1 type var = (* unique name *) int * (int * term) option * (*level*) int
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4 | Tapp of term * term
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8 let zero = Tvar 1010;;
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9 let dummy = Tvar 333;;
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12 (* mk_app & subst implementano la beta *)
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13 let rec mk_app t1 t2 = match t1 with
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14 | Tlam(v, t1') -> subst v t2 t1'
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15 | _ -> Tapp(t1, t2, false)
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17 let rec aux = function
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18 | Tapp(t1, t2, _) -> mk_app (aux t1) (aux t2)
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19 | Tvar v' as t -> if v = v' then tv else t
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20 | Tlam(v', t') as t -> if v = v' then t else Tlam(v', aux t')
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24 (* PARSING AND PRINTING *)
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27 let rec minus1 = function
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28 | Tvar n -> Tvar (n-1)
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29 | Tapp(t1, t2, b) -> Tapp(minus1 t1, minus1 t2, b)
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30 | Tlam(n, t) -> Tlam(n-1, minus1 t)
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31 (* in let open Parser *)
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32 in let rec myterm_of_term = function
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33 | Parser.Var n -> Tvar n
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34 | Parser.App(t1, t2) -> (*Tapp(myterm_of_term t1, myterm_of_term t2) WARNING! BETA DOWN HERE! *)
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35 mk_app (myterm_of_term t1) (myterm_of_term t2)
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36 | Parser.Lam(t) -> minus1 (Tlam(0, myterm_of_term t))
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38 let (tms, free) = Parser.parse_many strs
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39 in List.map myterm_of_term tms
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43 (* PRETTY PRINTING *)
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46 let fancy_of_term t =
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47 let rec string_of_term =
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48 let free = ["a"; "b"; "c"; "d"; "e"; "f"; "g"] in
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49 let bound = ["x"; "y"; "z"; "w"; "q"; "x1"; "x2"] in
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50 let string_of_int' n = if n >= 0 then "free" ^ string_of_int n else "bound" ^ string_of_int n in
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51 let rec string_of_var t =
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52 if Tvar t = dummy then "_" else if Tvar t = zero then "ZZ" else match t with
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53 | n -> string_of_int' n
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54 and string_of_term_w_pars = function
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55 | Tvar v -> string_of_var v
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56 | Tapp(t1, t2, _) -> "(" ^ (string_of_term_no_pars_app t1) ^ " " ^ (string_of_term_w_pars t2) ^ ")"
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57 | Tlam(_,_) as t -> "(" ^ (string_of_term_no_pars_lam t) ^ ")"
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58 and string_of_term_no_pars_app = function
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59 | Tapp(t1, t2,_) -> (string_of_term_no_pars_app t1) ^ " " ^ (string_of_term_w_pars t2)
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60 | _ as t -> string_of_term_w_pars t
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61 and string_of_term_no_pars_lam = function
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62 | Tlam(v, t) -> "λ" ^ (string_of_int' v) ^ ". " ^ (string_of_term_no_pars_lam t)
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63 | _ as t -> string_of_term_no_pars t
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64 and string_of_term_no_pars = function
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65 | Tlam(_, _) as t -> string_of_term_no_pars_lam t
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66 | _ as t -> string_of_term_no_pars_app t
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67 in string_of_term_no_pars
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68 in let rec html_of_term =
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69 let free = ["a"; "b"; "c"; "d"; "e"; "f"; "g"; "h"; "i"; "j"] in
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70 let bound = ["x"; "y"; "z"; "w"; "q"] in
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71 let string_of_int' n = if n >= 0 then List.nth free (n) else List.nth bound (-n-1) in
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72 let rec string_of_var t =
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73 if Tvar t = dummy then "#" else if Tvar t = zero then "Z" else string_of_int' t
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74 and string_of_term_w_pars = function
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75 | Tvar v -> string_of_var v
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76 | Tapp(t1, t2,_) -> "(" ^ (string_of_term_no_pars_app t1) ^ " " ^ (string_of_term_w_pars t2) ^ ")"
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77 | Tlam(_,_) as t -> "(" ^ (string_of_term_no_pars_lam t) ^ ")"
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78 and string_of_term_no_pars_app = function
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79 | Tapp(t1, t2,_) -> (string_of_term_no_pars_app t1) ^ " " ^ (string_of_term_w_pars t2)
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80 | _ as t -> string_of_term_w_pars t
