1.1 --- a/src/Tools/isac/Scripts/term_G.sml Wed Aug 25 15:15:01 2010 +0200
1.2 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000
1.3 @@ -1,1343 +0,0 @@
1.4 -(* extends Isabelle/src/Pure/term.ML
1.5 - (c) Walther Neuper 1999
1.6 -
1.7 -use"Scripts/term_G.sml";
1.8 -use"term_G.sml";
1.9 -*)
1.10 -
1.11 -(*
1.12 -> (cterm_of thy) a_term;
1.13 -val it = "empty" : cterm *)
1.14 -
1.15 -(*2003 fun match thy t pat =
1.16 - (snd (Pattern.match (Sign.tsig_of (sign_of thy)) (pat, t)))
1.17 - handle _ => [];
1.18 -fn : theory ->
1.19 - Term.term -> Term.term -> (Term.indexname * Term.term) list*)
1.20 -(*see src/Tools/eqsubst.ML fun clean_match*)
1.21 -(*2003 fun matches thy tm pa = if match thy tm pa = [] then false else true;*)
1.22 -fun matches thy tm pa =
1.23 - (Pattern.match thy (pa, tm) (Vartab.empty, Vartab.empty); true)
1.24 - handle _ => false
1.25 -
1.26 -fun atomtyp t = (*see raw_pp_typ*)
1.27 - let
1.28 - fun ato n (Type (s,[])) =
1.29 - ("\n*** "^indent n^"Type ("^s^",[])")
1.30 - | ato n (Type (s,Ts)) =
1.31 - ("\n*** "^indent n^"Type ("^s^",["^ atol (n+1) Ts)
1.32 -
1.33 - | ato n (TFree (s,sort)) =
1.34 - ("\n*** "^indent n^"TFree ("^s^",["^ strs2str' sort)
1.35 -
1.36 - | ato n (TVar ((s,i),sort)) =
1.37 - ("\n*** "^indent n^"TVar (("^s^","^
1.38 - string_of_int i ^ strs2str' sort)
1.39 - and atol n [] =
1.40 - ("\n*** "^indent n^"]")
1.41 - | atol n (T::Ts) = (ato n T ^ atol n Ts)
1.42 -(*in print (ato 0 t ^ "\n") end; TODO TUM10*)
1.43 -in writeln(ato 0 t) end;
1.44 -
1.45 -(*Prog.Tutorial.p.34*)
1.46 -local
1.47 - fun pp_pair (x, y) = Pretty.list "(" ")" [x, y]
1.48 - fun pp_list xs = Pretty.list "[" "]" xs
1.49 - fun pp_str s = Pretty.str s
1.50 - fun pp_qstr s = Pretty.quote (pp_str s)
1.51 - fun pp_int i = pp_str (string_of_int i)
1.52 - fun pp_sort S = pp_list (map pp_qstr S)
1.53 - fun pp_constr a args = Pretty.block [pp_str a, Pretty.brk 1, args]
1.54 -in
1.55 -fun raw_pp_typ (TVar ((a, i), S)) =
1.56 - pp_constr "TVar" (pp_pair (pp_pair (pp_qstr a, pp_int i), pp_sort S))
1.57 - | raw_pp_typ (TFree (a, S)) =
1.58 - pp_constr "TFree" (pp_pair (pp_qstr a, pp_sort S))
1.59 - | raw_pp_typ (Type (a, tys)) =
1.60 - pp_constr "Type" (pp_pair (pp_qstr a, pp_list (map raw_pp_typ tys)))
1.61 -end
1.62 -(* install
1.63 -PolyML.addPrettyPrinter
1.64 - (fn _ => fn _ => ml_pretty o Pretty.to_ML o raw_pp_typ);
1.65 -de-install
1.66 -PolyML.addPrettyPrinter
1.67 - (fn _ => fn _ => ml_pretty o Pretty.to_ML o Proof_Display.pp_typ Pure.thy);
1.68 -*)
1.69 -
1.70 -(*
1.71 -> val T = (type_of o term_of o the o (parse thy)) "a::[real,int] => nat";
1.72 -> atomtyp T;
1.73 -*** Type (fun,[
1.74 -*** Type (RealDef.real,[])
1.75 -*** Type (fun,[
1.76 -*** Type (IntDef.int,[])
1.77 -*** Type (nat,[])
1.78 -*** ]
1.79 -*** ]
1.80 -*)
1.81 -
1.82 -fun atomt t =
1.83 - let fun ato (Const(a,T)) n =
1.84 - ("\n*** "^indent n^"Const ("^a^")")
1.85 - | ato (Free (a,T)) n =
1.86 - ("\n*** "^indent n^"Free ("^a^", "^")")
1.87 - | ato (Var ((a,ix),T)) n =
1.88 - ("\n*** "^indent n^"Var (("^a^", "^(string_of_int ix)^"), "^")")
1.89 - | ato (Bound ix) n =
1.90 - ("\n*** "^indent n^"Bound "^(string_of_int ix))
1.91 - | ato (Abs(a,T,body)) n =
1.92 - ("\n*** "^indent n^"Abs("^a^",..")^ato body (n+1)
1.93 - | ato (f$t') n = (ato f n; ato t' (n+1))
1.94 - in writeln("\n*** -------------"^ ato t 0 ^"\n***") end;
1.95 -
1.96 -fun term_detail2str t =
1.97 - let fun ato (Const (a, T)) n =
1.98 - "\n*** "^indent n^"Const ("^a^", "^string_of_typ T^")"
1.99 - | ato (Free (a, T)) n =
1.100 - "\n*** "^indent n^"Free ("^a^", "^string_of_typ T^")"
1.101 - | ato (Var ((a, ix), T)) n =
1.102 - "\n*** "^indent n^"Var (("^a^", "^string_of_int ix^"), "^
1.103 - string_of_typ T^")"
1.104 - | ato (Bound ix) n =
1.105 - "\n*** "^indent n^"Bound "^string_of_int ix
1.106 - | ato (Abs(a, T, body)) n =
1.107 - "\n*** "^indent n^"Abs ("^a^", "^
1.108 - (string_of_typ T)^",.."
1.109 - ^ato body (n + 1)
1.110 - | ato (f $ t') n = ato f n^ato t' (n+1)
1.111 - in "\n*** "^ato t 0^"\n***" end;
1.112 -fun atomty t = (writeln o term_detail2str) t;
1.113 -
1.114 -fun term_str thy (Const(s,_)) = s
1.115 - | term_str thy (Free(s,_)) = s
1.116 - | term_str thy (Var((s,i),_)) = s^(string_of_int i)
1.117 - | term_str thy (Bound i) = "B."^(string_of_int i)
1.118 - | term_str thy (Abs(s,_,_)) = s
1.119 - | term_str thy t = raise error("term_str not for "^term2str t);
1.120 -
1.121 -(*.contains the fst argument the second argument (a leave! of term).*)
1.122 -fun contains_term (Abs(_,_,body)) t = contains_term body t
1.123 - | contains_term (f $ f') t =
1.124 - contains_term f t orelse contains_term f' t
1.125 - | contains_term s t = t = s;
1.126 -(*.contains the term a VAR(("*",_),_) ?.*)
1.127 -fun contains_Var (Abs(_,_,body)) = contains_Var body
1.128 - | contains_Var (f $ f') = contains_Var f orelse contains_Var f'
1.129 - | contains_Var (Var _) = true
1.130 - | contains_Var _ = false;
1.131 -(* contains_Var (str2term "?z = 3") (*true*);
1.132 - contains_Var (str2term "z = 3") (*false*);
1.133 - *)
1.134 -
1.135 -(*fun int_of_str str =
1.136 - let val ss = explode str
1.137 - val str' = case ss of
1.138 - "("::s => drop_last s | _ => ss
1.139 - in case BasisLibrary.Int.fromString (implode str') of
1.140 - SOME i => SOME i
1.141 - | NONE => NONE end;*)
1.142 -fun int_of_str str =
1.143 - let val ss = explode str
1.144 - val str' = case ss of
1.145 - "("::s => drop_last s | _ => ss
1.146 - in (SOME (Thy_Output.integer (implode str'))) handle _ => NONE end;
1.147 -(*
1.148 -> int_of_str "123";
1.149 -val it = SOME 123 : int option
1.150 -> int_of_str "(-123)";
1.151 -val it = SOME 123 : int option
1.152 -> int_of_str "#123";
1.153 -val it = NONE : int option
1.154 -> int_of_str "-123";
1.155 -val it = SOME ~123 : int option
1.156 -*)
1.157 -fun int_of_str' str =
1.158 - case int_of_str str of
1.159 - SOME i => i
1.160 - | NONE => raise TERM ("int_of_string: no int-string",[]);
1.161 -val str2int = int_of_str';
1.162 -
1.163 -fun is_numeral str = case int_of_str str of
1.164 - SOME _ => true
1.165 - | NONE => false;
1.166 -val is_no = is_numeral;
1.167 -fun is_num (Free (s,_)) = if is_numeral s then true else false
1.168 - | is_num _ = false;
1.169 -(*>
1.170 -> is_num ((term_of o the o (parse thy)) "#1");
1.171 -val it = true : bool
1.172 -> is_num ((term_of o the o (parse thy)) "#-1");
1.173 -val it = true : bool
1.174 -> is_num ((term_of o the o (parse thy)) "a123");
1.175 -val it = false : bool
1.176 -*)
1.177 -
1.178 -(*fun int_of_Free (Free (intstr, _)) =
1.179 - (case BasisLibrary.Int.fromString intstr of
1.180 - SOME i => i
1.181 - | NONE => raise error ("int_of_Free ( "^ intstr ^", _)"))
1.182 - | int_of_Free t = raise error ("int_of_Free ( "^ term2str t ^" )");*)
1.183 -fun int_of_Free (Free (intstr, _)) = (Thy_Output.integer intstr
1.184 - handle _ => raise error ("int_of_Free ( "^ intstr ^", _)"))
1.185 - | int_of_Free t = raise error ("int_of_Free ( "^ term2str t ^" )");
1.186 -
1.187 -fun vars t =
1.188 - let
1.189 - fun scan vs (Const(s,T)) = vs
1.190 - | scan vs (t as Free(s,T)) = if is_no s then vs else t::vs
