X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=ocaml%2Fnum.ml;h=2bc253d0554bbdec893c04d6878e2354cfb31020;hb=dcb2ece094f794f4e9f4f98b92f378998e92a919;hp=7f94b251fcf51d2fceed7f17773e776476d2102a;hpb=a56b79f325d6fc7e85ec0b65669047232674e98b;p=fireball-separation.git diff --git a/ocaml/num.ml b/ocaml/num.ml index 7f94b25..2bc253d 100644 --- a/ocaml/num.ml +++ b/ocaml/num.ml @@ -2,6 +2,9 @@ open Util open Util.Vars open Pure +(* debug options *) +let debug_display_arities = false;; + (************ Syntax ************************************) (* Normal forms*) @@ -15,13 +18,14 @@ open Pure and i = | I of int * nf listx ;;*) -type 'nf i_var_ = [ `I of int * 'nf Listx.listx | `Var of int ] +type var = int * (* arity of variable*) int;; +type 'nf i_var_ = [ `I of var * 'nf Listx.listx | `Var of var ] type 'nf i_n_var_ = [ `N of int | 'nf i_var_ ] type 'nf i_num_var_ = [ | 'nf i_n_var_ - | `Match of 'nf i_num_var_ * (* arity of branches *) int * (*lift*) int * (*branches*)(int * 'nf) list ref * (*args*)'nf list + | `Match of 'nf i_num_var_ * (* originating var *) var * (*lift*) int * (*branches*)(int * 'nf) list ref * (*args*)'nf list ] -type 'nf nf_ = [ `Lam of (* was_unpacked *) bool * (* arity of variable*) int * 'nf nf_ | 'nf i_num_var_ ] +type 'nf nf_ = [ `Lam of (* was_unpacked *) bool * 'nf nf_ | 'nf i_num_var_ ] type nf = nf nf_ type i_var = nf i_var_;; type i_n_var = nf i_n_var_;; @@ -29,28 +33,35 @@ type i_num_var = nf i_num_var_;; let hd_of_i_var = function - `I (v,_) - | `Var v -> v + `I ((v,_),_) + | `Var (v,_) -> v let hd_of = function - `I (v,_) - | `Var v -> Some v + `I ((v,_),_) + | `Var(v,_) -> Some v | `N _ -> None | `Match _ -> assert false +let arity_of_hd = +function + `I ((_,a),_) +| `Var(_,a) -> a +| _ -> 0 (* FIXME? *) + let lift m (t : nf) = + let aux_var l (n, ar) = (if n < l then n else n+m), ar in let rec aux_i_num_var l = function - `I(n,args) -> (`I((if n < l then n else n+m),Listx.map (aux l) args) : i_num_var) - | `Var n -> `Var (if n < l then n else n+m) + `I(v,args) -> `I(aux_var l v, Listx.map (aux l) args) + | `Var v -> `Var(aux_var l v) | `N _ as x -> x - | `Match(t,ar,lift,bs,args) -> - `Match(aux_i_num_var l t, ar,lift + m, bs, List.map (aux l) args) + | `Match(t,v,lift,bs,args) -> + `Match(aux_i_num_var l t, v, lift + m, bs, List.map (aux l) args) and aux l = function #i_num_var as x -> (aux_i_num_var l x :> nf) - | `Lam(b,ar,nf) -> `Lam (b,ar,aux (l+1) nf) + | `Lam(b,nf) -> `Lam (b, aux (l+1) nf) in (aux 0 t : nf) ;; @@ -59,23 +70,24 @@ let lift m (t : nf) = let rec make_lams t = function 0 -> t - | n when n > 0 -> `Lam (false,-666,lift 1 (make_lams t (n-1))) + | n when n > 0 -> `Lam (false, lift 1 (make_lams t (n-1))) | _ -> assert false -let free_vars = +let free_vars' = let rec aux n = function `N _ -> [] - | `Var x -> if x < n then [] else [x-n] - | `I(x,args) -> - (if x < n then [] else [x-n]) @ + | `Var(x,ar) -> if x < n then [] else [(x-n,ar)] + | `I((x,ar),args) -> + (if x < n then [] else [(x-n,ar)]) @ List.concat (List.map (aux n) (Listx.to_list args)) - | `Lam(_,_,t) -> aux (n+1) t + | `Lam(_,t) -> aux (n+1) t | `Match(t,_,liftno,bs,args) -> aux n (t :> nf) @ List.concat (List.map (fun (_,t) -> aux (n-liftno) t) !bs) @ List.concat (List.map (aux n) args) in aux 0 ;; +let free_vars = (List.map fst) ++ free_vars';; module ToScott = struct @@ -83,53 +95,41 @@ struct let rec t_of_i_num_var = function | `N n -> Scott.mk_n n - | `Var v -> Pure.V v + | `Var(v,_) -> Pure.V v | `Match(t,_,liftno,bs,args) -> let bs = List.map (fun (n,t) -> n, t_of_nf (lift liftno t)) !bs in let t = t_of_i_num_var t in let m = Scott.mk_match t bs in List.fold_left (fun acc t -> Pure.A(acc,t_of_nf t)) m args - | `I(v, args) -> Listx.fold_left (fun acc t -> Pure.A(acc,t_of_nf t)) (Pure.V v) args + | `I((v,_), args) -> Listx.fold_left (fun acc t -> Pure.A(acc,t_of_nf t)) (Pure.V v) args and t_of_nf = function | #i_num_var as x -> t_of_i_num_var x - | `Lam(b,_,f) -> Pure.L (t_of_nf f) + | `Lam(b,f) -> Pure.L (t_of_nf f) end (************ Pretty-printing ************************************) -let rec print ?(l=[]) = - function - `Var n -> print_name l n - | `N n -> string_of_int n - | `Match(t,_,bs_lift,bs,args) -> - "([" ^ print ~l (t :> nf) ^ - " ? " ^ String.concat " | " (List.map (fun (n,t) -> string_of_int n ^ " => " ^ print ~l (lift bs_lift t)) !bs) ^ "] " ^ - String.concat " " (List.map (print ~l) args) ^ ")" - | `I(n,args) -> "(" ^ print_name l n ^ " " ^ String.concat " " (Listx.to_list (Listx.map (print ~l) args)) ^ ")" - | `Lam(_,_,nf) -> - let name = string_of_var (List.length l) in - "λ" ^ name ^ "." ^ print ~l:(name::l) (nf : nf) -;; +(* let rec string_of_term l = fun _ -> "";; *) -let rec string_of_term l = - let rec string_of_term_w_pars l = function - | `Var n -> print_name l n +let rec string_of_term l = + let rec string_of_term_w_pars l = function + | `Var(n,ar) -> List.nth l n ^ (if debug_display_arities then ":" ^ string_of_int ar else "") | `N n -> string_of_int n | `I _ as t -> "(" ^ string_of_term_no_pars_app l (t :> nf) ^ ")" | `Lam _ as t -> "(" ^ string_of_term_no_pars_lam l t ^ ")" - | `Match(t,_,bs_lift,bs,args) -> - "(match " ^ string_of_term_no_pars l (t :> nf) ^ - " with " ^ String.concat " | " (List.map (fun (n,t) -> string_of_int n ^ " => " ^ string_of_term l (lift bs_lift t)) !bs) ^ "] " ^ - String.concat " " (List.map (string_of_term l) args) ^ ")" - and string_of_term_no_pars_app l = function - | `I(n, args) -> print_name l n ^ " " ^ String.concat " " (List.map (string_of_term_w_pars l) (Listx.to_list args)) + | `Match(t,(v,ar),bs_lift,bs,args) -> + "["^ List.nth l v ^ (if debug_display_arities then ":"^ string_of_int ar else "") ^",match " ^ string_of_term_no_pars l (t :> nf) ^ + " with " ^ String.concat " | " (List.map (fun (n,t) -> string_of_int n ^ " => " ^ string_of_term l (lift bs_lift (t :> nf))) !bs) ^ "] " ^ + String.concat " " (List.map (string_of_term l) (args :> nf list)) ^ ")" + and string_of_term_no_pars_app l = function + | `I((n,ar), args) -> List.nth l n ^ (if debug_display_arities then ":" ^ string_of_int ar else "") ^ " " ^ String.concat " " (List.map (string_of_term_w_pars l) (Listx.to_list args :> nf list)) | #nf as t -> string_of_term_w_pars l t and string_of_term_no_pars_lam l = function - | `Lam(_,_,t) -> let name = string_of_var (List.length l) in - "λ" ^ name ^ ". " ^ (string_of_term_no_pars_lam (name::l) t) + | `Lam(_,t) -> let name = "x" ^ string_of_int (List.length l) in + "λ" ^ name ^ ". " ^ (string_of_term_no_pars_lam (name::l) t) | _ as t -> string_of_term_no_pars l t and string_of_term_no_pars l : nf -> string = function | `Lam _ as t -> string_of_term_no_pars_lam l t @@ -163,13 +163,23 @@ let cast_to_i_num_var = prerr_endline (print (t :> nf)); assert false (* algorithm failed *) +let rec set_arity arity = function +(* FIXME because onlt variables should be in branches of matches, one day *) +| `Var(n,_) -> `Var(n,arity) +| `N _ as t -> t +| `Lam(false, t) -> `Lam(false, set_arity arity t) +| `Match(t,(n,_),bs_lift,bs,args) -> `Match(t,(n,arity),bs_lift,bs,args) +| `I _ | `Lam _ -> assert false + +let minus1 n = if n = min_int then n else n - 1;; + let rec mk_app (h : nf) (arg : nf) = (*let res =*) match h with - `I(n,args) -> `I(n,Listx.append (Listx.Nil arg) args) - | `Var n -> `I(n, Listx.Nil arg) - | `Lam(_,_,nf) -> subst true 0 arg (nf : nf) (* AC FIXME sanity check on arity *) - | `Match(t,ar,lift,bs,args) -> `Match(t,ar,lift,bs,List.append args [arg]) + `I(v,args) -> `I(v,Listx.append (Listx.Nil arg) args) + | `Var v -> `I(v, Listx.Nil arg) + | `Lam(truelam,nf) -> subst truelam true 0 arg (nf : nf) (* AC FIXME sanity check on arity *) + | `Match(t,v,lift,bs,args) -> `Match(t,v,lift,bs,List.append args [arg]) | `N _ -> assert false (* Numbers cannot be applied *) (*in let l = ["v0";"v1";"v2"] in prerr_endline ("mk_app h:" ^ print ~l h ^ " arg:" ^ print ~l:l arg ^ " res:" ^ print ~l:l res); res*) @@ -180,62 +190,58 @@ and mk_appl h args = and mk_appx h args = Listx.fold_left mk_app h args -and mk_match t ar bs_lift bs args = +and mk_match t (n,ar) bs_lift bs args = (*prerr_endline ("MK_MATCH: ([" ^ print t ^ "] " ^ String.concat " " (Listx.to_list (Listx.map (fun (n,t) -> string_of_int n ^ " => " ^ print t) bs)) ^ ") " ^ String.concat " " (List.map print args));*) match t with `N m -> (try let h = List.assoc m !bs in + let h = set_arity (minus1 ar) h in let h = lift bs_lift h in mk_appl h args with Not_found -> - `Match (t,ar,bs_lift,bs,args)) - | `I _ | `Var _ | `Match _ -> `Match(t,ar,bs_lift,bs,args) - -and subst delift_by_one what (with_what : nf) (where : nf) = + `Match (t,(n,ar),bs_lift,bs,args)) + | `I _ | `Var _ | `Match _ -> `Match(t,(n,ar),bs_lift,bs,args) + +and subst truelam delift_by_one what (with_what : nf) (where : nf) = + let rec aux_propagate_arity ar = function + | `Lam(false, t) when not delift_by_one -> `Lam(false, aux_propagate_arity ar t) + | `Match(`I(v,args),(x,_),liftno,bs,args') when not delift_by_one -> + `Match(`I(v,args),(x,ar),liftno,bs,args') + | `Var(i,oldar) -> `Var(i, if truelam then (assert (oldar = min_int); ar) else oldar) + | _ as t -> t in let rec aux_i_num_var l = function - `I(n,args) -> + `I((n,ar),args) -> if n = what + l then - mk_appx (lift l with_what) (Listx.map (aux l) args) + mk_appx (lift l (aux_propagate_arity ar with_what)) (Listx.map (aux l) args) else - `I ((if delift_by_one && n >= l then n-1 else n), Listx.map (aux l) args) - | `Var n -> + `I (((if delift_by_one && n >= l then n-1 else n), ar), Listx.map (aux l) args) + | `Var(n,ar) -> if n = what + l then - lift l with_what + lift l (aux_propagate_arity ar with_what) else - `Var (if delift_by_one && n >= l then n-1 else n) + `Var((if delift_by_one && n >= l then n-1 else n), ar) | `N _ as x -> x - | `Match(t,ar,bs_lift,bs,args) -> + | `Match(t,v,bs_lift,bs,args) -> let bs_lift = bs_lift + if delift_by_one then -1 else 0 in let l' = l - bs_lift in let with_what' = lift l' with_what in (* The following line should be the identity when delift_by_one = true because we are assuming the ts to not contain lambda-bound variables. *) - bs := List.map (fun (n,t) -> n,subst false what with_what' t) !bs ; - mk_match (cast_to_i_num_var (aux_i_num_var l t)) ar bs_lift bs (List.map (aux l) args) + bs := List.map (fun (n,t) -> n,subst truelam false what with_what' t) !bs ; + mk_match (cast_to_i_num_var (aux_i_num_var l t)) v bs_lift bs (List.map (aux l) args) and aux l(*lift*) = (*function iii -> let res = match iii with*) function | #i_num_var as x -> aux_i_num_var l x - | `Lam(b,ar,nf) -> `Lam(b,ar,aux (l+1) nf) + | `Lam(b, nf) -> `Lam(b, aux (l+1) nf) (*in let ll = ["v0";"v1";"v2"] in prerr_endline ("subst l:" ^ string_of_int l ^ " delift_by_one:" ^ string_of_bool delift_by_one ^ " what:" ^ (List.nth ll what) ^ " with_what:" ^ print ~l:ll with_what ^ " where:" ^ print ~l:ll iii ^ " res:" ^ print ~l:ll res); res*) in aux 0 where ;; -(************ Parsing ************************************) - -let parse' strs = - let rec aux = function - | Parser.Lam t -> `Lam (true,-666,aux t) - | Parser.App (t1, t2) -> mk_app (aux t1) (aux t2) - | Parser.Var v -> `Var v - in let (tms, free) = Parser.parse_many strs - in (List.map aux tms, free) -;; - (************** Algorithm(s) ************************) let eta_compare x y = @@ -249,14 +255,14 @@ let eta_compare x y = | _, [] -> 1 | x::xs, y::ys -> clex aux (lex aux) (x,xs) (y,ys) in let rec aux t1 t2 = match t1, t2 with - | `Var n , `Var m -> compare n m - | `I(n1, l1), `I(n2, l2) -> + | `Var(n,_) , `Var(m,_) -> compare n m + | `I((n1,_), l1), `I((n2,_), l2) -> clex compare (lex aux) (n1, Listx.to_list l1) (n2, Listx.to_list l2) | `Lam _, `N _ -> -1 | `N _, `Lam _ -> 1 - | `Lam(_,_,t1), `Lam(_,_,t2) -> aux t1 t2 - | `Lam(_,_,t1), t2 -> - aux t1 (mk_app (lift 1 t2) (`Var 0)) - | t2, `Lam(_,_,t1) -> aux t1 (mk_app (lift 1 t2) (`Var 0)) + | `Lam(_,t1), `Lam(_,t2) -> aux t1 t2 + | `Lam(_,t1), t2 -> - aux t1 (mk_app (lift 1 t2) (`Var(0,-666))) + | t2, `Lam(_,t1) -> aux t1 (mk_app (lift 1 t2) (`Var(0,-666))) | `N n1, `N n2 -> compare n1 n2 | `Match(u,_,bs_lift,bs,args), `Match(u',_,bs_lift',bs',args') -> let bs = List.sort (fun (n,_) (m,_) -> compare n m) !bs in @@ -276,14 +282,14 @@ let eta_eq (#nf as x) (#nf as y) = 0 = eta_compare x y ;; let rec eta_subterm sub t = if eta_eq sub t then true else match t with - | `Lam(_,_,t') -> eta_subterm (lift 1 sub) t' + | `Lam(_,t') -> eta_subterm (lift 1 sub) t' | `Match(u,ar,liftno,bs,args) -> eta_subterm sub (u :> nf) || List.exists (fun (_, t) -> eta_subterm sub (lift liftno t)) !bs - || List.exists (eta_subterm sub) args - | `I(v, args) -> List.exists (eta_subterm sub) (Listx.to_list args) || (match sub with - | `Var v' -> v = v' - | `I(v', args') -> v = v' + || List.exists (eta_subterm sub) (args :> nf list) + | `I((v,_), args) -> List.exists (eta_subterm sub) ((Listx.to_list args) :> nf list) || (match sub with + | `Var(v',_) -> v = v' + | `I((v',_), args') -> v = v' && Listx.length args' < Listx.length args && List.for_all (fun (x,y) -> eta_eq x y) (List.combine (Util.take (Listx.length args') (Listx.to_list args)) (Listx.to_list args')) | _ -> false @@ -292,3 +298,48 @@ let rec eta_subterm sub t = ;; let eta_subterm (#nf as x) (#nf as y) = eta_subterm x y;; + + +let max_arity_tms n = + let max a b = match a, b with + | None, None -> None + | None, Some x + | Some x, None -> Some x + | Some x, Some y -> Some (Pervasives.max x y) in + let aux_var l (m,a) = if n + l = m then Some a else None in + let rec aux l = function + | `Var v -> aux_var l v + | `I(v,tms) -> max (aux_var l v) (aux_tms l (Listx.to_list tms)) + | `Lam(_,t) -> aux (l+1) t + | `Match(u,_,_,bs,args) -> max (max (aux l (u :> nf)) (aux_tms l args)) (aux_tms l (List.map snd !bs)) + | `N _ -> None + and aux_tms l = + List.fold_left (fun acc t -> max acc (aux l t)) None in + fun tms -> aux_tms 0 (tms :> nf list) +;; + +let get_first_args var = +let rec aux l = function +| `Lam(_,t) -> aux (l+1) t +| `Match(u,orig,liftno,bs,args) -> Util.concat_map (aux l) args +| `I((n,_), args) -> if n = var + l then [Listx.last args] else [] +| `N _ +| `Var _ -> [] +in aux 0 +;; + +let compute_arities m = + let rec aux n tms = + if n = 0 + then [] + else + let tms = Util.filter_map (function `Lam(_,t) -> Some t | _ -> None ) tms in + let arity = match max_arity_tms (m-n) tms with None -> -666 | Some x -> x in + arity :: (aux (n-1) tms) + in fun tms -> List.rev (aux m tms) +;; + +let compute_arities var special_k all_tms = + let tms = List.fold_left (fun acc t -> acc @ (get_first_args var t)) [] all_tms in + compute_arities special_k tms +;;