wneuper/isa: src/Tools/isac/ProgLang/termC.sml@729c3ca4e5fc

     1 (* Title: extends Isabelle/src/Pure/term.ML

     2    Author: Walther Neuper 1999, Mathias Lehnfeld

     3    (c) due to copyright terms

     4 *)

     6 fun isastr_of_int i = if i >= 0 then string_of_int i else "-" ^ string_of_int (abs i)

     8 (*

     9 > (Thm.global_cterm_of thy) a_term;

    10 val it = "empty" : cterm        *)

    12 (*2003 fun match thy t pat =

    13     (snd (Pattern.match (Sign.tsig_of (sign_of thy)) (pat, t)))

    14     handle _ => [];

    15 fn : theory ->

    16      Term.term -> Term.term -> (Term.indexname * Term.term) list*)

    17 (*see src/Tools/eqsubst.ML fun clean_match*)

    18 (*2003 fun matches thy tm pa = if match thy tm pa = [] then false else true;*)

    19 fun matches thy tm pa =

    20     (Pattern.match thy (pa, tm) (Vartab.empty, Vartab.empty); true)

    21     handle _ => false

    23 (**

    24   transform  typ / term to a String, which is parsed by Scala

    25   after transport via libisabelle

    26 *)

    27 fun scala_of_typ (Type (s, typs)) =

    28     enclose "Type(" ")" (quote s ^ ", " ^

    29       (typs |> map scala_of_typ |> commas |> enclose "List(" ")"))

    30   | scala_of_typ (TFree (s, sort)) =

    31     enclose "TFree(" ")" (quote s ^ ", " ^ (sort |> map quote |> commas |> enclose "List(" ")"))

    32   | scala_of_typ (TVar ((s, i), sort)) =

    33     enclose "TVar(" ")" (

    34       enclose "(" ")," (quote s ^ "," ^ quote (string_of_int i)) ^

    35       (sort |> map quote |> commas |> enclose "List(" ")"))

    37 fun scala_of_term (Const (s, T)) =

    38     enclose "Const(" ")" (quote s ^ ", " ^ scala_of_typ T)

    39   | scala_of_term (Free (s, T)) =

    40     enclose "Free(" ")" (quote s ^ ", " ^ scala_of_typ T)

    41   | scala_of_term (Var ((s, i), T)) =

    42     enclose "TVar(" ")" (

    43       enclose "(" ")," (quote s ^ "," ^ quote (string_of_int i)) ^

    44       scala_of_typ T)

    45   | scala_of_term (Bound i) = enclose "Bound(" ")" (string_of_int i)

    46   | scala_of_term (Abs (s, T, t)) =

    47     enclose "Abs(" ")" (

    48       quote s ^ ", " ^

    49       scala_of_typ T ^ ", " ^

    50       scala_of_term t)

    51   | scala_of_term (t1 $ t2) =

    52     enclose "App(" ")" (scala_of_term t1 ^ ", " ^ scala_of_term t2)

    54 (** old versions *)

    55 fun atomtyp t = (*WN10 see raw_pp_typ*)

    56   let

    57     fun ato n (Type (s,[])) =

    58       ("\n*** "^indent n^"Type ("^s^",[])")

    59       | ato n (Type (s,Ts)) =

    60       ("\n*** "^indent n^"Type ("^s^",["^ atol (n+1) Ts)

    62       | ato n (TFree (s,sort)) =

    63       ("\n*** "^indent n^"TFree ("^s^",["^ strs2str' sort)

    65       | ato n (TVar ((s,i),sort)) =

    66       ("\n*** "^indent n^"TVar (("^s^","^

    67        string_of_int i ^ strs2str' sort)

    68     and atol n [] =

    69       ("\n*** "^indent n^"]")

    70       | atol n (T::Ts) = (ato n T ^ atol n Ts)

    71 in tracing (ato 0 t ^ "\n") end;

    72 (*

    73 > val T = (type_of o Thm.term_of o the o (parse thy)) "a::[real,int] => nat";

    74 > atomtyp T;

    75 *** Type (fun,[

    76 ***   Type (RealDef.real,[])

    77 ***   Type (fun,[

    78 ***     Type (IntDef.int,[])

    79 ***     Type (nat,[])

    80 ***     ]

    81 ***   ]

    82 *)

    84 (*Prog.Tutorial.p.34, Makarius 1005 does the above like this..*)

    85 local

    86    fun pp_pair (x, y) = Pretty.list "(" ")" [x, y]

    87    fun pp_list xs = Pretty.list "[" "]" xs

    88    fun pp_str s   = Pretty.str s

    89    fun pp_qstr s = Pretty.quote (pp_str s)

    90    fun pp_int i   = pp_str (string_of_int i)

    91    fun pp_sort S = pp_list (map pp_qstr S)

    92    fun pp_constr a args = Pretty.block [pp_str a, Pretty.brk 1, args]

    93 in

    94 fun raw_pp_typ (TVar ((a, i), S)) =

    95        pp_constr "TVar" (pp_pair (pp_pair (pp_qstr a, pp_int i), pp_sort S))

    96    | raw_pp_typ (TFree (a, S)) =

    97        pp_constr "TFree" (pp_pair (pp_qstr a, pp_sort S))

    98    | raw_pp_typ (Type (a, tys)) =

    99        pp_constr "Type" (pp_pair (pp_qstr a, pp_list (map raw_pp_typ tys)))

   100 end

   101 (* install

   102 PolyML.addPrettyPrinter

   103   (fn _ => fn _ => ml_pretty o Pretty.to_ML o raw_pp_typ);

   104 de-install

   105 PolyML.addPrettyPrinter

   106   (fn _ => fn _ => ml_pretty o Pretty.to_ML o Proof_Display.pp_typ Pure.thy);

   107 *)

   109 local

   110   fun ato (Const (a, _)) n =

   111 	           "\n*** " ^ indent n ^ "Const (" ^ a ^ ", _)"

   112 	  | ato (Free (a, _)) n =

   113 	           "\n*** " ^ indent n ^ "Free (" ^ a ^ ", _)"

   114 	  | ato (Var ((a, i), _)) n =

   115 	           "\n*** " ^ indent n ^ "Var (" ^ a ^ ", " ^

   116                                                string_of_int i ^ "), _)"

   117 	  | ato (Bound i) n =

   118 	           "\n*** " ^ indent n ^ "Bound " ^ string_of_int i

   119 	  | ato (Abs (a, _, body)) n =

   120 	           "\n*** " ^ indent n ^ "Abs(" ^ a ^ ", _" ^ ato body (n+1)

   121 	  | ato (f $ t) n = (ato f n ^ ato t (n + 1))

   122 in

   123 fun atomw t = writeln ("\n*** -------------" ^ ato t 0 ^ "\n***");

   124 fun atomt t = tracing ("\n*** -------------" ^ ato t 0 ^ "\n***");

   125 end;

   127 fun term_detail2str t =

   128     let fun ato (Const (a, T)) n =

   129 	    "\n*** " ^ indent n ^ "Const (" ^ a ^ ", " ^ string_of_typ T ^ ")"

   130 	  | ato (Free (a, T)) n =

   131 	    "\n*** " ^ indent n ^ "Free (" ^ a ^ ", " ^ string_of_typ T ^ ")"

   132 	  | ato (Var ((a, i), T)) n =

   133 	    "\n*** " ^ indent n ^ "Var ((" ^ a ^ ", " ^ string_of_int i ^ "), "^

   134 	    string_of_typ T ^ ")"

   135 	  | ato (Bound i) n =

   136 	    "\n*** " ^ indent n ^ "Bound " ^ string_of_int i

   137 	  | ato (Abs(a, T, body))  n =

   138 	    "\n*** " ^ indent n ^ "Abs (" ^ a ^ ", " ^ string_of_typ T ^ ",.."