1.191 - | scan vs (t as Var((s,i),T)) = t::vs
1.192 - | scan vs (Bound i) = vs
1.193 - | scan vs (Abs(s,T,t)) = scan vs t
1.194 - | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)
1.195 - in (distinct o (scan [])) t end;
1.196 -
1.197 -fun is_Free (Free _) = true
1.198 - | is_Free _ = false;
1.199 -fun is_fun_id (Const _) = true
1.200 - | is_fun_id (Free _) = true
1.201 - | is_fun_id _ = false;
1.202 -fun is_f_x (f $ x) = is_fun_id f andalso is_Free x
1.203 - | is_f_x _ = false;
1.204 -(* is_f_x (str2term "q_0/2 * L * x") (*false*);
1.205 - is_f_x (str2term "M_b x") (*true*);
1.206 - *)
1.207 -fun vars_str t =
1.208 - let
1.209 - fun scan vs (Const(s,T)) = vs
1.210 - | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs
1.211 - | scan vs (t as Var((s,i),T)) = (s^"_"^(string_of_int i))::vs
1.212 - | scan vs (Bound i) = vs
1.213 - | scan vs (Abs(s,T,t)) = scan vs t
1.214 - | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)
1.215 - in (distinct o (scan [])) t end;
1.216 -
1.217 -fun ids2str t =
1.218 - let
1.219 - fun scan vs (Const(s,T)) = if is_no s then vs else s::vs
1.220 - | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs
1.221 - | scan vs (t as Var((s,i),T)) = (s^"_"^(string_of_int i))::vs
1.222 - | scan vs (Bound i) = vs
1.223 - | scan vs (Abs(s,T,t)) = scan (s::vs) t
1.224 - | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)
1.225 - in (distinct o (scan [])) t end;
1.226 -fun is_bdv str =
1.227 - case explode str of
1.228 - "b"::"d"::"v"::_ => true
1.229 - | _ => false;
1.230 -fun is_bdv_ (Free (s,_)) = is_bdv s
1.231 - | is_bdv_ _ = false;
1.232 -
1.233 -fun free2str (Free (s,_)) = s
1.234 - | free2str t = raise error ("free2str not for "^ term2str t);
1.235 -fun free2int (t as Free (s, _)) = ((str2int s)
1.236 - handle _ => raise error ("free2int: "^term_detail2str t))
1.237 - | free2int t = raise error ("free2int: "^term_detail2str t);
1.238 -
1.239 -(*27.8.01: unused*)
1.240 -fun var2free (t as Const(s,T)) = t
1.241 - | var2free (t as Free(s,T)) = t
1.242 - | var2free (Var((s,i),T)) = Free(s,T)
1.243 - | var2free (t as Bound i) = t
1.244 - | var2free (Abs(s,T,t)) = Abs(s,T,var2free t)
1.245 - | var2free (t1 $ t2) = (var2free t1) $ (var2free t2);
1.246 -
1.247 -(*27.8.01: doesn't find some subterm ???!???*)
1.248 -(*2010 Logic.varify !!!*)
1.249 -fun free2var (t as Const(s,T)) = t
1.250 - | free2var (t as Free(s,T)) = if is_no s then t else Var((s,0),T)
1.251 - | free2var (t as Var((s,i),T)) = t
1.252 - | free2var (t as Bound i) = t
1.253 - | free2var (Abs(s,T,t)) = Abs(s,T,free2var t)
1.254 - | free2var (t1 $ t2) = (free2var t1) $ (free2var t2);
1.255 -
1.256 -
1.257 -fun mk_listT T = Type ("List.list", [T]);
1.258 -fun list_const T =
1.259 - Const("List.list.Cons", [T, mk_listT T] ---> mk_listT T);
1.260 -(*28.8.01: TODO: get type from head of list: 1 arg less!!!*)
1.261 -fun list2isalist T [] = Const("List.list.Nil",mk_listT T)
1.262 - | list2isalist T (t::ts) = (list_const T) $ t $ (list2isalist T ts);
1.263 -(*
1.264 -> val tt = (term_of o the o (parse thy)) "R=(R::real)";
1.265 -> val TT = type_of tt;
1.266 -> val ss = list2isalist TT [tt,tt,tt];
1.267 -> (cterm_of thy) ss;
1.268 -val it = "[R = R, R = R, R = R]" : cterm *)
1.269 -
1.270 -fun isapair2pair (Const ("Pair",_) $ a $ b) = (a,b)
1.271 - | isapair2pair t =
1.272 - raise error ("isapair2pair called with "^term2str t);
1.273 -
1.274 -val listType = Type ("List.list",[Type ("bool",[])]);
1.275 -fun isalist2list ls =
1.276 - let
1.277 - fun get es (Const("List.list.Cons",_) $ t $ ls) = get (t::es) ls
1.278 - | get es (Const("List.list.Nil",_)) = es
1.279 - | get _ t =
1.280 - raise error ("isalist2list applied to NON-list '"^term2str t^"'")
1.281 - in (rev o (get [])) ls end;
1.282 -(*
1.283 -> val il = str2term "[a=b,c=d,e=f]";
1.284 -> val l = isalist2list il;
1.285 -> (writeln o terms2str) l;
1.286 -["a = b","c = d","e = f"]
1.287 -
1.288 -> val il = str2term "ss___::bool list";
1.289 -> val l = isalist2list il;
1.290 -[Free ("ss___", "bool List.list")]
1.291 -*)
1.292 -
1.293 -
1.294 -(*review Isabelle2009/src/HOL/Tools/hologic.ML*)
1.295 -val prop = Type ("prop",[]); (* ~/Diss.99/Integers-Isa/tools.sml*)
1.296 -val bool = Type ("bool",[]); (* 2002 Integ.int *)
1.297 -val Trueprop = Const("Trueprop",bool-->prop);
1.298 -fun mk_prop t = Trueprop $ t;
1.299 -val true_as_term = Const("True",bool);
1.300 -val false_as_term = Const("False",bool);
1.301 -val true_as_cterm = cterm_of (theory "HOL") true_as_term;
1.302 -val false_as_cterm = cterm_of (theory "HOL") false_as_term;
1.303 -
1.304 -infixr 5 -->; (*2002 /Pure/term.ML *)
1.305 -infixr --->; (*2002 /Pure/term.ML *)
1.306 -fun S --> T = Type("fun",[S,T]); (*2002 /Pure/term.ML *)
1.307 -val op ---> = foldr (op -->); (*2002 /Pure/term.ML *)
1.308 -fun list_implies ([], B) = B : term (*2002 /term.ML *)
1.309 - | list_implies (A::AS, B) = Logic.implies $ A $ list_implies(AS,B);
1.310 -
1.311 -
1.312 -
1.313 -(** substitution **)
1.314 -
1.315 -fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = (* = thm.ML *)
1.316 - match_bvs(s, t, if x="" orelse y="" then al
1.317 - else (x,y)::al)
1.318 - | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
1.319 - | match_bvs(_,_,al) = al;
1.320 -fun ren_inst(insts,prop,pat,obj) = (* = thm.ML *)
1.321 - let val ren = match_bvs(pat,obj,[])
1.322 - fun renAbs(Abs(x,T,b)) =
1.323 - Abs(case assoc_string(ren,x) of NONE => x
1.324 - | SOME(y) => y, T, renAbs(b))
1.325 - | renAbs(f$t) = renAbs(f) $ renAbs(t)
1.326 - | renAbs(t) = t
1.327 - in subst_vars insts (if null(ren) then prop else renAbs(prop)) end;
1.328 -
1.329 -
1.330 -
1.331 -
1.332 -
1.333 -
1.334 -fun dest_equals' (Const("op =",_) $ t $ u) = (t,u)(* logic.ML: Const("=="*)
1.335 - | dest_equals' t = raise TERM("dest_equals'", [t]);
1.336 -val lhs_ = (fst o dest_equals');
1.337 -val rhs_ = (snd o dest_equals');
1.338 -
1.339 -fun is_equality (Const("op =",_) $ t $ u) = true (* logic.ML: Const("=="*)
1.340 - | is_equality _ = false;
1.341 -fun mk_equality (t,u) = (Const("op =",[type_of t,type_of u]--->bool) $ t $ u);
1.342 -fun is_expliceq (Const("op =",_) $ (Free _) $ u) = true
1.343 - | is_expliceq _ = false;
1.344 -fun strip_trueprop (Const("Trueprop",_) $ t) = t
1.345 - | strip_trueprop t = t;
1.346 -(* | strip_trueprop t = raise TERM("strip_trueprop", [t]);
1.347 -*)
1.348 -
1.349 -(*.(A1==>...An==>B) goes to (A1==>...An==>).*)
1.350 -fun strip_imp_prems' (Const("==>", T) $ A $ t) =
1.351 - let fun coll_prems As (Const("==>", _) $ A $ t) =
1.352 - coll_prems (As $ (Logic.implies $ A)) t
1.353 - | coll_prems As _ = SOME As
1.354 - in coll_prems (Logic.implies $ A) t end
1.355 - | strip_imp_prems' _ = NONE; (* logic.ML: term -> term list*)
1.356 -(*
1.357 - val thm = real_mult_div_cancel1;
1.358 - val prop = (#prop o rep_thm) thm;
1.359 - atomt prop;
1.360 -*** -------------
1.361 -*** Const ( ==>)
1.362 -*** . Const ( Trueprop)
1.363 -*** . . Const ( Not)
1.364 -*** . . . Const ( op =)
1.365 -*** . . . . Var ((k, 0), )
1.366 -*** . . . . Const ( 0)
1.367 -*** . Const ( Trueprop)
1.368 -*** . . Const ( op =) *** .............
