1 let (++) f g x = f (g x);;
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3 let print_hline = Console.print_hline;;
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19 ; sigma : (var * t) list (* substitutions *)
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20 ; stepped : var list
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23 let all_terms p = [p.div; p.conv];;
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25 exception Done of (var * t) list (* substitution *);;
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26 exception Fail of int * string;;
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29 let bound_vars = ["x"; "y"; "z"; "w"; "q"] in
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30 let rec string_of_term_w_pars level = function
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31 | V v -> if v >= level then "`" ^ string_of_int (v-level) else
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32 let nn = level - v-1 in
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33 if nn < 5 then List.nth bound_vars nn else "x" ^ (string_of_int (nn-4))
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35 | L _ as t -> "(" ^ string_of_term_no_pars_lam level t ^ ")"
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38 and string_of_term_no_pars_app level = function
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39 | A(t1,t2) -> (string_of_term_no_pars_app level t1) ^ " " ^ (string_of_term_w_pars level t2)
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40 | _ as t -> string_of_term_w_pars level t
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41 and string_of_term_no_pars_lam level = function
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42 | L t -> "λ" ^ string_of_term_w_pars (level+1) (V 0) ^ ". " ^ (string_of_term_no_pars_lam (level+1) t)
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43 | _ as t -> string_of_term_no_pars level t
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44 and string_of_term_no_pars level = function
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45 | L _ as t -> string_of_term_no_pars_lam level t
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46 | _ as t -> string_of_term_no_pars_app level t
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47 in string_of_term_no_pars 0
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50 let string_of_problem p =
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52 "[stepped] " ^ String.concat " " (List.map string_of_int p.stepped);
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53 "[DV] " ^ (string_of_t p p.div);
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54 "[CV] " ^ (string_of_t p p.conv);
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56 String.concat "\n" lines
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59 let problem_fail p reason =
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60 print_endline "!!!!!!!!!!!!!!! FAIL !!!!!!!!!!!!!!!";
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61 print_endline (string_of_problem p);
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62 raise (Fail (-1, reason))
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65 let freshvar ({freshno} as p) =
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66 {p with freshno=freshno+1}, freshno+1
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69 let rec is_inert p =
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71 | A(t,_) -> is_inert p t
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73 | L _ | B | P -> false
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76 let is_var = function V _ -> true | _ -> false;;
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77 let is_lambda = function L _ -> true | _ -> false;;
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78 let is_pacman = function P -> true | _ -> false;;
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80 let rec subst level delift fromdiv sub =
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82 | V v -> if v = level + fst sub then lift level (snd sub) else V (if delift && v > level then v-1 else v)
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83 | L t -> L (subst (level + 1) delift fromdiv sub t)
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85 let t1 = subst level delift fromdiv sub t1 in
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86 let t2 = subst level delift fromdiv sub t2 in
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87 if t1 = B || t2 = B then B else mk_app fromdiv t1 t2
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90 and mk_app fromdiv t1 t2 = let t1 = if t1 = P then L P else t1 in match t1 with
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91 | B | _ when t2 = B -> B
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92 | L t1 -> subst 0 true fromdiv (0, t2) t1
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97 | V m -> V (if m >= n' then m + n else m)
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98 | L t -> L (aux (n'+1) t)
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99 | A (t1, t2) -> A (aux n' t1, aux n' t2)
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104 let subst = subst 0 false;;
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106 let subst_in_problem (sub: var * t) (p: problem) =
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107 print_endline ("SUBST IN PROBLEM: " ^ string_of_t p (V (fst sub)) ^ " |-> " ^ string_of_t p (snd sub));
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108 let p = {p with stepped=(fst sub)::p.stepped} in
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109 let conv = subst false sub p.conv in
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110 let div = subst true sub p.div in
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111 let p = {p with div; conv} in
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112 (* print_endline ("after sub: \n" ^ string_of_problem p); *)
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113 {p with sigma=sub::p.sigma}
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116 let free_vars p t =
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117 let rec aux level = function
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118 | V v -> if v >= level then [v] else []
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119 | A(t1,t2) -> (aux level t1) @ (aux level t2)
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120 | L t -> aux (level+1) t
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122 in Util.sort_uniq (aux 0 t)
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125 let visible_vars p t =
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126 let rec aux = function
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128 | A(t1,t2) -> (aux t1) @ (aux t2)
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131 (* | Ptr n -> aux (get_conv p n) *)
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132 in Util.sort_uniq (aux t)
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135 let rec hd_of = function
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137 | A(t, _) -> hd_of t
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138 | _ -> assert false
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141 let rec nargs = function
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143 | A(t, _) -> 1 + nargs t
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144 | _ -> assert false
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147 let get_subterm_with_head_and_args hd_var n_args =
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148 let rec aux = function
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149 | V _ | L _ | B | P -> None
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151 if hd_of t1 = hd_var && n_args <= 1 + nargs t1
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153 else match aux t2 with
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155 | Some _ as res -> res
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159 let rec eta_eq l1 l2 t1 t2 = match t1, t2 with
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160 | L t1, L t2 -> eta_eq l1 l2 t1 t2
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161 | L t1, t2 -> eta_eq l1 (l2+1) t1 t2
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162 | t1, L t2 -> eta_eq (l1+1) l2 t1 t2
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163 | V a, V b -> a + l1 = b + l2
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164 | A(t1,t2), A(u1,u2) -> eta_eq l1 l2 t1 u1 && eta_eq l1 l2 t2 u2
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167 let eta_eq = eta_eq 0 0;;
