs = List.partition (fun e -> e.kind=EQUA) system in + let dise,ine = List.partition (fun e -> e.kind = DISE) ineqs in + let simp_eq,simp_ineq = redundancy_elimination new_eq_id ine in let system = (eqs @ simp_eq,simp_ineq @ dise) in let system' = loop1a system in - let diseq,ineq = filter (fun e -> e.kind = DISE) system' in + let diseq,ineq = List.partition (fun e -> e.kind = DISE) system' in let first_segment = history () in let sys_exploded,explode_map = explode_diseq (diseq,[[],ineq],[]) in let all_solutions = @@ -627,20 +674,21 @@ let simplify_strong system = try let _ = loop2 sys in raise NO_CONTRADICTION with UNSOLVABLE -> let relie_on,path = depend [] [] (history ()) in - let dc,_ = filter (fun (_,id,_) -> List.mem id relie_on) decomp in + let dc,_ = List.partition (fun (_,id,_) -> List.mem id relie_on) decomp in let red = List.map (fun (x,_,_) -> x) dc in (red,relie_on,decomp,path)) sys_exploded in let max_count sys = - let tbl = create 7 in + let tbl = Hashtbl.create 7 in let augment x = - try incr (find tbl x) with Not_found -> add tbl x (ref 1) in + try incr (Hashtbl.find tbl x) + with Not_found -> Hashtbl.add tbl x (ref 1) in let eq = ref (-1) and c = ref 0 in List.iter (function | ([],r_on,_,path) -> raise (FULL_SOLUTION (path,r_on)) | (l,_,_,_) -> List.iter augment l) sys; - iter (fun x v -> if !v > !c then begin eq := x; c := !v end) tbl; + Hashtbl.iter (fun x v -> if !v > !c then begin eq := x; c := !v end) tbl; !eq in let rec solve systems = @@ -649,17 +697,20 @@ let simplify_strong system = let rec sign = function | ((id',_,b)::l) -> if id=id' then b else sign l | [] -> failwith "solve" in - let s1,s2 = filter (fun (_,_,decomp,_) -> sign decomp) systems in + let s1,s2 = + List.partition (fun (_,_,decomp,_) -> sign decomp) systems in let s1' = - List.map (fun (dep,ro,dc,pa) -> (list_except id dep,ro,dc,pa)) s1 in + List.map (fun (dep,ro,dc,pa) -> (Util.list_except id dep,ro,dc,pa)) s1 in let s2' = - List.map (fun (dep,ro,dc,pa) -> (list_except id dep,ro,dc,pa)) s2 in + List.map (fun (dep,ro,dc,pa) -> (Util.list_except id dep,ro,dc,pa)) s2 in let (r1,relie1) = solve s1' and (r2,relie2) = solve s2' in let (eq,id1,id2) = List.assoc id explode_map in - [SPLIT_INEQ(eq,(id1,r1),(id2, r2))], eq.id :: list_union relie1 relie2 + [SPLIT_INEQ(eq,(id1,r1),(id2, r2))], eq.id :: Util.list_union relie1 relie2 with FULL_SOLUTION (x0,x1) -> (x0,x1) in let act,relie_on = solve all_solutions in snd(depend relie_on act first_segment) with UNSOLVABLE -> snd (depend [] [] (history ())) + +end |