1.369 - val SOME t = strip_imp_prems' ((#prop o rep_thm) thm);
1.370 - atomt t;
1.371 -*** -------------
1.372 -*** Const ( ==>)
1.373 -*** . Const ( Trueprop)
1.374 -*** . . Const ( Not)
1.375 -*** . . . Const ( op =)
1.376 -*** . . . . Var ((k, 0), )
1.377 -*** . . . . Const ( 0)
1.378 -
1.379 - val thm = real_le_anti_sym;
1.380 - val prop = (#prop o rep_thm) thm;
1.381 - atomt prop;
1.382 -*** -------------
1.383 -*** Const ( ==>)
1.384 -*** . Const ( Trueprop)
1.385 -*** . . Const ( op <=)
1.386 -*** . . . Var ((z, 0), )
1.387 -*** . . . Var ((w, 0), )
1.388 -*** . Const ( ==>)
1.389 -*** . . Const ( Trueprop)
1.390 -*** . . . Const ( op <=)
1.391 -*** . . . . Var ((w, 0), )
1.392 -*** . . . . Var ((z, 0), )
1.393 -*** . . Const ( Trueprop)
1.394 -*** . . . Const ( op =)
1.395 -*** .............
1.396 - val SOME t = strip_imp_prems' ((#prop o rep_thm) thm);
1.397 - atomt t;
1.398 -*** -------------
1.399 -*** Const ( ==>)
1.400 -*** . Const ( Trueprop)
1.401 -*** . . Const ( op <=)
1.402 -*** . . . Var ((z, 0), )
1.403 -*** . . . Var ((w, 0), )
1.404 -*** . Const ( ==>)
1.405 -*** . . Const ( Trueprop)
1.406 -*** . . . Const ( op <=)
1.407 -*** . . . . Var ((w, 0), )
1.408 -*** . . . . Var ((z, 0), )
1.409 -*)
1.410 -
1.411 -(*. (A1==>...An==>) (B) goes to (A1==>...An==>B), where B is lowest branch.*)
1.412 -fun ins_concl (Const("==>", T) $ A $ t) B = Logic.implies $ A $ (ins_concl t B)
1.413 - | ins_concl (Const("==>", T) $ A ) B = Logic.implies $ A $ B
1.414 - | ins_concl t B = raise TERM("ins_concl", [t, B]);
1.415 -(*
1.416 - val thm = real_le_anti_sym;
1.417 - val prop = (#prop o rep_thm) thm;
1.418 - val concl = Logic.strip_imp_concl prop;
1.419 - val SOME prems = strip_imp_prems' prop;
1.420 - val prop' = ins_concl prems concl;
1.421 - prop = prop';
1.422 - atomt prop;
1.423 - atomt prop';
1.424 -*)
1.425 -
1.426 -
1.427 -fun vperm (Var _, Var _) = true (*2002 Pure/thm.ML *)
1.428 - | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t)
1.429 - | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2)
1.430 - | vperm (t, u) = (t = u);
1.431 -
1.432 -(*2002 cp from Pure/term.ML --- since 2009 in Pure/old_term.ML*)
1.433 -fun mem_term (_, []) = false
1.434 - | mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts);
1.435 -fun subset_term ([], ys) = true
1.436 - | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys);
1.437 -fun eq_set_term (xs, ys) =
1.438 - xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));
1.439 -(*a total, irreflexive ordering on index names*)
1.440 -fun xless ((a,i), (b,j): indexname) = i<j orelse (i=j andalso a<b);
1.441 -(*a partial ordering (not reflexive) for atomic terms*)
1.442 -fun atless (Const (a,_), Const (b,_)) = a<b
1.443 - | atless (Free (a,_), Free (b,_)) = a<b
1.444 - | atless (Var(v,_), Var(w,_)) = xless(v,w)
1.445 - | atless (Bound i, Bound j) = i<j
1.446 - | atless _ = false;
1.447 -(*insert atomic term into partially sorted list, suppressing duplicates (?)*)
1.448 -fun insert_aterm (t,us) =
1.449 - let fun inserta [] = [t]
1.450 - | inserta (us as u::us') =
1.451 - if atless(t,u) then t::us
1.452 - else if t=u then us (*duplicate*)
1.453 - else u :: inserta(us')
1.454 - in inserta us end;
1.455 -
1.456 -(*Accumulates the Vars in the term, suppressing duplicates*)
1.457 -fun add_term_vars (t, vars: term list) = case t of
1.458 - Var _ => insert_aterm(t,vars)
1.459 - | Abs (_,_,body) => add_term_vars(body,vars)
1.460 - | f$t => add_term_vars (f, add_term_vars(t, vars))
1.461 - | _ => vars;
1.462 -fun term_vars t = add_term_vars(t,[]);
1.463 -
1.464 -
1.465 -fun var_perm (t, u) = (*2002 Pure/thm.ML *)
1.466 - vperm (t, u) andalso eq_set_term (term_vars t, term_vars u);
1.467 -
1.468 -(*2002 fun decomp_simp, Pure/thm.ML *)
1.469 -fun perm lhs rhs = var_perm (lhs, rhs) andalso not (lhs aconv rhs)
1.470 - andalso not (is_Var lhs);
1.471 -
1.472 -
1.473 -fun str_of_int n =
1.474 - if n < 0 then "-"^((string_of_int o abs) n)
1.475 - else string_of_int n;
1.476 -(*
1.477 -> str_of_int 1;
1.478 -val it = "1" : string > str_of_int ~1;
1.479 -val it = "-1" : string
1.480 -*)
1.481 -
1.482 -
1.483 -fun power b 0 = 1
1.484 - | power b n =
1.485 - if n>0 then b*(power b (n-1))
1.486 - else raise error ("power "^(str_of_int b)^" "^(str_of_int n));
1.487 -(*
1.488 -> power 2 3;
1.489 -val it = 8 : int
1.490 -> power ~2 3;
1.491 -val it = ~8 : int
1.492 -> power ~3 2;
1.493 -val it = 9 : int
1.494 -> power 3 ~2;
1.495 -*)
1.496 -fun gcd 0 b = b
1.497 - | gcd a b = if a < b then gcd (b mod a) a
1.498 - else gcd (a mod b) b;
1.499 -fun sign n = if n < 0 then ~1
1.500 - else if n = 0 then 0 else 1;
1.501 -fun sign2 n1 n2 = (sign n1) * (sign n2);
1.502 -
1.503 -infix dvd;
1.504 -fun d dvd n = n mod d = 0;
1.505 -
1.506 -fun divisors n =
1.507 - let fun pdiv ds d n =
1.508 - if d=n then d::ds
1.509 - else if d dvd n then pdiv (d::ds) d (n div d)
1.510 - else pdiv ds (d+1) n
1.511 - in pdiv [] 2 n end;
1.512 -
1.513 -divisors 30;
1.514 -divisors 32;
1.515 -divisors 60;
1.516 -divisors 11;
1.517 -
1.518 -fun doubles ds = (* ds is ordered *)
1.519 - let fun dbls ds [] = ds
1.520 - | dbls ds [i] = ds
1.521 - | dbls ds (i::i'::is) = if i=i' then dbls (i::ds) is
1.522 - else dbls ds (i'::is)
1.523 - in dbls [] ds end;
1.524 -(*> doubles [2,3,4];
1.525 -val it = [] : int list
1.526 -> doubles [2,3,3,5,5,7];
1.527 -val it = [5,3] : int list*)
1.528 -
1.529 -fun squfact 0 = 0
1.530 - | squfact 1 = 1
1.531 - | squfact n = foldl op* (1, (doubles o divisors) n);
1.532 -(*> squfact 30;
1.533 -val it = 1 : int
1.534 -> squfact 32;
1.535 -val it = 4 : int
1.536 -> squfact 60;
1.537 -val it = 2 : int
1.538 -> squfact 11;
1.539 -val it = 1 : int*)
1.540 -
1.541 -
1.542 -fun dest_type (Type(T,[])) = T
1.543 - | dest_type T =
1.544 - (atomtyp T;
1.545 - raise error ("... dest_type: not impl. for this type"));
1.546 -
1.547 -fun term_of_num ntyp n = Free (str_of_int n, ntyp);
1.548 -
1.549 -fun pairT T1 T2 = Type ("*", [T1, T2]);
1.550 -(*> val t = str2term "(1,2)";
1.551 -> type_of t = pairT HOLogic.realT HOLogic.realT;
1.552 -val it = true : bool
1.553 -*)
1.554 -fun PairT T1 T2 = ([T1, T2] ---> Type ("*", [T1, T2]));
1.555 -(*> val t = str2term "(1,2)";
1.556 -> val Const ("Pair",pT) $ _ $ _ = t;
1.557 -> pT = PairT HOLogic.realT HOLogic.realT;
