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, None, 0);;
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9 let dummy = Tvar(333, None, 0);;
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11 (* mk_app & subst implementano la beta *)
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12 let rec mk_app t1 t2 = match t1 with
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13 | Tlam(v, t1') -> subst v t2 t1'
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16 let rec aux = function
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17 | Tapp(t1, t2) -> mk_app (aux t1) (aux t2)
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18 | Tvar(v', _, _) as t -> if v = v' then tv else t
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19 | Tlam(v', t') as t -> if v = v' then t else Tlam(v', aux t')
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23 (* PARSING AND PRINTING *)
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26 let rec minus1 = function
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27 | Tvar(n, None, x) -> Tvar(n-1, None, x)
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28 | Tvar _ -> assert false
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29 | Tapp(t1, t2) -> Tapp(minus1 t1, minus1 t2)
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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, None, 0)
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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 = 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, None, _) -> (string_of_int' n)
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54 (* | (_, Some(n,t), _) -> "?" ^ string_of_int n *)
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55 | (_, Some(n,t), _) -> "{" ^ (string_of_term_no_pars t) ^ "|" ^ (string_of_int n) ^ "}"
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56 and string_of_term_w_pars = function
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57 | Tvar v -> string_of_var v
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58 | Tapp(t1, t2) -> "(" ^ (string_of_term_no_pars_app t1) ^ " " ^ (string_of_term_w_pars t2) ^ ")"
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59 | Tlam(_,_) as t -> "(" ^ (string_of_term_no_pars_lam t) ^ ")"
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60 and string_of_term_no_pars_app = function
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61 | Tapp(t1, t2) -> (string_of_term_no_pars_app t1) ^ " " ^ (string_of_term_w_pars t2)
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62 | _ as t -> string_of_term_w_pars t
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63 and string_of_term_no_pars_lam = function
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64 | Tlam(v, t) -> "λ" ^ (string_of_int' v) ^ ". " ^ (string_of_term_no_pars_lam t)
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65 | _ as t -> string_of_term_no_pars t
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66 and string_of_term_no_pars = function
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67 | Tlam(_, _) as t -> string_of_term_no_pars_lam t
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68 | _ as t -> string_of_term_no_pars_app t
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69 in string_of_term_no_pars
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70 in let rec html_of_term =
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71 let free = ["a"; "b"; "c"; "d"; "e"; "f"; "g"; "h"; "i"; "j"] in
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72 let bound = ["x"; "y"; "z"; "w"; "q"] in
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73 let string_of_int' n = string_of_int n in
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74 let rec string_of_var t =
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75 if Tvar t = dummy then "#" else if Tvar t = zero then "Z" else match t with
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76 | (n, None, _) -> (string_of_int' n)
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77 | (_, Some(n,t), _) -> "α<sup>" ^ (string_of_term_no_pars t) ^ "</sup><sub>" ^ (string_of_int n) ^ "</sub>"
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78 and string_of_term_w_pars = function
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79 | Tvar v -> string_of_var v
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80 | Tapp(t1, t2) -> "(" ^ (string_of_term_no_pars_app t1) ^ " " ^ (string_of_term_w_pars t2) ^ ")"
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81 | Tlam(_,_) as t -> "(" ^ (string_of_term_no_pars_lam t) ^ ")"
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82 and string_of_term_no_pars_app = function
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83 | Tapp(t1, t2) -> (string_of_term_no_pars_app t1) ^ " " ^ (string_of_term_w_pars t2)
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84 | _ as t -> string_of_term_w_pars t
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85 and string_of_term_no_pars_lam = function
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86 | Tlam(v, t) -> "λ" ^ (string_of_int' v) ^ ". " ^ (string_of_term_no_pars_lam t)
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87 | _ as t -> string_of_term_no_pars t
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88 and string_of_term_no_pars = function
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89 | Tlam(_, _) as t -> string_of_term_no_pars_lam t
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90 | _ as t -> string_of_term_no_pars_app t
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91 in string_of_term_no_pars
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93 string_of_term t / html_of_term t
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96 let fancy_of_nf t: Console.fancyobj =
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97 let rec print ?(l=[]) =
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99 `Var n -> Util.Vars.print_name l n
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100 | `N n -> string_of_int n
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101 | `Match(t,bs_lift,bs,args) ->
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102 "([" ^ print ~l (t :> Num.nf) ^
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103 " ? " ^ String.concat " | " (List.map (fun (n,t) -> string_of_int n ^ " => " ^ print ~l (Num.lift bs_lift t)) !bs) ^ "] " ^
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104 String.concat " " (List.map (print ~l) args) ^ ")"
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105 | `I(n,args) -> "(" ^ Util.Vars.print_name l n ^ " " ^ String.concat " " (Listx.to_list (Listx.map (print ~l) args)) ^ ")"
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107 let name = Util.Vars.string_of_var (List.length l) in