   139 	    ^ ato body (n + 1)

   140 	  | ato (f $ t) n = ato f n ^ ato t (n + 1)

   141     in "\n*** " ^ ato t 0 ^ "\n***" end;

   142 fun term_detail2str_thy thy t =

   143     let fun ato (Const (a, T)) n =

   144 	    "\n*** " ^ indent n ^ "Const (" ^ a ^ ", " ^ string_of_typ_thy thy T ^ ")"

   145 	  | ato (Free (a, T)) n =

   146 	    "\n*** " ^ indent n ^ "Free (" ^ a ^ ", " ^ string_of_typ_thy thy T ^ ")"

   147 	  | ato (Var ((a, i), T)) n =

   148 	    "\n*** " ^ indent n ^ "Var ((" ^ a ^ ", " ^ string_of_int i ^ "), "^

   149 	    string_of_typ_thy thy T ^ ")"

   150 	  | ato (Bound i) n =

   151 	    "\n*** " ^ indent n ^ "Bound " ^ string_of_int i

   152 	  | ato (Abs(a, T, body))  n =

   153 	    "\n*** " ^ indent n ^ "Abs (" ^ a ^ ", " ^ string_of_typ_thy thy T ^ ",.."

   154 	    ^ ato body (n + 1)

   155 	  | ato (f $ t) n = ato f n ^ ato t (n + 1)

   156     in "\n*** " ^ ato t 0 ^ "\n***" end;

   157 fun atomwy t = (writeln o term_detail2str) t;

   158 fun atomty t = (tracing o term_detail2str) t;

   159 fun atomty_thy thy t = (tracing o (term_detail2str_thy thy)) t;

   161 fun term_str thy (Const(s,_)) = s

   162   | term_str thy (Free(s,_)) = s

   163   | term_str thy (Var((s,i),_)) = s^(string_of_int i)

   164   | term_str thy (Bound i) = "B."^(string_of_int i)

   165   | term_str thy (Abs(s,_,_)) = s

   166   | term_str thy t = error("term_str not for "^term2str t);

   168 (*.contains the fst argument the second argument (a leave! of term).*)

   169 fun contains_term (Abs(_,_,body)) t = contains_term body t

   170   | contains_term (f $ f') t =

   171     contains_term f t orelse contains_term f' t

   172   | contains_term s t = t = s;

   173 (*.contains the term a VAR(("*",_),_) ?.*)

   174 fun contains_Var (Abs(_,_,body)) = contains_Var body

   175   | contains_Var (f $ f') = contains_Var f orelse contains_Var f'

   176   | contains_Var (Var _) = true

   177   | contains_Var _ = false;

   178 (* contains_Var (str2term "?z = 3") (*true*);

   179    contains_Var (str2term "z = 3")  (*false*);

   180    *)

   182 (*fun int_of_str str =

   183     let val ss = Symbol.explode str

   184 	val str' = case ss of

   185 	   "("::s => drop_last s | _ => ss

   186     in case BasisLibrary.Int.fromString (implode str') of

   187 	     SOME i => SOME i

   188 	   | NONE => NONE end;*)

   189 fun int_of_str str =

   190     let val ss = Symbol.explode str

   191 	val str' = case ss of

   192 	   "("::s => drop_last s | _ => ss

   193     in (SOME (Thy_Output.integer (implode str'))) handle _ => NONE end;

   194 (*

   195 > int_of_str "123";

   196 val it = SOME 123 : int option

   197 > int_of_str "(-123)";

   198 val it = SOME 123 : int option

   199 > int_of_str "#123";

   200 val it = NONE : int option

   201 > int_of_str "-123";

   202 val it = SOME ~123 : int option

   203 *)

   204 fun int_of_str' str =

   205     case int_of_str str of

   206 	SOME i => i

   207       | NONE => raise TERM ("int_of_string: no int-string",[]);

   208 val str2int = int_of_str';

   210 fun is_numeral str = case int_of_str str of

   211 			 SOME _ => true

   212 		       | NONE => false;

   213 val is_no = is_numeral;

   214 (* see /home/neuper/repos/FHpoly/src/HOL/Decision_Procs/Approximation.thy:

   216   val mk_int = HOLogic.mk_number @{typ int} o @{code integer_of_int};

   217   val dest_int = @{code int_of_integer} o snd o HOLogic.dest_number;

   219   fun nat_of_term t = @{code nat_of_integer}

   220     (HOLogic.dest_nat t handle TERM _ => snd (HOLogic.dest_number t));

   221   etc...

   222 *)

   223 fun is_num (Free (s,_)) = if is_numeral s then true else false

   224   | is_num _ = false;

   225 (*>

   226 > is_num ((Thm.term_of o the o (parse thy)) "#1");

   227 val it = true : bool

   228 > is_num ((Thm.term_of o the o (parse thy)) "#-1");

   229 val it = true : bool

   230 > is_num ((Thm.term_of o the o (parse thy)) "a123");

   231 val it = false : bool

   232 *)

   234 (*fun int_of_Free (Free (intstr, _)) =

   235     (case BasisLibrary.Int.fromString intstr of

   236 	     SOME i => i

   237 	   | NONE => error ("int_of_Free ( "^ intstr ^", _)"))

   238   | int_of_Free t = error ("int_of_Free ( "^ term2str t ^" )");*)

   239 fun int_of_Free (Free (intstr, _)) = (Thy_Output.integer intstr

   240     handle _ => error ("int_of_Free ( "^ intstr ^", _)"))

   241   | int_of_Free t = error ("int_of_Free ( "^ term2str t ^" )");

   243 fun vars t =

   244   let

   245     fun scan vs (Const(s,T)) = vs

   246       | scan vs (t as Free(s,T)) = if is_no s then vs else t::vs

   247       | scan vs (t as Var((s,i),T)) = t::vs

   248       | scan vs (Bound i) = vs

   249       | scan vs (Abs(s,T,t)) = scan vs t

   250       | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)

   251   in (distinct o (scan [])) t end;

   253 fun is_Free (Free _) = true

   254   | is_Free _ = false;

   255 fun is_fun_id (Const _) = true

   256   | is_fun_id (Free _) = true

   257   | is_fun_id _ = false;

   258 fun is_f_x (f $ x) = is_fun_id f andalso is_Free x

   259   | is_f_x _ = false;

   260 (* is_f_x (str2term "q_0/2 * L * x") (*false*);

   261    is_f_x (str2term "M_b x") (*true*);

   262   *)

   263 fun vars_str t =

   264   let

   265     fun scan vs (Const(s,T)) = vs

   266       | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs

   267       | scan vs (t as Var((s,i),T)) = (s^"_"^(string_of_int i))::vs

   268       | scan vs (Bound i) = vs

   269       | scan vs (Abs(s,T,t)) = scan vs t

   270       | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)

   271   in (distinct o (scan [])) t end;

   273 fun ids2str t =

   274   let

   275     fun scan vs (Const(s,T)) = if is_no s then vs else s::vs

   276       | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs

   277       | scan vs (t as Var((s,i),T)) = (s^"_"^(string_of_int i))::vs

   278       | scan vs (Bound i) = vs

   279       | scan vs (Abs(s,T,t)) = scan (s::vs) t

   280       | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)