1.558 -val it = true : bool
1.559 -*)
1.560 -fun pairt t1 t2 =
1.561 - Const ("Pair", PairT (type_of t1) (type_of t2)) $ t1 $ t2;
1.562 -(*> val t = str2term "(1,2)";
1.563 -> val (t1, t2) = (str2term "1", str2term "2");
1.564 -> t = pairt t1 t2;
1.565 -val it = true : bool*)
1.566 -
1.567 -
1.568 -fun num_of_term (t as Free (s,_)) =
1.569 - (case int_of_str s of
1.570 - SOME s' => s'
1.571 - | NONE => raise error ("num_of_term not for "^ term2str t))
1.572 - | num_of_term t = raise error ("num_of_term not for "^term2str t);
1.573 -
1.574 -fun mk_factroot op_(*=thy.sqrt*) T fact root =
1.575 - Const ("op *", [T, T] ---> T) $ (term_of_num T fact) $
1.576 - (Const (op_, T --> T) $ term_of_num T root);
1.577 -(*
1.578 -val T = (type_of o term_of o the) (parse thy "#12::real");
1.579 -val t = mk_factroot "SqRoot.sqrt" T 2 3;
1.580 -(cterm_of thy) t;
1.581 -val it = "#2 * sqrt #3 " : cterm
1.582 -*)
1.583 -fun var_op_num v op_ optype ntyp n =
1.584 - Const (op_, optype) $ v $
1.585 - Free (str_of_int n, ntyp);
1.586 -
1.587 -fun num_op_var v op_ optype ntyp n =
1.588 - Const (op_,optype) $
1.589 - Free (str_of_int n, ntyp) $ v;
1.590 -
1.591 -fun num_op_num T1 T2 (op_,Top) n1 n2 =
1.592 - Const (op_,Top) $
1.593 - Free (str_of_int n1, T1) $ Free (str_of_int n2, T2);
1.594 -(*
1.595 -> val t = num_op_num "Int" 3 4;
1.596 -> atomty t;
1.597 -> string_of_cterm ((cterm_of thy) t);
1.598 -*)
1.599 -
1.600 -fun const_in str (Const _) = false
1.601 - | const_in str (Free (s,_)) = if strip_thy s = str then true else false
1.602 - | const_in str (Bound _) = false
1.603 - | const_in str (Var _) = false
1.604 - | const_in str (Abs (_,_,body)) = const_in str body
1.605 - | const_in str (f$u) = const_in str f orelse const_in str u;
1.606 -(*
1.607 -> val t = (term_of o the o (parse thy)) "6 + 5 * sqrt 4 + 3";
1.608 -> const_in "sqrt" t;
1.609 -val it = true : bool
1.610 -> val t = (term_of o the o (parse thy)) "6 + 5 * 4 + 3";
1.611 -> const_in "sqrt" t;
1.612 -val it = false : bool
1.613 -*)
1.614 -
1.615 -(*used for calculating built in binary operations in Isabelle2002->Float.ML*)
1.616 -(*fun calc "op +" (n1, n2) = n1+n2
1.617 - | calc "op -" (n1, n2) = n1-n2
1.618 - | calc "op *" (n1, n2) = n1*n2
1.619 - | calc "HOL.divide"(n1, n2) = n1 div n2
1.620 - | calc "Atools.pow"(n1, n2) = power n1 n2
1.621 - | calc op_ _ = raise error ("calc: operator = "^op_^" not defined");-----*)
1.622 -fun calc_equ "op <" (n1, n2) = n1 < n2
1.623 - | calc_equ "op <=" (n1, n2) = n1 <= n2
1.624 - | calc_equ op_ _ =
1.625 - raise error ("calc_equ: operator = "^op_^" not defined");
1.626 -fun sqrt (n:int) = if n < 0 then 0
1.627 - (*FIXME ~~~*) else (trunc o Math.sqrt o Real.fromInt) n;
1.628 -
1.629 -fun mk_thmid thmid op_ n1 n2 =
1.630 - thmid ^ (strip_thy n1) ^ "_" ^ (strip_thy n2);
1.631 -
1.632 -fun dest_binop_typ (Type("fun",[range,Type("fun",[arg2,arg1])])) =
1.633 - (arg1,arg2,range)
1.634 - | dest_binop_typ _ = raise error "dest_binop_typ: not binary";
1.635 -(* -----
1.636 -> val t = (term_of o the o (parse thy)) "#3^#4";
1.637 -> val hT = type_of (head_of t);
1.638 -> dest_binop_typ hT;
1.639 -val it = ("'a","nat","'a") : typ * typ * typ
1.640 - ----- *)
1.641 -
1.642 -
1.643 -(** transform binary numeralsstrings **)
1.644 -(*Makarius 100308, hacked by WN*)
1.645 -val numbers_to_string =
1.646 - let
1.647 - fun dest_num t =
1.648 - (case try HOLogic.dest_number t of
1.649 - SOME (T, i) =>
1.650 - (*if T = @{typ int} orelse T = @{typ real} then WN*)
1.651 - SOME (Free (signed_string_of_int i, T))
1.652 - (*else NONE WN*)
1.653 - | NONE => NONE);
1.654 -
1.655 - fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)
1.656 - | to_str (t as (u1 $ u2)) =
1.657 - (case dest_num t of
1.658 - SOME t' => t'
1.659 - | NONE => to_str u1 $ to_str u2)
1.660 - | to_str t = perhaps dest_num t;
1.661 - in to_str end
1.662 -
1.663 -(*.make uminus uniform:
1.664 - Const ("uminus", _) $ Free ("2", "RealDef.real") --> Free ("-2", _)
1.665 -to be used immediately before evaluation of numerals;
1.666 -see Scripts/calculate.sml .*)
1.667 -(*2002 fun(*app_num_tr'2 (Const("0",T)) = Free("0",T)
1.668 - | app_num_tr'2 (Const("1",T)) = Free("1",T)
1.669 - |*)app_num_tr'2 (t as Const("uminus",_) $ Free(s,T)) =
1.670 - (case int_of_str s of SOME i =>
1.671 - if i > 0 then Free("-"^s,T) else Free(s,T)
1.672 - | NONE => t)
1.673 -(*| app_num_tr'2 (t as Const(s,T)) = t
1.674 - | app_num_tr'2 (Const("Numeral.number_of",Type ("fun", [_, T])) $ t) =
1.675 - Free(NumeralSyntax.dest_bin_str t, T)
1.676 - | app_num_tr'2 (t as Free(s,T)) = t
1.677 - | app_num_tr'2 (t as Var(n,T)) = t
1.678 - | app_num_tr'2 (t as Bound i) = t
1.679 -*)| app_num_tr'2 (Abs(s,T,body)) = Abs(s,T, app_num_tr'2 body)
1.680 - | app_num_tr'2 (t1 $ t2) = (app_num_tr'2 t1) $ (app_num_tr'2 t2)
1.681 - | app_num_tr'2 t = t;
1.682 -*)
1.683 -val uminus_to_string =
1.684 - let
1.685 - fun dest_num t =
1.686 - (case t of
1.687 - (Const ("HOL.uminus_class.uminus", _) $ Free (s, T)) =>
1.688 - (case int_of_str s of
1.689 - SOME i =>
1.690 - SOME (Free (signed_string_of_int (~1 * i), T))
1.691 - | NONE => NONE)
1.692 - | _ => NONE);
1.693 -
1.694 - fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)
1.695 - | to_str (t as (u1 $ u2)) =
1.696 - (case dest_num t of
1.697 - SOME t' => t'
1.698 - | NONE => to_str u1 $ to_str u2)
1.699 - | to_str t = perhaps dest_num t;
1.700 - in to_str end;
1.701 -
1.702 -
1.703 -(*2002 fun num_str thm =
1.704 - let
1.705 - val {sign_ref = sign_ref, der = der, maxidx = maxidx,
1.706 - shyps = shyps, hyps = hyps, (*tpairs = tpairs,*) prop = prop} =
1.707 - rep_thm_G thm;
1.708 - val prop' = app_num_tr'1 prop;
1.709 - in assbl_thm sign_ref der maxidx shyps hyps (*tpairs*) prop' end;*)
1.710 -fun num_str thm =
1.711 - let val (deriv,
1.712 - {thy_ref = thy_ref, tags = tags, maxidx = maxidx, shyps = shyps,
1.713 - hyps = hyps, tpairs = tpairs, prop = prop}) = rep_thm_G thm
1.714 - val prop' = numbers_to_string prop;
1.715 - in assbl_thm deriv thy_ref tags maxidx shyps hyps tpairs prop' end;
1.716 -
1.717 -fun get_thm' xstring = (*?covers 2009 Thm?!, replaces 2002 fun get_thm :
1.718 -val it = fn : theory -> xstring -> Thm.thm*)
1.719 - Thm (xstring,
1.720 - num_str (ProofContext.get_thm (thy2ctxt' "Isac") xstring));