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108 "" ^ name ^ "." ^ print ~l:(name::l) (nf : Num.nf)
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110 in let rec print_html ?(l=[]) =
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112 `Var n -> Util.Vars.print_name l n
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113 | `N n -> string_of_int n
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114 | `Match(t,bs_lift,bs,args) ->
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115 "(<b>match</b> " ^ print_html ~l (t :> Num.nf) ^
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116 " <b>with</b> " ^ String.concat " <b>|</b> " (List.map (fun (n,t) -> string_of_int n ^ " <b>⇒</b> " ^ print_html ~l (Num.lift bs_lift t)) !bs) ^ "..." (* Attenzion non sto stampando gli argomenti applicati! Perche' non ce ne sono mai *)
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117 | `I(n,args) -> "(" ^ Util.Vars.print_name l n ^ " " ^ String.concat " " (Listx.to_list (Listx.map (print_html ~l) args)) ^ ")"
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119 let name = Util.Vars.string_of_var (List.length l) in
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120 "λ" ^ name ^ ". " ^ print_html ~l:(name::l) (nf : Num.nf)
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122 print t / print_html t
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125 let print_term t = print_endline (fancy_of_term t :> Console.fancyobj);;
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129 let varcount = ref 0;;
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131 let freshvar () = (
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132 varcount := (!varcount + 1);
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139 | Tapp(t1,t2) -> hd t1
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140 | Tlam _ -> assert false
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143 let alive (_, _, n) = n;;
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144 let rec setalive c = function
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145 | Tvar(a,b,_) as v -> if v <> zero && v <> dummy then Tvar(a,b,c) else v
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146 | Tapp(a,b) -> Tapp(setalive c a, setalive c b)
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147 | Tlam(n, t) -> Tlam(n, setalive c t)
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150 let mk_vars t lev =
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154 else Tvar(0, Some(n, t), lev) :: (aux (n-1))
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158 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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161 let compute_special_k tms =
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162 let rec aux k t = match t with
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164 | Tapp(t1,t2) -> Pervasives.max (aux 0 t1) (aux 0 t2)
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165 | Tlam(v,t) -> Pervasives.max (k+1) (aux (k + 1) t)
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166 in List.fold_left (fun b a -> Pervasives.max (aux 0 a) b) 0 tms
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169 let compute_special_h tms =
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170 let rec eat_lam = function
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171 | Tlam(_,t) -> eat_lam t
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174 let rec aux t = match t with
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176 | Tapp(t1,t2) -> Pervasives.max (aux t1) (aux t2)
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177 | Tlam(v,t) -> 1 + (aux (eat_lam t))
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178 in 1 + List.fold_left (fun b a -> Pervasives.max (aux a) b) 0 tms
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181 (* funzione di traduzione brutta & cattiva *)
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183 let rec aux = function
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184 | Tlam _ -> assert false
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189 let t1' = aux t1 in
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192 else mk_apps t2 ((List.rev (mk_vars t1' (a-1) k)) @ [zero])
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193 in Tapp(t1', aux t2')
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197 (* sostituisce gli argomenti dummy (delle variabili morte) con 'dummy' *)
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198 let rec dummize = function
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199 | Tlam _ -> assert false
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200 | Tvar (a,Some(b,t), c) -> Tvar(a, Some (b, dummize t), c)
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203 if alive (hd t1) = 0
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204 then Tapp(dummize t1, dummy)
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205 else Tapp(dummize t1, dummize t2)
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208 (* lista di sottotermini applicativi *)
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209 let rec subterms = function
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210 | Tlam _ -> assert false
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211 | Tvar _ as v -> [v]
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212 | Tapp(t1, t2) -> Tapp(t1, t2) :: ((subterms t1) @ (subterms t2))
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215 (* filtra dai sottotermini le variabili *)
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216 let rec vars subs = List.filter (function Tvar _ -> true | _ -> false) subs;;
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219 let rec stupid_uniq = function
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221 | x::xs -> if List.mem x xs then (stupid_uniq xs) else x::(stupid_uniq xs)
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223 let stupid_compare a b =
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224 let rec size = function
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225 | Tvar(_,None,_) -> 0
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226 | Tvar(_,Some(_,t),_) -> 1 + size t
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227 | Tapp(t1,t2) -> 1 + size t1 + size t2
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228 | Tlam _ -> assert false
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229 in compare (size a) (size b)
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231 let stupid_sort_uniq l = stupid_uniq (List.sort stupid_compare l);;
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233 (* crea i match ricorsivamente.