   281   in (distinct o (scan [])) t end;

   282 fun is_bdv str =

   283     case Symbol.explode str of

   284 	"b"::"d"::"v"::_ => true

   285       | _ => false;

   286 fun is_bdv_ (Free (s,_)) = is_bdv s

   287   | is_bdv_ _ = false;

   289 (* is a term a substitution for a bdv as found in programs *)

   290 fun is_bdv_subst (Const ("List.list.Cons", _) $

   291       (Const ("Product_Type.Pair", _) $ Free (str, _) $ _) $ _) = is_bdv str

   292   | is_bdv_subst _ = false;

   294 fun free2str (Free (s,_)) = s

   295   | free2str t = error ("free2str not for " ^ term2str t);

   296 fun str_of_free_opt (Free (s,_)) = SOME s

   297   | str_of_free_opt _ = NONE

   298 fun free2int (t as Free (s, _)) = ((str2int s)

   299     handle _ => error ("free2int: " ^ term_detail2str t))

   300   | free2int t = error ("free2int: " ^ term_detail2str t);

   302 (*compare Logic.unvarify_global, which rejects Free*)

   303 fun var2free (t as Const(s,T)) = t

   304   | var2free (t as Free(s,T)) = t

   305   | var2free (Var((s,i),T)) = Free(s,T)

   306   | var2free (t as Bound i) = t

   307   | var2free (Abs(s,T,t)) = Abs(s,T,var2free t)

   308   | var2free (t1 $ t2) = (var2free t1) $ (var2free t2);

   310 (*27.8.01: doesn't find some subterm ???!???*)

   311 (*2010 free2var -> Logic.varify, but take care of 'Free ("1",_)'*)

   312 fun free2var (t as Const (s, T)) = t

   313   | free2var (t as Free (s, T)) = if is_no s then t else Var ((s, 0), T)

   314   | free2var (t as Var ((s, i), T)) = t

   315   | free2var (t as Bound i) = t

   316   | free2var (Abs (s, T, t)) = Abs (s, T, free2var t)

   317   | free2var (t1 $ t2) = (free2var t1) $ (free2var t2);

   320 fun mk_listT T = Type ("List.list", [T]);

   321 fun list_const T =

   322   Const("List.list.Cons", [T, mk_listT T] ---> mk_listT T);

   323 (*28.8.01: TODO: get type from head of list: 1 arg less!!!*)

   324 fun list2isalist T [] = Const("List.list.Nil",mk_listT T)

   325   | list2isalist T (t::ts) = (list_const T) $ t $ (list2isalist T ts);

   326 (*

   327 > val tt = (Thm.term_of o the o (parse thy)) "R=(R::real)";

   328 > val TT = type_of tt;

   329 > val ss = list2isalist TT [tt,tt,tt];

   330 > (Thm.global_cterm_of thy) ss;

   331 val it = "[R = R, R = R, R = R]" : cterm  *)

   333 fun isapair2pair (Const ("Product_Type.Pair",_) $ a $ b) = (a,b)

   334   | isapair2pair t =

   335     error ("isapair2pair called with "^term2str t);

   337 val listType = Type ("List.list",[Type ("bool",[])]);

   338 fun isalist2list ls =

   339   let

   340     fun get es (Const("List.list.Cons",_) $ t $ ls) = get (t::es) ls

   341       | get es (Const("List.list.Nil",_)) = es

   342       | get _ t =

   343 	error ("isalist2list applied to NON-list '"^term2str t^"'")

   344   in (rev o (get [])) ls end;

   345 (*

   346 > val il = str2term "[a=b,c=d,e=f]";

   347 > val l = isalist2list il;

   348 > (tracing o terms2str) l;

   349 ["a = b","c = d","e = f"]

   351 > val il = str2term "ss___::bool list";

   352 > val l = isalist2list il;

   353 [Free ("ss___", "bool List.list")]

   354 *)

   356 (*review Isabelle2009/src/HOL/Tools/hologic.ML*)

   357 (*val prop = Type ("HOL.Trueprop",[]);      ~/Diss.99/Integers-Isa/tools.sml*)

   358 val bool = Type ("HOL.bool",[]);     (* 2002 Integ.int *)

   359 val Trueprop = HOLogic.Trueprop;

   360 fun mk_prop t = HOLogic.mk_Trueprop t;

   361 val true_as_cterm = Thm.global_cterm_of (Thy_Info.get_theory "HOL.HOL") @{term True};

   362 val false_as_cterm = Thm.global_cterm_of (Thy_Info.get_theory "HOL.HOL") @{term False};

   364 infixr 5 -->;                    (*2002 /Pure/term.ML *)

   365 infixr --->;			 (*2002 /Pure/term.ML *)

   366 fun S --> T = Type("fun",[S,T]); (*2002 /Pure/term.ML *)

   367 val op ---> = foldr (op -->);    (*2002 /Pure/term.ML *)

   368 fun list_implies ([], B) = B : term (*2002 /term.ML *)

   369   | list_implies (A::AS, B) = Logic.implies $ A $ list_implies(AS,B);

   372 (** substitution **)

   374 fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =      (* = thm.ML *)

   375       match_bvs(s, t, if x="" orelse y="" then al

   376                                           else (x,y)::al)

   377   | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))

   378   | match_bvs(_,_,al) = al;

   379 fun ren_inst(insts,prop,pat,obj) =              (* = thm.ML *)

   380   let val ren = match_bvs(pat,obj,[])

   381       fun renAbs(Abs(x,T,b)) =

   382             Abs(case assoc_string(ren,x) of NONE => x

   383 	  | SOME(y) => y, T, renAbs(b))

   384         | renAbs(f$t) = renAbs(f) $ renAbs(t)

   385         | renAbs(t) = t

   386   in subst_vars insts (if null(ren) then prop else renAbs(prop)) end;

   393 fun dest_equals' (Const("HOL.eq",_) $ t $ u)  =  (t,u)(* logic.ML: Const("=="*)

   394   | dest_equals' t = raise TERM("dest_equals'", [t]);

   395 val lhs_ = (fst o dest_equals');

   396 val rhs_ = (snd o dest_equals');

   398 fun is_equality (Const("HOL.eq",_) $ t $ u)  =  true  (* logic.ML: Const("=="*)

   399   | is_equality _ = false;

   400 fun mk_equality (t,u) = (Const("HOL.eq",[type_of t,type_of u]--->bool) $ t $ u);

   401 fun is_expliceq (Const("HOL.eq",_) $ (Free _) $ u)  =  true

   402   | is_expliceq _ = false;

   403 fun strip_trueprop (Const("HOL.Trueprop",_) $ t) = t

   404   | strip_trueprop t = t;

   405 (*  | strip_trueprop t = raise TERM("strip_trueprop", [t]);

   406 *)

   408 (*.(A1==>...An==>B) goes to (A1==>...An==>).*)

   409 fun strip_imp_prems' (Const("==>", T) $ A $ t) =

   410     let fun coll_prems As (Const("==>", _) $ A $ t) =

   411 	    coll_prems (As $ (Logic.implies $ A)) t

   412 	  | coll_prems As _ = SOME As

   413     in coll_prems (Logic.implies $ A) t end

   414   | strip_imp_prems' _ = NONE;  (* logic.ML: term -> term list*)

   415 (*

   416   val thm = real_mult_div_cancel1;

   417   val prop = (#prop o rep_thm) thm;

   418   atomt prop;

   419 *** -------------

   420 *** Const ( ==>)

   421 *** . Const ( Trueprop)

   422 *** . . Const ( Not)

   423 *** . . . Const ( op =)

   424 *** . . . . Var ((k, 0), )

   425 *** . . . . Const ( 0)

   426 *** . Const ( Trueprop)

   427 *** . . Const ( op =)                                                          *** .............