1.721 -
1.722 -(** get types of Free and Abs for parse' **)
1.723 -(*11.1.00: not used, fix-typed +,*,-,^ instead *)
1.724 -
1.725 -val dummyT = Type ("dummy",[]);
1.726 -val dummyT = TVar (("DUMMY",0),[]);
1.727 -
1.728 -(* assumes only 1 type for numerals
1.729 - and different identifiers for Const, Free and Abs *)
1.730 -fun get_types t =
1.731 - let
1.732 - fun get ts (Const(s,T)) = (s,T)::ts
1.733 - | get ts (Free(s,T)) = if is_no s
1.734 - then ("#",T)::ts else (s,T)::ts
1.735 - | get ts (Var(n,T)) = ts
1.736 - | get ts (Bound i) = ts
1.737 - | get ts (Abs(s,T,body)) = get ((s,T)::ts) body
1.738 - | get ts (t1 $ t2) = (get ts t1) @ (get ts t2)
1.739 - in distinct (get [] t) end;
1.740 -(*
1.741 -val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)";
1.742 -get_types t;
1.743 -*)
1.744 -
1.745 -(*11.1.00: not used, fix-typed +,*,-,^ instead *)
1.746 -fun set_types al (Const(s,T)) =
1.747 - (case assoc (al,s) of
1.748 - SOME T' => Const(s,T')
1.749 - | NONE => (warning ("set_types: no type for "^s); Const(s,dummyT)))
1.750 - | set_types al (Free(s,T)) =
1.751 - if is_no s then
1.752 - (case assoc (al,"#") of
1.753 - SOME T' => Free(s,T')
1.754 - | NONE => (warning ("set_types: no type for numerals"); Free(s,T)))
1.755 - else (case assoc (al,s) of
1.756 - SOME T' => Free(s,T')
1.757 - | NONE => (warning ("set_types: no type for "^s); Free(s,T)))
1.758 - | set_types al (Var(n,T)) = Var(n,T)
1.759 - | set_types al (Bound i) = Bound i
1.760 - | set_types al (Abs(s,T,body)) =
1.761 - (case assoc (al,s) of
1.762 - SOME T' => Abs(s,T', set_types al body)
1.763 - | NONE => (warning ("set_types: no type for "^s);
1.764 - Abs(s,T, set_types al body)))
1.765 - | set_types al (t1 $ t2) = (set_types al t1) $ (set_types al t2);
1.766 -(*
1.767 -val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)";
1.768 -val al = get_types t;
1.769 -
1.770 -val t = (term_of o the o (parse thy)) "x = #0 + #-1 * #-4";
1.771 -atomty t; (* 'a *)
1.772 -val t' = set_types al t;
1.773 -atomty t'; (*real*)
1.774 -(cterm_of thy) t';
1.775 -val it = "x = #0 + #-1 * #-4" : cterm
1.776 -
1.777 -val t = (term_of o the o (parse thy))
1.778 - "#5 * x + x ^^^ #2 = (#2 + x) ^^^ #2";
1.779 -atomty t;
1.780 -val t' = set_types al t;
1.781 -atomty t';
1.782 -(cterm_of thy) t';
1.783 -uncaught exception TYPE (*^^^ is new, NOT in al*)
1.784 -*)
1.785 -
1.786 -
1.787 -(** from Descript.ML **)
1.788 -
1.789 -(** decompose an isa-list to an ML-list
1.790 - i.e. [] belong to the meta-language, too **)
1.791 -
1.792 -fun is_list ((Const("List.list.Cons",_)) $ _ $ _) = true
1.793 - | is_list _ = false;
1.794 -(* val (SOME ct) = parse thy "lll::real list";
1.795 -> val ty = (#t o rep_cterm) ct;
1.796 -> is_list ty;
1.797 -val it = false : bool
1.798 -> val (SOME ct) = parse thy "[lll]";
1.799 -> val ty = (#t o rep_cterm) ct;
1.800 -> is_list ty;
1.801 -val it = true : bool *)
1.802 -
1.803 -
1.804 -
1.805 -fun mk_Free (s,T) = Free(s,T);
1.806 -fun mk_free T s = Free(s,T);
1.807 -
1.808 -(*instantiate let; necessary for ass_up*)
1.809 -fun inst_abs thy (Const sT) = Const sT
1.810 - | inst_abs thy (Free sT) = Free sT
1.811 - | inst_abs thy (Bound n) = Bound n
1.812 - | inst_abs thy (Var iT) = Var iT
1.813 - | inst_abs thy (Const ("Let",T1) $ e $ (Abs (v,T2,b))) =
1.814 - let val (v',b') = variant_abs (v,T2,b); (*fun variant_abs: term.ML*)
1.815 - in Const ("Let",T1) $ inst_abs thy e $ (Abs (v',T2,inst_abs thy b')) end
1.816 - | inst_abs thy (t1 $ t2) = inst_abs thy t1 $ inst_abs thy t2
1.817 - | inst_abs thy t =
1.818 - (writeln("inst_abs: unchanged t= "^ term2str t);
1.819 - t);
1.820 -(*val scr as (Script sc) = Script ((term_of o the o (parse thy))
1.821 - "Script Testeq (e_::bool) = \
1.822 - \While (contains_root e_) Do \
1.823 - \ (let e_ = Try (Repeat (Rewrite rroot_square_inv False e_)); \
1.824 - \ e_ = Try (Repeat (Rewrite square_equation_left True e_)) \
1.825 - \ in Try (Repeat (Rewrite radd_0 False e_))) ");
1.826 -ML> atomt sc;
1.827 -*** Const ( Script.Testeq)
1.828 -*** . Free ( e_, )
1.829 -*** . Const ( Script.While)
1.830 -*** . . Const ( RatArith.contains'_root)
1.831 -*** . . . Free ( e_, )
1.832 -*** . . Const ( Let)
1.833 -*** . . . Const ( Script.Try)
1.834 -*** . . . . Const ( Script.Repeat)
1.835 -*** . . . . . Const ( Script.Rewrite)
1.836 -*** . . . . . . Free ( rroot_square_inv, )
1.837 -*** . . . . . . Const ( False)
1.838 -*** . . . . . . Free ( e_, )
1.839 -*** . . . Abs( e_,..
1.840 -*** . . . . Const ( Let)
1.841 -*** . . . . . Const ( Script.Try)
1.842 -*** . . . . . . Const ( Script.Repeat)
1.843 -*** . . . . . . . Const ( Script.Rewrite)
1.844 -*** . . . . . . . . Free ( square_equation_left, )
1.845 -*** . . . . . . . . Const ( True)
1.846 -*** . . . . . . . . Bound 0 <-- !!!
1.847 -*** . . . . . Abs( e_,..
1.848 -*** . . . . . . Const ( Script.Try)
1.849 -*** . . . . . . . Const ( Script.Repeat)
1.850 -*** . . . . . . . . Const ( Script.Rewrite)
1.851 -*** . . . . . . . . . Free ( radd_0, )
1.852 -*** . . . . . . . . . Const ( False)
1.853 -*** . . . . . . . . . Bound 0 <-- !!!
1.854 -val it = () : unit
1.855 -ML> atomt (inst_abs thy sc);
1.856 -*** Const ( Script.Testeq)
1.857 -*** . Free ( e_, )
1.858 -*** . Const ( Script.While)
1.859 -*** . . Const ( RatArith.contains'_root)
1.860 -*** . . . Free ( e_, )
1.861 -*** . . Const ( Let)
1.862 -*** . . . Const ( Script.Try)
1.863 -*** . . . . Const ( Script.Repeat)
1.864 -*** . . . . . Const ( Script.Rewrite)
1.865 -*** . . . . . . Free ( rroot_square_inv, )
1.866 -*** . . . . . . Const ( False)
1.867 -*** . . . . . . Free ( e_, )
1.868 -*** . . . Abs( e_,..
1.869 -*** . . . . Const ( Let)
1.870 -*** . . . . . Const ( Script.Try)
1.871 -*** . . . . . . Const ( Script.Repeat)
1.872 -*** . . . . . . . Const ( Script.Rewrite)
1.873 -*** . . . . . . . . Free ( square_equation_left, )
1.874 -*** . . . . . . . . Const ( True)
1.875 -*** . . . . . . . . Free ( e_, ) <-- !!!
1.876 -*** . . . . . Abs( e_,..
1.877 -*** . . . . . . Const ( Script.Try)
1.878 -*** . . . . . . . Const ( Script.Repeat)
1.879 -*** . . . . . . . . Const ( Script.Rewrite)
1.880 -*** . . . . . . . . . Free ( radd_0, )
1.881 -*** . . . . . . . . . Const ( False)
1.882 -*** . . . . . . . . . Free ( e_, ) <-- ZUFALL vor 5.03!!!