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234 - k e' lo special-K
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235 - subs e' l'insieme dei sottotermini
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236 TODO: riscrivere la funzione per evitare/ottimizzare la ricorsione
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238 let crea_match k subs (acc : (term * Num.nf) list) : term -> Num.nf =
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239 let req t = try List.assoc t acc with Not_found -> `Var 9999 in
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241 if t1 = dummy then `Var 99999 else
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242 (* let _ = print_term t1 in *)
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243 let cont = List.filter (fun t2 -> List.mem (Tapp(t1,t2)) subs) subs
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244 in if cont = [] then
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245 try `N (Util.index_of t1 subs) with Not_found -> `Var 999 (* variabile dummy qui *) else
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246 let a = alive (hd t1) in
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247 if a = 0 then `Lam (true, req (Tapp(t1, dummy)))
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249 let vars = (List.rev (mk_vars t1 (a-1) k)) @ [zero]
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250 (* in let _ = print_endline (String.concat " " (List.map string_of_term vars))
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251 in let _ = print_term (mk_apps dummy vars) *)
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252 in let vars = List.map req vars
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253 in let vars = List.map (Num.lift 1) vars (* forse lift non necessario *)
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254 in let vars = Listx.from_list vars
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255 in let body = `I(0, vars)
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256 in let branches = List.map (fun t2 -> (Util.index_of t2 subs, req (Tapp(t1, t2)))) cont
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257 in let bs = ref(branches)
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260 in `Lam (true, `Match(body, lift, bs, args))
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266 let rec aux n prev =
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267 if n = 0 then [zero]
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268 else let prev = aux (n-1) prev in let x = mk_app (List.hd prev) dummy in x :: prev
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272 let is_scott_n t n =
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273 let open Pure.Pure in
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274 let rec aux n = function
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275 | L (L (A (V 1, L (V 0)))) -> n = 0
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276 | L (L (A (V 0, t))) -> assert (n > 0); aux (n-1) t
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277 | _ -> assert false
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281 let pure_subst delift_by_one what with_what =
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282 let open Pure.Pure in
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285 | A(t1,t2) -> A(aux l t1, aux l t2)
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287 if n = what + l then
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290 V (if delift_by_one && n >= l then n-1 else n)
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291 | L t -> L (aux (l+1) t)
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297 let open Pure.Pure in
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300 let t2 = pure_whd t2 in
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301 let t1 = pure_whd t1 in
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303 | L f -> pure_whd (pure_subst true 0 t2 f)
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311 let magic strings k h = (
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312 let tms = parse strings
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313 in let tms = List.map (fun x -> Tapp(x, zero)) tms
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314 in let tms' = List.map (setalive h) tms
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315 in let tms' = List.map (translate k) tms'
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316 in let tms' = List.map dummize tms'
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317 in let progress s = print_bullet (fancy_of_string s)
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318 in let _ = progress "traduzione completata"
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319 (* in let _ = List.map print_term tms' *)
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320 in let _ = progress "ordino i sottotermini"
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321 in let subs = List.concat (List.map subterms tms')
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322 in let subs = stupid_sort_uniq subs
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323 (* metti gli zeri in testa, perche' vanno calcolati per primi *)
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324 in let zeros = mk_zeros k
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325 in let subs = (List.filter (fun t -> not (List.mem t zeros)) subs) @ (List.rev zeros)
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326 in let _ = progress ("sottotermini generati: " ^ string_of_int (List.length subs))
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327 in let vars = vars subs
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328 (* in let _ = List.iter print_term subs *)
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329 (* in let _ = 0/0 *)
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330 in let fv = List.filter (function Tvar(_, None, _) as v -> v <> dummy | _ -> false) vars
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331 (* in let _ = print_string ("> free vars: " ^ String.concat ", " (List.map (string_of_term) fv)) *)