   428   val SOME t = strip_imp_prems' ((#prop o rep_thm) thm);

   429   atomt t;

   430 *** -------------

   431 *** Const ( ==>)

   432 *** . Const ( Trueprop)

   433 *** . . Const ( Not)

   434 *** . . . Const ( op =)

   435 *** . . . . Var ((k, 0), )

   436 *** . . . . Const ( 0)

   438   val thm = real_le_anti_sym;

   439   val prop = (#prop o rep_thm) thm;

   440   atomt prop;

   441 *** -------------

   442 *** Const ( ==>)

   443 *** . Const ( Trueprop)

   444 *** . . Const ( op <=)

   445 *** . . . Var ((z, 0), )

   446 *** . . . Var ((w, 0), )

   447 *** . Const ( ==>)

   448 *** . . Const ( Trueprop)

   449 *** . . . Const ( op <=)

   450 *** . . . . Var ((w, 0), )

   451 *** . . . . Var ((z, 0), )

   452 *** . . Const ( Trueprop)

   453 *** . . . Const ( op =)

   454 *** .............

   455   val SOME t = strip_imp_prems' ((#prop o rep_thm) thm);

   456   atomt t;

   457 *** -------------

   458 *** Const ( ==>)

   459 *** . Const ( Trueprop)

   460 *** . . Const ( op <=)

   461 *** . . . Var ((z, 0), )

   462 *** . . . Var ((w, 0), )

   463 *** . Const ( ==>)

   464 *** . . Const ( Trueprop)

   465 *** . . . Const ( op <=)

   466 *** . . . . Var ((w, 0), )

   467 *** . . . . Var ((z, 0), )

   468 *)

   470 (*. (A1==>...An==>) (B) goes to (A1==>...An==>B), where B is lowest branch.*)

   471 fun ins_concl (Const("==>", T) $ A $ t) B = Logic.implies $ A $ (ins_concl t B)

   472   | ins_concl (Const("==>", T) $ A    ) B = Logic.implies $ A $ B

   473   | ins_concl t B =  raise TERM("ins_concl", [t, B]);

   474 (*

   475   val thm = real_le_anti_sym;

   476   val prop = (#prop o rep_thm) thm;

   477   val concl = Logic.strip_imp_concl prop;

   478   val SOME prems = strip_imp_prems' prop;

   479   val prop' = ins_concl prems concl;

   480   prop = prop';

   481   atomt prop;

   482   atomt prop';

   483 *)

   486 fun vperm (Var _, Var _) = true  (*2002 Pure/thm.ML *)

   487   | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t)

   488   | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2)

   489   | vperm (t, u) = (t = u);

   491 (*2002 cp from Pure/term.ML --- since 2009 in Pure/old_term.ML*)

   492 fun mem_term (_, []) = false

   493   | mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts);

   494 fun subset_term ([], ys) = true

   495   | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys);

   496 fun eq_set_term (xs, ys) =

   497     xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));

   498 (*a total, irreflexive ordering on index names*)

   499 fun xless ((a,i), (b,j): indexname) = i<j  orelse  (i=j andalso a<b);

   500 (*a partial ordering (not reflexive) for atomic terms*)

   501 fun atless (Const (a,_), Const (b,_))  =  a<b

   502   | atless (Free (a,_), Free (b,_)) =  a<b

   503   | atless (Var(v,_), Var(w,_))  =  xless(v,w)

   504   | atless (Bound i, Bound j)  =   i<j

   505   | atless _  =  false;

   506 (*insert atomic term into partially sorted list, suppressing duplicates (?)*)

   507 fun insert_aterm (t,us) =

   508   let fun inserta [] = [t]

   509         | inserta (us as u::us') =

   510               if atless(t,u) then t::us

   511               else if t=u then us (*duplicate*)

   512               else u :: inserta(us')

   513   in  inserta us  end;

   515 (*Accumulates the Vars in the term, suppressing duplicates*)

   516 fun add_term_vars (t, vars: term list) = case t of

   517     Var   _ => insert_aterm(t,vars)

   518   | Abs (_,_,body) => add_term_vars(body,vars)

   519   | f$t =>  add_term_vars (f, add_term_vars(t, vars))

   520   | _ => vars;

   521 fun term_vars t = add_term_vars(t,[]);

   524 fun var_perm (t, u) = (*2002 Pure/thm.ML *)

   525   vperm (t, u) andalso eq_set_term (term_vars t, term_vars u);

   527 (*2002 fun decomp_simp, Pure/thm.ML *)

   528 fun perm lhs rhs = var_perm (lhs, rhs) andalso not (lhs aconv rhs)

   529     andalso not (is_Var lhs);

   532 fun str_of_int n =

   533   if n < 0 then "-"^((string_of_int o abs) n)

   534   else string_of_int n;

   535 (*

   536 > str_of_int 1;

   537 val it = "1" : string                                                          > str_of_int ~1;

   538 val it = "-1" : string

   539 *)

   542 fun power b 0 = 1

   543   | power b n =

   544   if n>0 then b*(power b (n-1))

   545   else error ("power "^(str_of_int b)^" "^(str_of_int n));

   546 (*

   547 > power 2 3;

   548 val it = 8 : int

   549 > power ~2 3;

   550 val it = ~8 : int

   551 > power ~3 2;

   552 val it = 9 : int

   553 > power 3 ~2;

   554 *)

   555 fun gcd 0 b = b

   556   | gcd a b = if a < b then gcd (b mod a) a

   557 	      else gcd (a mod b) b;

   558 fun sign n = if n < 0 then ~1

   559 	     else if n = 0 then 0 else 1;

   560 fun sign2 n1 n2 = (sign n1) * (sign n2);

   562 infix dvd;

   563 fun d dvd n = n mod d = 0;

   565 fun divisors n =

   566   let fun pdiv ds d n =

   567     if d=n then d::ds

   568     else if d dvd n then pdiv (d::ds) d (n div d)

   569 	 else pdiv ds (d+1) n

   570   in pdiv [] 2 n end;

   572 divisors 30;

   573 divisors 32;

   574 divisors 60;

   575 divisors 11;

   577 fun doubles ds = (* ds is ordered *)

   578   let fun dbls ds [] = ds

   579 	| dbls ds [i] = ds

   580 	| dbls ds (i::i'::is) = if i=i' then dbls (i::ds) is

   581 				else dbls ds (i'::is)

   582   in dbls [] ds end;

   583 (*> doubles [2,3,4];

   584 val it = [] : int list

   585 > doubles [2,3,3,5,5,7];

   586 val it = [5,3] : int list*)

   588 fun squfact 0 = 0

   589   | squfact 1 = 1

   590   | squfact n = foldl op* (1, (doubles o divisors) n);

   591 (*> squfact 30;

   592 val it = 1 : int

   593 > squfact 32;

   594 val it = 4 : int

   595 > squfact 60;

   596 val it = 2 : int

   597 > squfact 11;

   598 val it = 1 : int*)

   601 fun dest_type (Type(T,[])) = T

   602   | dest_type T =

   603     (atomtyp T;