1.883 -val it = () : unit*)
1.884 -
1.885 -
1.886 -
1.887 -
1.888 -fun inst_abs thy (Const sT) = Const sT
1.889 - | inst_abs thy (Free sT) = Free sT
1.890 - | inst_abs thy (Bound n) = Bound n
1.891 - | inst_abs thy (Var iT) = Var iT
1.892 - | inst_abs thy (Const ("Let",T1) $ e $ (Abs (v,T2,b))) =
1.893 - let val b' = subst_bound (Free(v,T2),b);
1.894 - (*fun variant_abs: term.ML*)
1.895 - in Const ("Let",T1) $ inst_abs thy e $ (Abs (v,T2,inst_abs thy b')) end
1.896 - | inst_abs thy (t1 $ t2) = inst_abs thy t1 $ inst_abs thy t2
1.897 - | inst_abs thy t =
1.898 - (writeln("inst_abs: unchanged t= "^ term2str t);
1.899 - t);
1.900 -(*val scr =
1.901 - "Script Make_fun_by_explicit (f_::real) (v_::real) (eqs_::bool list) = \
1.902 - \ (let h_ = (hd o (filterVar f_)) eqs_; \
1.903 - \ e_1 = hd (dropWhile (ident h_) eqs_); \
1.904 - \ vs_ = dropWhile (ident f_) (Vars h_); \
1.905 - \ v_1 = hd (dropWhile (ident v_) vs_); \
1.906 - \ (s_1::bool list)=(SubProblem(DiffApp_,[univar,equation],[no_met])\
1.907 - \ [bool_ e_1, real_ v_1])\
1.908 - \ in Substitute [(v_1 = (rhs o hd) s_1)] h_)";
1.909 -> val ttt = (term_of o the o (parse thy)) scr;
1.910 -> writeln(term2str ttt);
1.911 -> atomt ttt;
1.912 -*** -------------
1.913 -*** Const ( DiffApp.Make'_fun'_by'_explicit)
1.914 -*** . Free ( f_, )
1.915 -*** . Free ( v_, )
1.916 -*** . Free ( eqs_, )
1.917 -*** . Const ( Let)
1.918 -*** . . Const ( Fun.op o)
1.919 -*** . . . Const ( List.hd)
1.920 -*** . . . Const ( DiffApp.filterVar)
1.921 -*** . . . . Free ( f_, )
1.922 -*** . . . Free ( eqs_, )
1.923 -*** . . Abs( h_,..
1.924 -*** . . . Const ( Let)
1.925 -*** . . . . Const ( List.hd)
1.926 -*** . . . . . Const ( List.dropWhile)
1.927 -*** . . . . . . Const ( Atools.ident)
1.928 -*** . . . . . . . Bound 0 <---- Free ( h_, )
1.929 -*** . . . . . . Free ( eqs_, )
1.930 -*** . . . . Abs( e_1,..
1.931 -*** . . . . . Const ( Let)
1.932 -*** . . . . . . Const ( List.dropWhile)
1.933 -*** . . . . . . . Const ( Atools.ident)
1.934 -*** . . . . . . . . Free ( f_, )
1.935 -*** . . . . . . . Const ( Tools.Vars)
1.936 -*** . . . . . . . . Bound 1 <---- Free ( h_, )
1.937 -*** . . . . . . Abs( vs_,..
1.938 -*** . . . . . . . Const ( Let)
1.939 -*** . . . . . . . . Const ( List.hd)
1.940 -*** . . . . . . . . . Const ( List.dropWhile)
1.941 -*** . . . . . . . . . . Const ( Atools.ident)
1.942 -*** . . . . . . . . . . . Free ( v_, )
1.943 -*** . . . . . . . . . . Bound 0 <---- Free ( vs_, )
1.944 -*** . . . . . . . . Abs( v_1,..
1.945 -*** . . . . . . . . . Const ( Let)
1.946 -*** . . . . . . . . . . Const ( Script.SubProblem)
1.947 -*** . . . . . . . . . . . Const ( Pair)
1.948 -*** . . . . . . . . . . . . Free ( DiffApp_, )
1.949 -*** . . . . . . . . . . . . Const ( Pair)
1.950 -*** . . . . . . . . . . . . . Const ( List.list.Cons)
1.951 -*** . . . . . . . . . . . . . . Free ( univar, )
1.952 -*** . . . . . . . . . . . . . . Const ( List.list.Cons)
1.953 -*** . . . . . . . . . . . . . . . Free ( equation, )
1.954 -*** . . . . . . . . . . . . . . . Const ( List.list.Nil)
1.955 -*** . . . . . . . . . . . . . Const ( List.list.Cons)
1.956 -*** . . . . . . . . . . . . . . Free ( no_met, )
1.957 -*** . . . . . . . . . . . . . . Const ( List.list.Nil)
1.958 -*** . . . . . . . . . . . Const ( List.list.Cons)
1.959 -*** . . . . . . . . . . . . Const ( Script.bool_)
1.960 -*** . . . . . . . . . . . . . Bound 2 <----- Free ( e_1, )
1.961 -*** . . . . . . . . . . . . Const ( List.list.Cons)
1.962 -*** . . . . . . . . . . . . . Const ( Script.real_)
1.963 -*** . . . . . . . . . . . . . . Bound 0 <----- Free ( v_1, )
1.964 -*** . . . . . . . . . . . . . Const ( List.list.Nil)
1.965 -*** . . . . . . . . . . Abs( s_1,..
1.966 -*** . . . . . . . . . . . Const ( Script.Substitute)
1.967 -*** . . . . . . . . . . . . Const ( List.list.Cons)
1.968 -*** . . . . . . . . . . . . . Const ( Pair)
1.969 -*** . . . . . . . . . . . . . . Bound 1 <----- Free ( v_1, )
1.970 -*** . . . . . . . . . . . . . . Const ( Fun.op o)
1.971 -*** . . . . . . . . . . . . . . . Const ( Tools.rhs)
1.972 -*** . . . . . . . . . . . . . . . Const ( List.hd)
1.973 -*** . . . . . . . . . . . . . . . Bound 0 <----- Free ( s_1, )
1.974 -*** . . . . . . . . . . . . . Const ( List.list.Nil)
1.975 -*** . . . . . . . . . . . . Bound 4 <----- Free ( h_, )
1.976 -
1.977 -> val ttt' = inst_abs thy ttt;
1.978 -> writeln(term2str ttt');
1.979 -Script Make_fun_by_explicit f_ v_ eqs_ =
1.980 - ... as above ...
1.981 -> atomt ttt';
1.982 -*** -------------
1.983 -*** Const ( DiffApp.Make'_fun'_by'_explicit)
1.984 -*** . Free ( f_, )
1.985 -*** . Free ( v_, )
1.986 -*** . Free ( eqs_, )
1.987 -*** . Const ( Let)
1.988 -*** . . Const ( Fun.op o)
1.989 -*** . . . Const ( List.hd)
1.990 -*** . . . Const ( DiffApp.filterVar)
1.991 -*** . . . . Free ( f_, )
1.992 -*** . . . Free ( eqs_, )
1.993 -*** . . Abs( h_,..
1.994 -*** . . . Const ( Let)
1.995 -*** . . . . Const ( List.hd)
1.996 -*** . . . . . Const ( List.dropWhile)
1.997 -*** . . . . . . Const ( Atools.ident)
1.998 -*** . . . . . . . Free ( h_, ) <---- Bound 0
1.999 -*** . . . . . . Free ( eqs_, )
1.1000 -*** . . . . Abs( e_1,..
1.1001 -*** . . . . . Const ( Let)
1.1002 -*** . . . . . . Const ( List.dropWhile)
1.1003 -*** . . . . . . . Const ( Atools.ident)
1.1004 -*** . . . . . . . . Free ( f_, )
1.1005 -*** . . . . . . . Const ( Tools.Vars)
1.1006 -*** . . . . . . . . Free ( h_, ) <---- Bound 1
1.1007 -*** . . . . . . Abs( vs_,..
1.1008 -*** . . . . . . . Const ( Let)
1.1009 -*** . . . . . . . . Const ( List.hd)
1.1010 -*** . . . . . . . . . Const ( List.dropWhile)
1.1011 -*** . . . . . . . . . . Const ( Atools.ident)
1.1012 -*** . . . . . . . . . . . Free ( v_, )
1.1013 -*** . . . . . . . . . . Free ( vs_, ) <---- Bound 0
1.1014 -*** . . . . . . . . Abs( v_1,..