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332 in let _ = progress "sto creando i match"
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333 (* in let sigma = List.map (fun x -> x, crea_match k subs x) fv *)
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334 in let f t acc = let res = crea_match k subs acc t in (t,res)::acc
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335 in let acc = List.fold_right f subs []
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336 in let sigma = List.filter (fun (t,res) -> List.mem t fv) acc
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337 in let _ = progress "match creati"
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338 in let _ = List.iter (fun (x,y) -> print_endline (fancy_of_term x ^^ (" : " / " ↦ ") ^^ fancy_of_nf y)) sigma
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340 in let _ = progress "controllo di purezza";
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341 in let ps, _ = Num.parse' strings
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342 in let ps = List.map (fun x -> Num.mk_app x (`Var 1010)) ps
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343 in let ps = List.map (fun t -> Num.ToScott.t_of_nf (t :> Num.nf)) ps
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344 in let sigma = List.map (
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345 function (Tvar(n,_,_), inst) -> n, Num.ToScott.t_of_nf inst | _ -> assert false
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348 List.fold_left (fun ps (x,inst) -> List.map (pure_subst false x inst) ps) ps sigma
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349 in let _ = List.iteri (fun i n ->
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350 (* print_string_endline ((string_of_int i) ^ ":: " ^ (Pure.print (Pure.whd n))); *)
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351 (* assert (Pure.whd n = Scott.mk_n (Util.index_of (List.nth tms' i) subs))) ps *)
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352 assert (is_scott_n (pure_whd n) (Util.index_of (List.nth tms' i) subs))) ps
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353 in let _ = progress "fatto." in ()
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356 let no_subterms strings k h =
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357 let tms = parse strings
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358 in let tms = List.map (fun x -> Tapp(x, zero)) tms
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359 in let tms' = List.map (setalive h) tms
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360 in let tms' = List.map (translate k) tms'
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361 in let tms' = List.map dummize tms'
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362 in let progress s = print_bullet (fancy_of_string s)
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363 in let _ = progress "traduzione completata"
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364 (* in let _ = List.map print_term tms' *)
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365 in let _ = progress "ordino i sottotermini"
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366 in let subs = List.concat (List.map subterms tms')
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367 in let subs = stupid_sort_uniq subs
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368 (* metti gli zeri in testa, perche' vanno calcolati per primi *)
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369 in let zeros = mk_zeros k
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370 in let subs = (List.filter (fun t -> not (List.mem t zeros)) subs) @ (List.rev zeros)
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371 in let subno = List.length subs
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372 in let _ = progress ("sottotermini generati: " ^ string_of_int subno)
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376 let do_everything tms =
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377 let tms' = parse tms in
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378 let _ = List.iter print_term tms' in
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379 let k = compute_special_k tms' in
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380 let h = compute_special_h tms' in
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381 (* let _ = print_string_endline (string_of_int h) in *)
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382 no_subterms tms k h
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386 let tms = ["a a"; "a b"; "b a"; "b (x. y.x y a)"] in
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388 (* let tms = ["x c" ; "b (x c d e)"; "b"] in *)
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390 (* let tms = ["x x x"] in *)
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391 let tms' = parse tms in
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392 let _ = List.iter print_term tms' in
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393 let k = compute_special_k tms' in
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394 let h = compute_special_h tms' in
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395 (* let _ = print_string_endline (string_of_int h) in *)
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396 no_subterms tms k h
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399 (* type var' = (* unique name *) int * (int * term') option * (*dead*) bool option
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402 | Tapp' of term' * term' * (* active *) bool
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403 | Tlam' of int * term'
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406 let rec iter mustapply =
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408 | Tvar'(n, Some(m,t), b) -> Tvar(n, Some(m, aux t), b)
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409 | Tvar' _ as v -> v
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410 | Tapp'(t1, t2, b) -> if b &&
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