   604      error ("... dest_type: not impl. for this type"));

   606 fun term_of_num ntyp n = Free (str_of_int n, ntyp);

   608 fun pairT T1 T2 = Type ("*", [T1, T2]);

   609 (*> val t = str2term "(1,2)";

   610 > type_of t = pairT HOLogic.realT HOLogic.realT;

   611 val it = true : bool

   612 *)

   613 fun PairT T1 T2 = ([T1, T2] ---> Type ("*", [T1, T2]));

   614 (*> val t = str2term "(1,2)";

   615 > val Const ("Product_Type.Pair",pT) $ _ $ _ = t;

   616 > pT = PairT HOLogic.realT HOLogic.realT;

   617 val it = true : bool

   618 *)

   619 fun pairt t1 t2 =

   620     Const ("Product_Type.Pair", PairT (type_of t1) (type_of t2)) $ t1 $ t2;

   621 (*> val t = str2term "(1,2)";

   622 > val (t1, t2) = (str2term "1", str2term "2");

   623 > t = pairt t1 t2;

   624 val it = true : bool*)

   627 fun num_of_term (t as Free (s,_)) =

   628     (case int_of_str s of

   629 	 SOME s' => s'

   630        | NONE => error ("num_of_term not for "^ term2str t))

   631   | num_of_term t = error ("num_of_term not for "^term2str t);

   633 fun mk_factroot op_(*=thy.sqrt*) T fact root =

   634   Const ("Groups.times_class.times", [T, T] ---> T) $ (term_of_num T fact) $

   635   (Const (op_, T --> T) $ term_of_num T root);

   636 (*

   637 val T =  (type_of o Thm.term_of o the) (parse thy "#12::real");

   638 val t = mk_factroot "SqRoot.sqrt" T 2 3;

   639 (Thm.global_cterm_of thy) t;

   640 val it = "#2 * sqrt #3 " : cterm

   641 *)

   642 fun var_op_num v op_ optype ntyp n =

   643   Const (op_, optype) $ v $

   644    Free (str_of_int  n, ntyp);

   646 fun num_op_var v op_ optype ntyp n =

   647   Const (op_,optype) $

   648    Free (str_of_int n, ntyp) $ v;

   650 fun num_op_num T1 T2 (op_,Top) n1 n2 =

   651   Const (op_,Top) $

   652   Free (str_of_int n1, T1) $ Free (str_of_int n2, T2);

   653 (*

   654 > val t = num_op_num "Int" 3 4;

   655 > atomty t;

   656 > string_of_cterm ((Thm.global_cterm_of thy) t);

   657 *)

   661 fun const_in str (Const _) = false

   662   | const_in str (Free (s,_)) = if strip_thy s = str then true else false

   663   | const_in str (Bound _) = false

   664   | const_in str (Var _) = false

   665   | const_in str (Abs (_,_,body)) = const_in str body

   666   | const_in str (f$u) = const_in str f orelse const_in str u;

   667 (*

   668 > val t = (Thm.term_of o the o (parse thy)) "6 + 5 * sqrt 4 + 3";

   669 > const_in "sqrt" t;

   670 val it = true : bool

   671 > val t = (Thm.term_of o the o (parse thy)) "6 + 5 * 4 + 3";

   672 > const_in "sqrt" t;

   673 val it = false : bool

   674 *)

   676 (*used for calculating built in binary operations in Isabelle2002->Float.ML*)

   677 (*fun calc "Groups.plus_class.plus"  (n1, n2) = n1+n2

   678   | calc "Groups.minus_class.minus"  (n1, n2) = n1-n2

   679   | calc "Groups.times_class.times"  (n1, n2) = n1*n2

   680   | calc "Rings.divide_class.divide"(n1, n2) = n1 div n2

   681   | calc "Atools.pow"(n1, n2) = power n1 n2

   682   | calc op_ _ = error ("calc: operator = "^op_^" not defined");-----*)

   683 fun calc_equ "less"  (n1, n2) = n1 < n2

   684   | calc_equ "less_eq" (n1, n2) = n1 <= n2

   685   | calc_equ op_ _ =

   686   error ("calc_equ: operator = "^op_^" not defined");

   687 fun sqrt (n:int) = if n < 0 then 0

   688     (*FIXME ~~~*)  else (trunc o Math.sqrt o Real.fromInt) n;

   690 fun mk_thmid thmid op_ n1 n2 =

   691   thmid ^ (strip_thy n1) ^ "_" ^ (strip_thy n2);

   693 fun dest_binop_typ (Type("fun",[range,Type("fun",[arg2,arg1])])) =

   694   (arg1,arg2,range)

   695   | dest_binop_typ _ = error "dest_binop_typ: not binary";

   696 (* -----

   697 > val t = (Thm.term_of o the o (parse thy)) "#3^#4";

   698 > val hT = type_of (head_of t);

   699 > dest_binop_typ hT;

   700 val it = ("'a","nat","'a") : typ * typ * typ

   701  ----- *)

   704 (** transform binary numeralsstrings **)

   705 (*Makarius 100308, hacked by WN*)

   706 val numbers_to_string =

   707   let

   708     fun dest_num t =

   709       (case try HOLogic.dest_number t of

   710         SOME (T, i) =>

   711           (*if T = @{typ int} orelse T = @{typ real} then WN*)

   712             SOME (Free (signed_string_of_int i, T))

   713           (*else NONE  WN*)

   714       | NONE => NONE);

   716     fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)

   717       | to_str (t as (u1 $ u2)) =

   718           (case dest_num t of

   719             SOME t' => t'

   720           | NONE => to_str u1 $ to_str u2)

   721       | to_str t = perhaps dest_num t;

   722   in to_str end

   724 (*.make uminus uniform:

   725    Const ("uminus", _) $ Free ("2", "RealDef.real") --> Free ("-2", _)

   726 to be used immediately before evaluation of numerals;

   727 see Scripts/calculate.sml .*)

   728 (*2002 fun(*app_num_tr'2 (Const("0",T)) = Free("0",T)

   729   | app_num_tr'2 (Const("1",T)) = Free("1",T)

   730   |*)app_num_tr'2 (t as Const("uminus",_) $ Free(s,T)) =

   731     (case int_of_str s of SOME i =>

   732 			  if i > 0 then Free("-"^s,T) else Free(s,T)

   733 		       | NONE => t)

   734 (*| app_num_tr'2 (t as Const(s,T)) = t

   735   | app_num_tr'2 (Const("Numeral.number_of",Type ("fun", [_, T])) $ t) =

   736     Free(NumeralSyntax.dest_bin_str t, T)

   737   | app_num_tr'2 (t as Free(s,T)) = t

   738   | app_num_tr'2 (t as Var(n,T)) = t

   739   | app_num_tr'2 (t as Bound i) = t

   740 *)| app_num_tr'2 (Abs(s,T,body)) = Abs(s,T, app_num_tr'2 body)

   741   | app_num_tr'2 (t1 $ t2) = (app_num_tr'2 t1) $ (app_num_tr'2 t2)

   742   | app_num_tr'2 t = t;

   743 *)

   744 val uminus_to_string =

   745     let

   746 	fun dest_num t =

   747 	    (case t of

   748 		 (Const ("Groups.uminus_class.uminus", _) $ Free (s, T)) =>

   749 		 (case int_of_str s of

   750 		      SOME i =>

   751 		      SOME (Free (signed_string_of_int (~1 * i), T))

   752 		    | NONE => NONE)