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81 and string_of_term_no_pars_lam = function
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82 | Tlam(v, t) -> "λ" ^ (string_of_int' v) ^ ". " ^ (string_of_term_no_pars_lam t)
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83 | _ as t -> string_of_term_no_pars t
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84 and string_of_term_no_pars = function
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85 | Tlam(_, _) as t -> string_of_term_no_pars_lam t
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86 | _ as t -> string_of_term_no_pars_app t
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87 in string_of_term_no_pars
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89 string_of_term t / "html_of_term t"
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92 let fancy_of_nf t: Console.fancyobj =
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93 let rec print ?(l=[]) =
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95 `Var n -> Util.Vars.print_name l n
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96 | `N n -> string_of_int n
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97 | `Match(t,bs_lift,bs,args) ->
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98 "([" ^ print ~l (t :> Num.nf) ^
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99 " ? " ^ String.concat " | " (List.map (fun (n,t) -> string_of_int n ^ " => " ^ print ~l (Num.lift bs_lift t)) !bs) ^ "] " ^
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100 String.concat " " (List.map (print ~l) args) ^ ")"
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101 | `I(n,args) -> "(" ^ Util.Vars.print_name l n ^ " " ^ String.concat " " (Listx.to_list (Listx.map (print ~l) args)) ^ ")"
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103 let name = Util.Vars.string_of_var (List.length l) in
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104 "" ^ name ^ "." ^ print ~l:(name::l) (nf : Num.nf)
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106 (* in let rec print_html ?(l=[]) =
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108 `Var n -> Lambda3.print_name l n
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109 | `N n -> string_of_int n
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110 | `Match(t,bs_lift,bs,args) ->
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111 "(<b>match</b> " ^ print_html ~l (t :> Lambda3.nf) ^
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112 " <b>with</b> " ^ String.concat " <b>|</b> " (List.map (fun (n,t) -> string_of_int n ^ " <b>⇒</b> " ^ print_html ~l (Lambda3.lift bs_lift t)) !bs) ^ "..." (* Attenzion non sto stampando gli argomenti applicati! Perche' non ce ne sono mai *)
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113 | `I(n,args) -> "(" ^ Lambda3.print_name l n ^ " " ^ String.concat " " (Listx.to_list (Listx.map (print_html ~l) args)) ^ ")"
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115 let name = Lambda3.string_of_var (List.length l) in
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116 "λ" ^ name ^ ". " ^ print_html ~l:(name::l) (nf : Lambda3.nf) *)
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121 let print_term t = print_endline (fancy_of_term t :> Console.fancyobj);;
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125 let varcount = ref 11;;
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127 let freshvar () = (
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128 varcount := (!varcount + 1);
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134 (* magic ["x (x x x)"; "x (y. y x)"; "x x (y. y y (x x y))"] ;; *)
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135 (* magic ["((x x) (x. x))";"x x"];; *)
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137 let alive (_, _, n) = n;;
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138 let rec setalive c = function
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139 | Tvar(a,b,_) as v -> if v <> zero && v <> dummy then Tvar(a,b,c) else v
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140 | Tapp(a,b) -> Tapp(setalive c a, setalive c b)
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141 | Tlam(n, t) -> Tlam(n, setalive c t)
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144 let mk_vars t lev =
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148 else Tvar(0, Some(n, t), lev) :: (aux (n-1))
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152 let mk_apps t ts = List.fold_right (fun x y -> mk_app y x) (List.rev ts) t;; (* which FOLD? FIXME *)
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155 let compute_special_k tms =
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156 let rec aux k t = match t with
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158 | Tapp(t1,t2) -> Pervasives.max (aux 0 t1) (aux 0 t2)
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159 | Tlam(v,t) -> Pervasives.max (k+1) (aux (k + 1) t)
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160 in List.fold_left (fun b a -> Pervasives.max (aux 0 a) b) 0 tms
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163 let compute_special_h tms =
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164 let rec eat_lam = function
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165 | Tlam(_,t) -> eat_lam t
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168 let rec aux t = match t with
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170 | Tapp(t1,t2) -> Pervasives.max (aux t1) (aux t2)
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171 | Tlam(v,t) -> 1 + (aux (eat_lam t))
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172 in 1 + List.fold_left (fun b a -> Pervasives.max (aux a) b) 0 tms
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175 (* funzione di traduzione brutta & cattiva *)
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177 let rec aux = function
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178 | Tlam _ -> assert false
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183 let t1' = aux t1 in