1.1015 -*** . . . . . . . . . Const ( Let)
1.1016 -*** . . . . . . . . . . Const ( Script.SubProblem)
1.1017 -*** . . . . . . . . . . . Const ( Pair)
1.1018 -*** . . . . . . . . . . . . Free ( DiffApp_, )
1.1019 -*** . . . . . . . . . . . . Const ( Pair)
1.1020 -*** . . . . . . . . . . . . . Const ( List.list.Cons)
1.1021 -*** . . . . . . . . . . . . . . Free ( univar, )
1.1022 -*** . . . . . . . . . . . . . . Const ( List.list.Cons)
1.1023 -*** . . . . . . . . . . . . . . . Free ( equation, )
1.1024 -*** . . . . . . . . . . . . . . . Const ( List.list.Nil)
1.1025 -*** . . . . . . . . . . . . . Const ( List.list.Cons)
1.1026 -*** . . . . . . . . . . . . . . Free ( no_met, )
1.1027 -*** . . . . . . . . . . . . . . Const ( List.list.Nil)
1.1028 -*** . . . . . . . . . . . Const ( List.list.Cons)
1.1029 -*** . . . . . . . . . . . . Const ( Script.bool_)
1.1030 -*** . . . . . . . . . . . . . Free ( e_1, ) <----- Bound 2
1.1031 -*** . . . . . . . . . . . . Const ( List.list.Cons)
1.1032 -*** . . . . . . . . . . . . . Const ( Script.real_)
1.1033 -*** . . . . . . . . . . . . . . Free ( v_1, ) <----- Bound 0
1.1034 -*** . . . . . . . . . . . . . Const ( List.list.Nil)
1.1035 -*** . . . . . . . . . . Abs( s_1,..
1.1036 -*** . . . . . . . . . . . Const ( Script.Substitute)
1.1037 -*** . . . . . . . . . . . . Const ( List.list.Cons)
1.1038 -*** . . . . . . . . . . . . . Const ( Pair)
1.1039 -*** . . . . . . . . . . . . . . Free ( v_1, ) <----- Bound 1
1.1040 -*** . . . . . . . . . . . . . . Const ( Fun.op o)
1.1041 -*** . . . . . . . . . . . . . . . Const ( Tools.rhs)
1.1042 -*** . . . . . . . . . . . . . . . Const ( List.hd)
1.1043 -*** . . . . . . . . . . . . . . . Free ( s_1, ) <----- Bound 0
1.1044 -*** . . . . . . . . . . . . . Const ( List.list.Nil)
1.1045 -*** . . . . . . . . . . . . Free ( h_, ) <----- Bound 4
1.1046 -
1.1047 -Note numbering of de Bruijn indexes !
1.1048 -
1.1049 -Script Make_fun_by_explicit f_ v_ eqs_ =
1.1050 - let h_ = (hd o filterVar f_) eqs_;
1.1051 - e_1 = hd (dropWhile (ident h_ BOUND_0) eqs_);
1.1052 - vs_ = dropWhile (ident f_) (Vars h_ BOUND_1);
1.1053 - v_1 = hd (dropWhile (ident v_) vs_ BOUND_0);
1.1054 - s_1 =
1.1055 - SubProblem (DiffApp_, [univar, equation], [no_met])
1.1056 - [bool_ e_1 BOUND_2, real_ v_1 BOUND_0]
1.1057 - in Substitute [(v_1 BOUND_1 = (rhs o hd) s_1 BOUND_0)] h_ BOUND_4
1.1058 -*)
1.1059 -
1.1060 -
1.1061 -fun T_a2real (Type (s, [])) =
1.1062 - if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else Type (s, [])
1.1063 - | T_a2real (Type (s, Ts)) = Type (s, map T_a2real Ts)
1.1064 - | T_a2real (TFree (s, srt)) =
1.1065 - if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else TFree (s, srt)
1.1066 - | T_a2real (TVar (("DUMMY",_),srt)) = HOLogic.realT;
1.1067 -
1.1068 -(*FIXME .. fixes the type (+see Typefix.thy*)
1.1069 -fun typ_a2real (Const( s, T)) = (Const( s, T_a2real T))
1.1070 - | typ_a2real (Free( s, T)) = (Free( s, T_a2real T))
1.1071 - | typ_a2real (Var( n, T)) = (Var( n, T_a2real T))
1.1072 - | typ_a2real (Bound i) = (Bound i)
1.1073 - | typ_a2real (Abs(s,T,t)) = Abs(s, T, typ_a2real t)
1.1074 - | typ_a2real (t1 $ t2) = (typ_a2real t1) $ (typ_a2real t2);
1.1075 -(*
1.1076 -----------------6.8.02---------------------------------------------------
1.1077 - val str = "1";
1.1078 - val t = read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[])));
1.1079 - atomty (term_of t);
1.1080 -*** -------------
1.1081 -*** Const ( 1, 'a)
1.1082 - val t = (app_num_tr' o term_of) t;
1.1083 - atomty t;
1.1084 -*** -------------
1.1085 -*** Const ( 1, 'a)
1.1086 - val t = typ_a2real t;
1.1087 - atomty t;
1.1088 -*** -------------
1.1089 -*** Const ( 1, real)
1.1090 -
1.1091 - val str = "2";
1.1092 - val t = read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[])));
1.1093 - atomty (term_of t);
1.1094 -*** -------------
1.1095 -*** Const ( Numeral.number_of, bin => 'a)
1.1096 -*** . Const ( Numeral.bin.Bit, [bin, bool] => bin)
1.1097 -*** . . Const ( Numeral.bin.Bit, [bin, bool] => bin)
1.1098 -*** . . . Const ( Numeral.bin.Pls, bin)
1.1099 -*** . . . Const ( True, bool)
1.1100 -*** . . Const ( False, bool)
1.1101 - val t = (app_num_tr' o term_of) t;
1.1102 - atomty t;
1.1103 -*** -------------
1.1104 -*** Free ( 2, 'a)
1.1105 - val t = typ_a2real t;
1.1106 - atomty t;
1.1107 -*** -------------
1.1108 -*** Free ( 2, real)
1.1109 -----------------6.8.02---------------------------------------------------
1.1110 -
1.1111 -
1.1112 -> val str = "R";
1.1113 -> val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));
1.1114 -val t = Free ("R","?DUMMY") : term
1.1115 -> val t' = typ_a2real t;
1.1116 -> (cterm_of thy) t';
1.1117 -val it = "R::RealDef.real" : cterm
1.1118 -
1.1119 -> val str = "R=R";
1.1120 -> val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));
1.1121 -> atomty (typ_a2real t);
1.1122 -*** -------------
1.1123 -*** Const ( op =, [RealDef.real, RealDef.real] => bool)
1.1124 -*** Free ( R, RealDef.real)
1.1125 -*** Free ( R, RealDef.real)
1.1126 -> val t' = typ_a2real t;
1.1127 -> (cterm_of thy) t';
1.1128 -val it = "(R::RealDef.real) = R" : cterm
1.1129 -
1.1130 -> val str = "fixed_values [R=R]";
1.1131 -> val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));
1.1132 -> val t' = typ_a2real t;
1.1133 -> (cterm_of thy) t';
1.1134 -val it = "fixed_values [(R::RealDef.real) = R]" : cterm
1.1135 -*)
1.1136 -
1.1137 -(*TODO.WN0609: parse should return a term or a string
1.1138 - (or even more comprehensive datastructure for error-messages)
1.1139 - i.e. in wrapping with SOME term or NONE the latter is not sufficient*)
1.1140 -(*2002 fun parseold thy str =
1.1141 - (let
1.1142 - val sgn = sign_of thy;
1.1143 - val t = ((*typ_a2real o*) app_num_tr'1 o term_of)
1.1144 - (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));
1.1145 - in SOME (cterm_of sgn t) end)
1.1146 - handle _ => NONE;*)
1.1147 -
1.1148 -
1.1149 -
1.1150 -fun parseold thy str =
1.1151 - (let val t = ((*typ_a2real o*) numbers_to_string)
1.1152 - (Syntax.read_term_global thy str)
1.1153 - in SOME (cterm_of thy t) end)
1.1154 - handle _ => NONE;
1.1155 -(*2002 fun parseN thy str =
1.1156 - (let
1.1157 - val sgn = sign_of thy;
1.1158 - val t = ((*typ_a2real o app_num_tr'1 o*) term_of)
1.1159 - (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));
1.1160 - in SOME (cterm_of sgn t) end)
1.1161 - handle _ => NONE;*)
1.1162 -fun parseN thy str =
1.1163 - (let val t = (*(typ_a2real o numbers_to_string)*)
1.1164 - (Syntax.read_term_global thy str)
1.1165 - in SOME (cterm_of thy t) end)
1.1166 - handle _ => NONE;
1.1167 -(*2002 fun parse thy str =
1.1168 - (let
1.1169 - val sgn = sign_of thy;
1.1170 - val t = (typ_a2real o app_num_tr'1 o term_of)
1.1171 - (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));
1.1172 - in SOME (cterm_of sgn t) end) (*FIXXXXME 10.8.02: return term !!!*)
1.1173 - handle _ => NONE;*)
1.1174 -(*2010 fun parse thy str =
1.1175 - (let val t = (typ_a2real o app_num_tr'1) (Syntax.read_term_global thy str)
1.1176 - in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)