   753 	       | _ => NONE);

   755 	fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)

   756 	  | to_str (t as (u1 $ u2)) =

   757             (case dest_num t of

   758 		 SOME t' => t'

   759                | NONE => to_str u1 $ to_str u2)

   760 	  | to_str t = perhaps dest_num t;

   761     in to_str end;

   764 (*2002 fun num_str thm =

   765   let

   766     val {sign_ref = sign_ref, der = der, maxidx = maxidx,

   767 	    shyps = shyps, hyps = hyps, (*tpairs = tpairs,*) prop = prop} =

   768 	Thm.rep_thm_G thm;

   769     val prop' = app_num_tr'1 prop;

   770   in Thm.assbl_thm sign_ref der maxidx shyps hyps (*tpairs*) prop' end;*)

   771 fun num_str thm =

   772   let val (deriv,

   773 	   {cert = cert, tags = tags, maxidx = maxidx, shyps = shyps,

   774 	    hyps = hyps, tpairs = tpairs, prop = prop}) = Thm.rep_thm_G thm

   775     val prop' = numbers_to_string prop;

   776   in Thm.assbl_thm deriv cert tags maxidx shyps hyps tpairs prop' end;

   778 fun get_thm' xstring = (*?covers 2009 Thm?!, replaces 2002 fun get_thm :

   779 val it = fn : theory -> xstring -> Thm.thm*)

   780     Thm (xstring,

   781 	 num_str (Proof_Context.get_thm (thy2ctxt' "Isac") xstring));

   783 (** get types of Free and Abs for parse' **)

   784 (*11.1.00: not used, fix-typed +,*,-,^ instead *)

   786 val dummyT = Type ("dummy",[]);

   787 val dummyT = TVar (("DUMMY",0),[]);

   789 (* assumes only 1 type for numerals

   790    and different identifiers for Const, Free and Abs *)

   791 fun get_types t =

   792   let

   793     fun get ts  (Const(s,T)) = (s,T)::ts

   794       | get ts  (Free(s,T)) = if is_no s

   795 				then ("#",T)::ts else (s,T)::ts

   796       | get ts  (Var(n,T)) = ts

   797       | get ts  (Bound i) = ts

   798       | get ts  (Abs(s,T,body)) = get ((s,T)::ts)  body

   799       | get ts  (t1 $ t2) = (get ts  t1) @ (get ts  t2)

   800   in distinct (get [] t) end;

   801 (*

   802 val t = (Thm.term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)";

   803 get_types t;

   804 *)

   806 (*11.1.00: not used, fix-typed +,*,-,^ instead *)

   807 fun set_types al (Const(s,T)) =

   808     (case assoc (al,s) of

   809        SOME T' => Const(s,T')

   810      | NONE => (warning ("set_types: no type for "^s); Const(s,dummyT)))

   811   | set_types al (Free(s,T)) =

   812   if is_no s then

   813     (case assoc (al,"#") of

   814       SOME T' => Free(s,T')

   815     | NONE => (warning ("set_types: no type for numerals"); Free(s,T)))

   816   else (case assoc (al,s) of

   817 	       SOME T' => Free(s,T')

   818 	     | NONE => (warning ("set_types: no type for "^s); Free(s,T)))

   819   | set_types al (Var(n,T)) = Var(n,T)

   820   | set_types al (Bound i) = Bound i

   821   | set_types al (Abs(s,T,body)) =

   822 		 (case assoc (al,s) of

   823 		    SOME T'  => Abs(s,T', set_types al body)

   824 		  | NONE => (warning ("set_types: no type for "^s);

   825 			     Abs(s,T, set_types al body)))

   826   | set_types al (t1 $ t2) = (set_types al t1) $ (set_types al t2);

   827 (*

   828 val t = (Thm.term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)";

   829 val al = get_types t;

   831 val t = (Thm.term_of o the o (parse thy)) "x = #0 + #-1 * #-4";

   832 atomty t;                         (* 'a *)

   833 val t' = set_types al t;

   834 atomty t';                        (*real*)

   835 (Thm.global_cterm_of thy) t';

   836 val it = "x = #0 + #-1 * #-4" : cterm

   838 val t = (Thm.term_of o the o (parse thy))

   839   "#5 * x + x ^^^ #2 = (#2 + x) ^^^ #2";

   840 atomty t;

   841 val t' = set_types al t;

   842 atomty t';

   843 (Thm.global_cterm_of thy) t';

   844 uncaught exception TYPE               (*^^^ is new, NOT in al*)

   845 *)

   848 (** from Descript.ML **)

   850 (** decompose an isa-list to an ML-list

   851     i.e. [] belong to the meta-language, too **)

   853 fun is_list ((Const("List.list.Cons",_)) $ _ $ _) = true

   854   | is_list _ = false;

   855 (* val (SOME ct) = parse thy "lll::real list";

   856 > val ty = (#t o rep_cterm) ct;

   857 > is_list ty;

   858 val it = false : bool

   859 > val (SOME ct) = parse thy "[lll]";

   860 > val ty = (#t o rep_cterm) ct;

   861 > is_list ty;

   862 val it = true : bool *)

   866 fun mk_Free (s,T) = Free(s,T);

   867 fun mk_free T s =  Free(s,T);

   869 (*Special case: one argument cp from Isabelle2002/src/Pure/term.ML*)

   870 fun subst_bound (arg, t) : term = (*WN100908 neglects 'raise Same.SAME'*)

   871   let fun subst (t as Bound i, lev) =

   872             if i<lev then  t    (*var is locally bound*)

   873             else  if i=lev then incr_boundvars lev arg

   874                            else Bound(i-1)  (*loose: change it*)

   875         | subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))

   876         | subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)

   877         | subst (t,lev) = t

   878   in  subst (t,0)  end;

   880 (*instantiate let; necessary for ass_up*)

   881 fun inst_abs thy (Const sT) = Const sT  (*TODO.WN100907 drop thy*)

   882   | inst_abs thy (Free sT) = Free sT

   883   | inst_abs thy (Bound n) = Bound n

   884   | inst_abs thy (Var iT) = Var iT

   885   | inst_abs thy (Const ("HOL.Let",T1) $ e $ (Abs (v, T2, b))) =

   886     let val b' = subst_bound (Free (v, T2), b);

   887     (*fun variant_abs: term.ML*)

   888     in Const ("HOL.Let", T1) $ inst_abs thy e $ (Abs (v, T2, inst_abs thy b')) end

   889   | inst_abs thy (t1 $ t2) = inst_abs thy t1 $ inst_abs thy t2

   890   | inst_abs thy t = t;

   891 (*val scr =

   892    "Script Make_fun_by_explicit (f_::real) (v_::real) (eqs_::bool list) = \

   893    \ (let h_ = (hd o (filterVar f_)) eqs_;                    \

   894    \      e_1 = hd (dropWhile (ident h_) eqs_);       \

   895    \      vs_ = dropWhile (ident f_) (Vars h_);                \

   896    \      v_1 = hd (dropWhile (ident v_) vs_);                \

   897    \      (s_1::bool list)=(SubProblem(DiffApp_,[univar,equation],[no_met])\

   898    \                          [BOOL e_1, REAL v_1])\

   899    \ in Substitute [(v_1 = (rhs o hd) s_1)] h_)";

   900 > val ttt = (Thm.term_of o the o (parse thy)) scr;

   901 > tracing(term2str ttt);

   902 > atomt ttt;

   903 *** -------------

   904 *** Const ( DiffApp.Make'_fun'_by'_explicit)

   905 *** . Free ( f_, )

   906 *** . Free ( v_, )

   907 *** . Free ( eqs_, )

   908 *** . Const ( Let)

   909 *** . . Const ( Fun.op o)

   910 *** . . . Const ( List.hd)

   911 *** . . . Const ( DiffApp.filterVar)

   912 *** . . . . Free ( f_, )

   913 *** . . . Free ( eqs_, )

   914 *** . . Abs( h_,..