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186 else mk_apps t2 ((List.rev (mk_vars t1' (a-1) k)) @ [zero])
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187 in Tapp(t1', aux t2')
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191 (* sostituisce gli argomenti dummy (delle variabili morte) con 'dummy' *)
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192 let rec dummize = function
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193 | Tlam _ -> assert false
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194 | Tvar (a,Some(b,t), c) -> Tvar(a, Some (b, dummize t), c)
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197 if alive (hd t1) = 0
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198 then Tapp(dummize t1, dummy)
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199 else Tapp(dummize t1, dummize t2)
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202 (* lista di sottotermini applicativi *)
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203 let rec subterms = function
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204 | Tlam _ -> assert false
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205 | Tvar _ as v -> [v]
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206 | Tapp(t1, t2) -> Tapp(t1, t2) :: ((subterms t1) @ (subterms t2))
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209 (* filtra dai sottotermini le variabili *)
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210 let rec vars subs = List.filter (function Tvar _ -> true | _ -> false) subs;;
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213 let rec stupid_uniq = function
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215 | x::xs -> if List.mem x xs then (stupid_uniq xs) else x::(stupid_uniq xs)
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217 let stupid_compare a b =
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218 let rec size = function
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219 | Tvar(_,None,_) -> 0
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220 | Tvar(_,Some(_,t),_) -> 1 + size t
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221 | Tapp(t1,t2) -> 1 + size t1 + size t2
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222 | Tlam _ -> assert false
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223 in compare (size a) (size b)
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225 let stupid_sort_uniq l = stupid_uniq (List.sort stupid_compare l);;
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227 (* crea i match ricorsivamente.
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228 - k e' lo special-K
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229 - subs e' l'insieme dei sottotermini
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230 TODO: riscrivere la funzione per evitare/ottimizzare la ricorsione
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232 let crea_match k subs (acc : (term * Lambda3.nf) list) : term -> Lambda3.nf =
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233 let req t = try List.assoc t acc with Not_found -> `Var 9999 in
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235 if t1 = dummy then `Var 99999 else
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236 (* let _ = print_term t1 in *)
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237 let cont = List.filter (fun t2 -> List.mem (Tapp(t1,t2)) subs) subs
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238 in if cont = [] then
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239 try `N (Lambda3.index_of t1 subs) with Not_found -> `Var 999 (* variabile dummy qui *) else
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240 let a = alive (hd t1) in
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241 if a = 0 then `Lam (req (Tapp(t1, dummy)))
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243 let vars = (List.rev (mk_vars t1 (a-1) k)) @ [zero]
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244 (* in let _ = print_endline (String.concat " " (List.map string_of_term vars))
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245 in let _ = print_term (mk_apps dummy vars) *)
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246 in let vars = List.map req vars
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247 in let vars = List.map (Lambda3.lift 1) vars (* forse lift non necessario *)
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248 in let vars = Listx.from_list vars
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249 in let body = `I(0, vars)
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250 in let branches = List.map (fun t2 -> (Lambda3.index_of t2 subs, req (Tapp(t1, t2)))) cont
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251 in let bs = ref(branches)
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254 in `Lam (`Match(body, lift, bs, args))
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260 let rec aux n prev =
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261 if n = 0 then [zero]
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262 else let prev = aux (n-1) prev in let x = mk_app (List.hd prev) dummy in x :: prev
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266 let is_scott_n t n =
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267 let open Lambda3 in let open Pure in
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268 let rec aux n = function
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269 | L (L (A (V 1, L (V 0)))) -> n = 0
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270 | L (L (A (V 0, t))) -> aux (n-1) t
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271 | _ -> assert false
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276 let magic strings k h = (
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277 let tms = parse strings
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278 in let tms = List.map (fun x -> Tapp(x, zero)) tms
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279 in let tms' = List.map (setalive h) tms
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280 in let tms' = List.map (translate k) tms'