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170 let rec simple_explode p =
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173 let subst = var, B in
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174 sanity (subst_in_problem subst p)
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178 (* Sanity checks: *)
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179 if (function | P | L _ -> true | _ -> false) p.div then problem_fail p "p.div converged";
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180 if p.conv = B then problem_fail p "p.conv diverged";
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182 print_endline (string_of_problem p); (* non cancellare *)
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183 if p.div = B then raise (Done p.sigma);
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184 let p = if is_var p.div then simple_explode p else p in
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188 let print_cmd s1 s2 = print_endline (">> " ^ s1 ^ " " ^ s2);;
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191 print_cmd "EAT" "";
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192 let var = hd_of p.div in
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193 let n = nargs p.div in
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197 else L (aux (m-1) t) in
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198 let subst = var, aux n B in
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199 sanity (subst_in_problem subst p)
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203 let var = hd_of p.div in
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204 print_cmd "STEP" ("on " ^ string_of_t p (V var) ^ " (of:" ^ string_of_int n ^ ")");
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205 let rec aux' p m t =
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209 let p, v = freshvar p in
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210 let p, t = aux' p (m-1) t in
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211 p, A(t, V (v + k + 1)) in
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212 let p, t = aux' p n (V 0) in
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213 let rec aux' m t = if m < 0 then t else A(aux' (m-1) t, V (k-m)) in
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217 else L (aux (m-1) t) in
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219 let subst = var, t in
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220 sanity (subst_in_problem subst p)
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224 let rec aux level = function
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225 | Parser.Lam t -> L (aux (level + 1) t)
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226 | Parser.App (t1, t2) ->
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227 if level = 0 then mk_app false (aux level t1) (aux level t2)
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228 else A(aux level t1, aux level t2)
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229 | Parser.Var v -> V v
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230 in let (tms, free) = Parser.parse_many strs
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231 in (List.map (aux 0) tms, free)
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234 let problem_of div conv =
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236 let all_tms, var_names = parse ([div; conv]) in
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237 let div, conv = List.hd all_tms, List.hd (List.tl all_tms) in
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238 let varno = List.length var_names in
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239 let p = {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; stepped=[]} in
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240 (* activate bombs *)
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242 let subst = Util.index_of "BOMB" var_names, L B in
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243 subst_in_problem subst p
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244 with Not_found -> p in
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245 (* activate pacmans *)
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247 let subst = Util.index_of "PACMAN" var_names, P in
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248 let p = subst_in_problem subst p in
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249 (print_endline ("after subst in problem " ^ string_of_problem p); p)
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250 with Not_found -> p in
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251 (* initial sanity check *)
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255 let exec div conv cmds =
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256 let p = problem_of div conv in
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258 problem_fail (List.fold_left (|>) p cmds) "Problem not completed"
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268 let k', t' = aux t1 in
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269 if k' = n then n, t'
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271 | _ -> assert false
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275 let find_difference p t n_args =
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276 let t = cut_app n_args t in
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277 let rec aux t u k = match t, u with
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278 | V _, V _ -> assert false (* div subterm of conv *)
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279 | A(t1,t2), A(u1,u2) ->
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280 if not (eta_eq t2 u2) then (print_endline((string_of_t p t2) ^ " <> " ^ (string_of_t p u2)); k)
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281 else aux t1 u1 (k-1)
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282 | _, _ -> assert false
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283 in aux p.div t n_args
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286 let rec count_lams = function
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287 | L t -> 1 + count_lams t
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291 let compute_k_from_args p hd_var j =
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292 let rec aux hd = function
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293 | A(t1,t2) -> max (
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294 if hd_of t1 = hd && (nargs t1) = j
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295 then (print_endline(string_of_t p t2);if t2 = V hd then j else count_lams t2)
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296 else 0) (max (aux hd t1) (aux hd t2))
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297 | L t -> aux (hd+1) t
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299 | _ -> assert false
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304 let hd_var = hd_of p.div in
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305 let n_args = nargs p.div in
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306 match get_subterm_with_head_and_args hd_var n_args p.conv with
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308 (try let p = eat p in problem_fail p "Auto did not complete the problem" with Done _ -> ())
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310 let j = find_difference p t n_args - 1 in
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312 (compute_k_from_args p hd_var j p.div)
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313 (compute_k_from_args p hd_var j p.conv) in
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314 let p = step j k p in
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318 let interactive div conv cmds =
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319 let p = problem_of div conv in
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321 let p = List.fold_left (|>) p cmds in
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323 let nth spl n = int_of_string (List.nth spl n) in
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325 let s = read_line () in
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326 let spl = Str.split (Str.regexp " +") s in
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327 s, let uno = List.hd spl in
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328 try if uno = "eat" then eat
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329 else if uno = "step" then step (nth spl 1) (nth spl 2)
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330 else failwith "Wrong input."