   915 *** . . . Const ( Let)

   916 *** . . . . Const ( List.hd)

   917 *** . . . . . Const ( List.dropWhile)

   918 *** . . . . . . Const ( Atools.ident)

   919 *** . . . . . . . Bound 0                     <---- Free ( h_, )

   920 *** . . . . . . Free ( eqs_, )

   921 *** . . . . Abs( e_1,..

   922 *** . . . . . Const ( Let)

   923 *** . . . . . . Const ( List.dropWhile)

   924 *** . . . . . . . Const ( Atools.ident)

   925 *** . . . . . . . . Free ( f_, )

   926 *** . . . . . . . Const ( Tools.Vars)

   927 *** . . . . . . . . Bound 1                       <---- Free ( h_, )

   928 *** . . . . . . Abs( vs_,..

   929 *** . . . . . . . Const ( Let)

   930 *** . . . . . . . . Const ( List.hd)

   931 *** . . . . . . . . . Const ( List.dropWhile)

   932 *** . . . . . . . . . . Const ( Atools.ident)

   933 *** . . . . . . . . . . . Free ( v_, )

   934 *** . . . . . . . . . . Bound 0                   <---- Free ( vs_, )

   935 *** . . . . . . . . Abs( v_1,..

   936 *** . . . . . . . . . Const ( Let)

   937 *** . . . . . . . . . . Const ( Script.SubProblem)

   938 *** . . . . . . . . . . . Const ( Pair)

   939 *** . . . . . . . . . . . . Free ( DiffApp_, )

   940 *** . . . . . . . . . . . . Const ( Pair)

   941 *** . . . . . . . . . . . . . Const ( List.list.Cons)

   942 *** . . . . . . . . . . . . . . Free ( univar, )

   943 *** . . . . . . . . . . . . . . Const ( List.list.Cons)

   944 *** . . . . . . . . . . . . . . . Free ( equation, )

   945 *** . . . . . . . . . . . . . . . Const ( List.list.Nil)

   946 *** . . . . . . . . . . . . . Const ( List.list.Cons)

   947 *** . . . . . . . . . . . . . . Free ( no_met, )

   948 *** . . . . . . . . . . . . . . Const ( List.list.Nil)

   949 *** . . . . . . . . . . . Const ( List.list.Cons)

   950 *** . . . . . . . . . . . . Const ( Script.BOOL)

   951 *** . . . . . . . . . . . . . Bound 2                   <----- Free ( e_1, )

   952 *** . . . . . . . . . . . . Const ( List.list.Cons)

   953 *** . . . . . . . . . . . . . Const ( Script.real_)

   954 *** . . . . . . . . . . . . . . Bound 0                 <----- Free ( v_1, )

   955 *** . . . . . . . . . . . . . Const ( List.list.Nil)

   956 *** . . . . . . . . . . Abs( s_1,..

   957 *** . . . . . . . . . . . Const ( Script.Substitute)

   958 *** . . . . . . . . . . . . Const ( List.list.Cons)

   959 *** . . . . . . . . . . . . . Const ( Pair)

   960 *** . . . . . . . . . . . . . . Bound 1                 <----- Free ( v_1, )

   961 *** . . . . . . . . . . . . . . Const ( Fun.op o)

   962 *** . . . . . . . . . . . . . . . Const ( Tools.rhs)

   963 *** . . . . . . . . . . . . . . . Const ( List.hd)

   964 *** . . . . . . . . . . . . . . . Bound 0               <----- Free ( s_1, )

   965 *** . . . . . . . . . . . . . Const ( List.list.Nil)

   966 *** . . . . . . . . . . . . Bound 4                     <----- Free ( h_, )

   968 > val ttt' = inst_abs thy ttt;

   969 > tracing(term2str ttt');

   970 Script Make_fun_by_explicit f_ v_ eqs_ =

   971   ... as above ...

   972 > atomt ttt';

   973 *** -------------

   974 *** Const ( DiffApp.Make'_fun'_by'_explicit)

   975 *** . Free ( f_, )

   976 *** . Free ( v_, )

   977 *** . Free ( eqs_, )

   978 *** . Const ( Let)

   979 *** . . Const ( Fun.op o)

   980 *** . . . Const ( List.hd)

   981 *** . . . Const ( DiffApp.filterVar)

   982 *** . . . . Free ( f_, )

   983 *** . . . Free ( eqs_, )

   984 *** . . Abs( h_,..

   985 *** . . . Const ( Let)

   986 *** . . . . Const ( List.hd)

   987 *** . . . . . Const ( List.dropWhile)

   988 *** . . . . . . Const ( Atools.ident)

   989 *** . . . . . . . Free ( h_, )                <---- Bound 0

   990 *** . . . . . . Free ( eqs_, )

   991 *** . . . . Abs( e_1,..

   992 *** . . . . . Const ( Let)

   993 *** . . . . . . Const ( List.dropWhile)

   994 *** . . . . . . . Const ( Atools.ident)

   995 *** . . . . . . . . Free ( f_, )

   996 *** . . . . . . . Const ( Tools.Vars)

   997 *** . . . . . . . . Free ( h_, )                  <---- Bound 1

   998 *** . . . . . . Abs( vs_,..

   999 *** . . . . . . . Const ( Let)

  1000 *** . . . . . . . . Const ( List.hd)

  1001 *** . . . . . . . . . Const ( List.dropWhile)

  1002 *** . . . . . . . . . . Const ( Atools.ident)

  1003 *** . . . . . . . . . . . Free ( v_, )

  1004 *** . . . . . . . . . . Free ( vs_, )             <---- Bound 0

  1005 *** . . . . . . . . Abs( v_1,..

  1006 *** . . . . . . . . . Const ( Let)

  1007 *** . . . . . . . . . . Const ( Script.SubProblem)

  1008 *** . . . . . . . . . . . Const ( Pair)

  1009 *** . . . . . . . . . . . . Free ( DiffApp_, )

  1010 *** . . . . . . . . . . . . Const ( Pair)

  1011 *** . . . . . . . . . . . . . Const ( List.list.Cons)

  1012 *** . . . . . . . . . . . . . . Free ( univar, )

  1013 *** . . . . . . . . . . . . . . Const ( List.list.Cons)

  1014 *** . . . . . . . . . . . . . . . Free ( equation, )

  1015 *** . . . . . . . . . . . . . . . Const ( List.list.Nil)

  1016 *** . . . . . . . . . . . . . Const ( List.list.Cons)

  1017 *** . . . . . . . . . . . . . . Free ( no_met, )

  1018 *** . . . . . . . . . . . . . . Const ( List.list.Nil)

  1019 *** . . . . . . . . . . . Const ( List.list.Cons)

  1020 *** . . . . . . . . . . . . Const ( Script.BOOL)

  1021 *** . . . . . . . . . . . . . Free ( e_1, )             <----- Bound 2

  1022 *** . . . . . . . . . . . . Const ( List.list.Cons)

  1023 *** . . . . . . . . . . . . . Const ( Script.real_)

  1024 *** . . . . . . . . . . . . . . Free ( v_1, )           <----- Bound 0

  1025 *** . . . . . . . . . . . . . Const ( List.list.Nil)

  1026 *** . . . . . . . . . . Abs( s_1,..