1.1177 - handle _ => NONE;*)
1.1178 -fun parse thy str =
1.1179 - (let val t = (typ_a2real o numbers_to_string)
1.1180 - (Syntax.read_term_global thy str)
1.1181 - in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)
1.1182 - handle _ => NONE;
1.1183 -
1.1184 -(* 10.8.02: for this reason we still have ^^^--------------------
1.1185 - val thy = SqRoot.thy;
1.1186 - val str = "(1::real) ^ (2::nat)";
1.1187 - val sgn = sign_of thy;
1.1188 - val ct = (read_cterm sgn (str,(TVar(("DUMMY",0),[])))) handle e =>print_exn e;
1.1189 -(*1*)"(1::real) ^ 2";
1.1190 - atomty (term_of ct);
1.1191 -*** -------------
1.1192 -*** Const ( Nat.power, [real, nat] => real)
1.1193 -*** . Const ( 1, real)
1.1194 -*** . Const ( Numeral.number_of, bin => nat)
1.1195 -*** . . Const ( Numeral.bin.Bit, [bin, bool] => bin)
1.1196 -*** . . . Const ( Numeral.bin.Bit, [bin, bool] => bin)
1.1197 -*** . . . . Const ( Numeral.bin.Pls, bin)
1.1198 -*** . . . . Const ( True, bool)
1.1199 -*** . . . Const ( False, bool)
1.1200 - val t = ((app_num_tr' o term_of)
1.1201 - (read_cterm sgn (str,(TVar(("DUMMY",0),[])))))handle e => print_exn e;
1.1202 - val ct = (cterm_of sgn t) handle e => print_exn e;
1.1203 -(*2*)"(1::real) ^ (2::nat)";
1.1204 - atomty (term_of ct);
1.1205 -*** -------------
1.1206 -*** Const ( Nat.power, [real, nat] => real)
1.1207 -*** . Free ( 1, real)
1.1208 -*** . Free ( 2, nat) (*1*) Const("2",_) (*2*) Free("2",_)
1.1209 -
1.1210 -
1.1211 - val str = "(2::real) ^ (2::nat)";
1.1212 - val t = (read_cterm sgn (str,(TVar(("DUMMY",0),[])))) handle e => print_exn e;
1.1213 -val t = "(2::real) ^ 2" : cterm
1.1214 - val t = ((app_num_tr' o term_of)
1.1215 - (read_cterm sgn (str,(TVar(("DUMMY",0),[])))))handle e => print_exn e;
1.1216 - val ct = (cterm_of sgn t) handle e => print_exn e;
1.1217 -Variable "2" has two distinct types
1.1218 -real
1.1219 -nat
1.1220 -uncaught exception TYPE
1.1221 - raised at: sign.ML:672.26-673.56
1.1222 - goals.ML:1100.61
1.1223 -
1.1224 -
1.1225 - val str = "(3::real) ^ (2::nat)";
1.1226 - val t = (read_cterm sgn (str,(TVar(("DUMMY",0),[])))) handle e => print_exn e;
1.1227 -val t = "(3::real) ^ 2" : cterm
1.1228 - val t = ((app_num_tr' o term_of)
1.1229 - (read_cterm sgn (str,(TVar(("DUMMY",0),[])))))handle e => print_exn e;
1.1230 - val ct = (cterm_of sgn t) handle e => print_exn e;
1.1231 -val ct = "(3::real) ^ (2::nat)" : cterm
1.1232 -
1.1233 -
1.1234 -Conclusion: The type inference allows different types
1.1235 - for one and the same Numeral.number_of
1.1236 - BUT the type inference doesn't allow
1.1237 - Free ( 2, real) and Free ( 2, nat) within one term
1.1238 ---------------- ~~~~ ~~~ *)
1.1239 -(*
1.1240 -> val (SOME ct) = parse thy "(-#5)^^^#3";
1.1241 -> atomty (term_of ct);
1.1242 -*** -------------
1.1243 -*** Const ( Nat.op ^, ['a, nat] => 'a)
1.1244 -*** Const ( uminus, 'a => 'a)
1.1245 -*** Free ( #5, 'a)
1.1246 -*** Free ( #3, nat)
1.1247 -> val (SOME ct) = parse thy "R=R";
1.1248 -> atomty (term_of ct);
1.1249 -*** -------------
1.1250 -*** Const ( op =, [real, real] => bool)
1.1251 -*** Free ( R, real)
1.1252 -*** Free ( R, real)
1.1253 -
1.1254 -THIS IS THE OUTPUT FOR VERSION (3) above at typ_a2real !!!!!
1.1255 -*** -------------
1.1256 -*** Const ( op =, [RealDef.real, RealDef.real] => bool)
1.1257 -*** Free ( R, RealDef.real)
1.1258 -*** Free ( R, RealDef.real) *)
1.1259 -
1.1260 -(*version for testing local to theories*)
1.1261 -fun str2term_ thy str = (term_of o the o (parse thy)) str;
1.1262 -fun str2term str = (term_of o the o (parse (theory "Isac"))) str;
1.1263 -fun strs2terms ss = map str2term ss;
1.1264 -fun str2termN str = (term_of o the o (parseN (theory "Isac"))) str;
1.1265 -
1.1266 -(*+ makes a substitution from the output of Pattern.match +*)
1.1267 -(*fun mk_subs ((id, _):indexname, t:term) = (Free (id,type_of t), t);*)
1.1268 -fun mk_subs (subs: ((string * int) * (Term.typ * Term.term)) list) =
1.1269 -let fun mk_sub ((id, _), (ty, tm)) = (Free (id, ty), tm) in
1.1270 -map mk_sub subs end;
1.1271 -
1.1272 -val atomthm = atomt o #prop o rep_thm;
1.1273 -
1.1274 -(*.instantiate #prop thm with bound variables (as Free).*)
1.1275 -fun inst_bdv [] t = t : term
1.1276 - | inst_bdv (instl: (term*term) list) t =
1.1277 - let fun subst (v as Var((s,_),T)) =
1.1278 - (case explode s of
1.1279 - "b"::"d"::"v"::_ =>
1.1280 - if_none (assoc(instl,Free(s,T))) (Free(s,T))
1.1281 - | _ => v)
1.1282 - | subst (Abs(a,T,body)) = Abs(a, T, subst body)
1.1283 - | subst (f$t') = subst f $ subst t'
1.1284 - | subst t = if_none (assoc(instl,t)) t
1.1285 - in subst t end;
1.1286 -
1.1287 -
1.1288 -(*WN050829 caution: is_atom (str2term"q_0/2 * L * x") = true !!!
1.1289 - use length (vars term) = 1 instead*)
1.1290 -fun is_atom (Const ("Float.Float",_) $ _) = true
1.1291 - | is_atom (Const ("ComplexI.I'_'_",_)) = true
1.1292 - | is_atom (Const ("op *",_) $ t $ Const ("ComplexI.I'_'_",_)) = is_atom t
1.1293 - | is_atom (Const ("op +",_) $ t1 $ Const ("ComplexI.I'_'_",_)) = is_atom t1
1.1294 - | is_atom (Const ("op +",_) $ t1 $
1.1295 - (Const ("op *",_) $ t2 $ Const ("ComplexI.I'_'_",_))) =
1.1296 - is_atom t1 andalso is_atom t2
1.1297 - | is_atom (Const _) = true
1.1298 - | is_atom (Free _) = true
1.1299 - | is_atom (Var _) = true
1.1300 - | is_atom _ = false;
1.1301 -(* val t = str2term "q_0/2 * L * x";
1.1302 -
1.1303 -
1.1304 -*)
1.1305 -(*val t = str2term "Float ((1,2),(0,0))";
1.1306 -> is_atom t;
1.1307 -val it = true : bool
1.1308 -> val t = str2term "Float ((1,2),(0,0)) * I__";
1.1309 -> is_atom t;
1.1310 -val it = true : bool
1.1311 -> val t = str2term "Float ((1,2),(0,0)) + Float ((3,4),(0,0)) * I__";
1.1312 -> is_atom t;
1.1313 -val it = true : bool
1.1314 -> val t = str2term "1 + 2*I__";
1.1315 -> val Const ("op +",_) $ t1 $ (Const ("op *",_) $ t2 $ Const ("ComplexI.I'_'_",_)) = t;
1.1316 -*)
1.1317 -
1.1318 -(*.adaption from Isabelle/src/Pure/term.ML; reports if ALL Free's
1.1319 - have found a substitution (required for evaluating the preconditions
1.1320 - of _incomplete_ models).*)
1.1321 -fun subst_atomic_all [] t = (false, (*TODO may be 'true' for some terms ?*)
1.1322 - t : term)
1.1323 - | subst_atomic_all (instl: (term*term) list) t =
1.1324 - let fun subst (Abs(a,T,body)) =
1.1325 - let val (all, body') = subst body
1.1326 - in (all, Abs(a, T, body')) end
1.1327 - | subst (f$tt) =
1.1328 - let val (all1, f') = subst f
1.1329 - val (all2, tt') = subst tt
1.1330 - in (all1 andalso all2, f' $ tt') end
1.1331 - | subst (t as Free _) =
1.1332 - if is_num t then (true, t) (*numerals cannot be subst*)
1.1333 - else (case assoc(instl,t) of
1.1334 - SOME t' => (true, t')
1.1335 - | NONE => (false, t))
1.1336 - | subst t = (true, if_none (assoc(instl,t)) t)
1.1337 - in subst t end;
1.1338 -
1.1339 -(*.add two terms with a type given.*)
1.1340 -fun mk_add t1 t2 =
1.1341 - let val T1 = type_of t1
1.1342 - val T2 = type_of t2
1.1343 - in if T1 <> T2 then raise TYPE ("mk_add gets ",[T1, T2],[t1,t2])
1.1344 - else (Const ("op +", [T1, T2] ---> T1) $ t1 $ t2)
1.1345 - end;
1.1346 -