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331 with Failure s -> print_endline s; (fun x -> x) in
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332 let str, cmd = read_cmd () in
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333 let cmds = (" " ^ str ^ ";")::cmds in
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335 let p = cmd p in f p cmds
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337 | Done _ -> print_endline "Done! Commands history: "; List.iter print_endline (List.rev cmds)
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339 ) with Done _ -> ()
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344 "@ (x y) (y y) (y x)"
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348 auto (problem_of "x x" "@ (x y) (y y) (y x)");;
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349 auto (problem_of "x y" "@ (x (_. x)) (y z) (y x)");;
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350 auto (problem_of "a (x. x b) (x. x c)" "@ (a (x. b b) @) (a @ c) (a (x. x x) a) (a (a a a) (a c c))");;
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353 "@ (x x) (y x) (y z)" [step 0 0; step 0 1; eat] ;;
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355 auto (problem_of "x (y. x y y)" "x (y. x y x)");;
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357 let rec conv_join = function
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359 | x::xs -> conv_join xs ^ " ("^ x ^")"
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362 (* auto (problem_of "x a a a" (conv_join[
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368 auto (problem_of "x a a a a" (conv_join[
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375 (* Controesempio ad usare un conto dei lambda che non considere le permutazioni *)
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376 auto (problem_of "x a a a a (x (x. x x) @ @ (_._.x. x x) x) b b b" (conv_join[
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377 "x a a a a (_. a) b b b";
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378 "x a a a a (_. _. _. _. x. y. x y)";
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383 [ "x x"; "y z"; "y x" ]
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384 [ step 0 0 0; step 1 0 1; eat 5; ]
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389 [ "a b @"; "a @ c"; "a a a" ]
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390 [ step 0 0 0; step 1 1 0; eat 2; ]
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394 "a (a b c) (a d e)"
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395 [ "a (a b @) (a @ e)"; "a a a" ]
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396 [ step 0 0 0; step 1 1 0; eat 2]
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400 print_endline "ALL DONE. "
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402 (* TEMPORARY TESTING FACILITY BELOW HERE *)
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405 let n = Random.int (List.length l) in
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410 let n1 = List.length l1 in
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411 let n = Random.int (n1 + List.length l2) in
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412 if n >= n1 then List.nth l2 (n - n1) else List.nth l1 n
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416 let rec aux n inerts lams =
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417 if n = 0 then List.hd inerts, List.hd (Util.sort_uniq (List.tl inerts))
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418 else let inerts, lams = if Random.int 2 = 0
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419 then inerts, ("(" ^ acaso vars ^ ". " ^ acaso2 inerts lams ^ ")") :: lams
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420 else ("(" ^ acaso inerts ^ " " ^ acaso2 inerts lams^ ")") :: inerts, lams
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421 in aux (n-1) inerts lams
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422 in aux (2*n) vars []
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426 let complex = 200 in
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427 let vars = ["x"; "y"; "z"; "v" ; "w"; "a"; "b"; "c"] in
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430 let rec repeat f n =
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431 prerr_endline "\n########################### NEW TEST ###########################";
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433 if n > 0 then repeat f (n-1)
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438 Random.self_init ();
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440 let div, conv = f () in
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441 auto (problem_of div conv)
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