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281 in let tms' = List.map dummize tms'
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282 (* in let bullet = ">" / "•" *)
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283 (* in let progress s = print_endline (bullet ^^ fancy_of_string s) *)
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284 in let progress = print_h1
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285 in let _ = progress "traduzione completata"
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286 (* in let _ = List.map print_term tms' *)
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287 in let _ = progress "ordino i sottotermini"
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288 in let subs = List.concat (List.map subterms tms')
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289 in let subs = stupid_sort_uniq subs
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290 (* metti gli zeri in testa, perche' vanno calcolati per primi *)
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291 in let zeros = mk_zeros k
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292 in let subs = (List.filter (fun t -> not (List.mem t zeros)) subs) @ (List.rev zeros)
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293 in let _ = progress ("sottotermini generati: " ^ string_of_int (List.length subs))
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294 in let vars = vars subs
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295 (* in let _ = List.iter print_term subs *)
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296 (* in let _ = 0/0 *)
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297 in let fv = List.filter (function Tvar(_, None, _) as v -> v <> dummy | _ -> false) vars
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298 (* in let _ = print_string ("> free vars: " ^ String.concat ", " (List.map (string_of_term) fv)) *)
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299 in let _ = progress "sto creando i match"
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300 (* in let sigma = List.map (fun x -> x, crea_match k subs x) fv *)
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301 in let f t acc = let res = crea_match k subs acc t in (t,res)::acc
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302 in let acc = List.fold_right f subs []
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303 in let sigma = List.filter (fun (t,res) -> List.mem t fv) acc
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304 in let _ = progress "match creati"
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305 in let _ = List.iter (fun (x,y) -> print_endline (fancy_of_term x ^^ (" : " / " ↦ ") ^^ fancy_of_nf y)) sigma
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307 in let _ = progress "controllo di purezza";
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308 in let open Lambda3
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309 in let ps, _ = Lambda3.parse' strings
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310 in let ps = List.map (fun x -> Lambda3.mk_app x (`Var 1010)) ps
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311 in let ps = List.map (fun t -> ToScott.t_of_nf (t :> nf)) ps
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312 in let sigma = List.map (
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313 function (Tvar(n,_,_), inst) -> n, ToScott.t_of_nf inst | _ -> assert false
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316 List.fold_left (fun ps (x,inst) -> List.map (Pure.subst false x inst) ps) ps sigma
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317 in let _ = List.iteri (fun i n ->
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318 (* print_string_endline ((string_of_int i) ^ ":: " ^ (Pure.print (Pure.whd n))); *)
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319 (* assert (Pure.whd n = Scott.mk_n (Lambda3.index_of (List.nth tms' i) subs))) ps *)
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320 assert (is_scott_n (Pure.whd n) (Lambda3.index_of (List.nth tms' i) subs))) ps
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321 in let _ = progress "fatto." in ()
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324 let do_everything tms =
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325 let tms' = parse tms in
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326 let k = compute_special_k tms' in
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327 let h = compute_special_h tms' in
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328 (* let _ = print_string_endline (string_of_int h) in *)
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333 let tms = ["a a"; "a b"; "b a"; "b (x. y.x y a)"] in
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335 (* let tms = ["x c" ; "b (x c d e)"; "b"] in *)
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337 (* let tms = ["x x x"] in *)
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338 let tms' = parse tms in
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339 let k = compute_special_k tms' in
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340 let h = compute_special_h tms' in
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341 (* let _ = print_string_endline (string_of_int h) in *)
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345 (* type var' = (* unique name *) int * (int * term') option * (*dead*) bool option
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348 | Tapp' of term' * term' * (* active *) bool
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349 | Tlam' of int * term'
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352 let rec iter mustapply =
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354 | Tvar'(n, Some(m,t), b) -> Tvar(n, Some(m, aux t), b)
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355 | Tvar' _ as v -> v
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356 | Tapp'(t1, t2, b) -> if b &&
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