  1027 *** . . . . . . . . . . . Const ( Script.Substitute)

  1028 *** . . . . . . . . . . . . Const ( List.list.Cons)

  1029 *** . . . . . . . . . . . . . Const ( Pair)

  1030 *** . . . . . . . . . . . . . . Free ( v_1, )           <----- Bound 1

  1031 *** . . . . . . . . . . . . . . Const ( Fun.op o)

  1032 *** . . . . . . . . . . . . . . . Const ( Tools.rhs)

  1033 *** . . . . . . . . . . . . . . . Const ( List.hd)

  1034 *** . . . . . . . . . . . . . . . Free ( s_1, )         <----- Bound 0

  1035 *** . . . . . . . . . . . . . Const ( List.list.Nil)

  1036 *** . . . . . . . . . . . . Free ( h_, )                <----- Bound 4

  1038 Note numbering of de Bruijn indexes !

  1040 Script Make_fun_by_explicit f_ v_ eqs_ =

  1041  let h_ = (hd o filterVar f_) eqs_;

  1042      e_1 = hd (dropWhile (ident h_ BOUND_0) eqs_);

  1043      vs_ = dropWhile (ident f_) (Vars h_ BOUND_1);

  1044      v_1 = hd (dropWhile (ident v_) vs_ BOUND_0);

  1045      s_1 =

  1046        SubProblem (DiffApp_, [univar, equation], [no_met])

  1047         [BOOL e_1 BOUND_2, REAL v_1 BOUND_0]

  1048  in Substitute [(v_1 BOUND_1 = (rhs o hd) s_1 BOUND_0)] h_ BOUND_4

  1049 *)

  1051 (* for parse and parse_patt: fix all types to real *)

  1052 fun T_a2real (Type (s, [])) =

  1053     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT

  1054     else Type (s, [])

  1055   | T_a2real (Type (s, Ts)) = Type (s, map T_a2real Ts)

  1056   | T_a2real (TFree (s, srt)) =

  1057     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT

  1058     else TFree (s, srt)

  1059   | T_a2real (TVar ((s, i), srt)) =

  1060     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT

  1061     else TVar ((s, i), srt)

  1062   | T_a2real (TVar (("DUMMY",_), srt)) = HOLogic.realT;

  1064 (*FIXME .. fixes the type (+see Typefix.thy*)

  1065 fun typ_a2real (Const( s, T)) = (Const( s, T_a2real T))

  1066   | typ_a2real (Free( s, T)) = (Free( s, T_a2real T))

  1067   | typ_a2real (Var( n, T)) = (Var( n, T_a2real T))

  1068   | typ_a2real (Bound i) = (Bound i)

  1069   | typ_a2real (Abs(s,T,t)) = Abs(s, T, typ_a2real t)

  1070   | typ_a2real (t1 $ t2) = (typ_a2real t1) $ (typ_a2real t2);

  1073 (* before 2002 *)

  1074 fun parseold thy str =

  1075   (let val t = ((*typ_a2real o*) numbers_to_string)

  1076 		   (Syntax.read_term_global thy str)

  1077    in SOME (Thm.global_cterm_of thy t) end)

  1078     handle _ => NONE;

  1079 (*2002 fun parseN thy str =

  1080   (let

  1081      val sgn = sign_of thy;

  1082      val t = ((*typ_a2real o app_num_tr'1 o*) term_of)

  1083        (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));

  1084    in SOME (Thm.global_cterm_of sgn t) end)

  1085      handle _ => NONE;*)

  1086 fun parseN thy str =

  1087   (let val t = (*(typ_a2real o numbers_to_string)*)

  1088 	   (Syntax.read_term_global thy str)

  1089    in SOME (Thm.global_cterm_of thy t) end)

  1090     handle _ => NONE;

  1091 (*2002 fun parse thy str =

  1092   (let

  1093      val sgn = sign_of thy;

  1094      val t = (typ_a2real o app_num_tr'1 o Thm.term_of)

  1095        (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));

  1096    in SOME (Thm.global_cterm_of sgn t) end) (*FIXXXXME 10.8.02: return term !!!*)

  1097      handle _ => NONE;*)

  1098 (*2010 fun parse thy str =

  1099   (let val t = (typ_a2real o app_num_tr'1) (Syntax.read_term_global thy str)

  1100    in SOME (Thm.global_cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)

  1101      handle _ => NONE;*)

  1102 fun parse thy str =

  1103   (let val t = (typ_a2real o numbers_to_string)

  1104 		   (Syntax.read_term_global thy str)

  1105    in SOME (Thm.global_cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)

  1106      handle _ => NONE;

  1107 (*

  1108 > val (SOME ct) = parse thy "(-#5)^^^#3";

  1109 > atomty (Thm.term_of ct);

  1110 *** -------------

  1111 *** Const ( Nat.op ^, ['a, nat] => 'a)

  1112 ***   Const ( uminus, 'a => 'a)

  1113 ***     Free ( #5, 'a)

  1114 ***   Free ( #3, nat)

  1115 > val (SOME ct) = parse thy "R=R";

  1116 > atomty (Thm.term_of ct);

  1117 *** -------------

  1118 *** Const ( op =, [real, real] => bool)

  1119 ***   Free ( R, real)

  1120 ***   Free ( R, real)

  1122 THIS IS THE OUTPUT FOR VERSION (3) above at typ_a2real !!!!!

  1123 *** -------------

  1124 *** Const ( op =, [RealDef.real, RealDef.real] => bool)

  1125 ***   Free ( R, RealDef.real)

  1126 ***   Free ( R, RealDef.real)                  *)

  1128 (*WN110317 parseNEW will replace parse after introduction of ctxt completed*)

  1129 fun parseNEW ctxt str = SOME (Syntax.read_term ctxt str |> numbers_to_string)

  1130       handle _ => NONE;

  1132 (* parse term patterns; Var ("v",_), i.e. "?v", are required for instantiation

  1133   WN130613 probably compare to

  1134   http://www.mail-archive.com/isabelle-dev@mailbroy.informatik.tu-muenchen.de/msg04249.html*)

  1135 fun parse_patt thy str = (thy, str) |>> thy2ctxt

  1136                                     |-> Proof_Context.read_term_pattern

  1137                                     |> numbers_to_string (*TODO drop*)

  1138                                     |> typ_a2real;       (*TODO drop*)

  1140 (*version for testing local to theories*)

  1141 fun str2term_ thy str = (Thm.term_of o the o (parse thy)) str;

  1142 (*WN110520

  1143 fun str2term str = (Thm.term_of o the o (parse (Thy_Info_get_theory "Isac"))) str;*)

  1144 fun str2term str = parse_patt (Thy_Info_get_theory "Isac") str

  1145 fun strs2terms ss = map str2term ss;

  1146 fun str2termN str = (Thm.term_of o the o (parseN (Thy_Info_get_theory "Isac"))) str;

  1148 (*+ makes a substitution from the output of Pattern.match +*)

  1149 (*fun mk_subs ((id, _):indexname, t:term) = (Free (id,type_of t), t);*)

  1150 fun mk_subs (subs: ((string * int) * (Term.typ * Term.term)) list) =

  1151 let fun mk_sub ((id, _), (ty, tm)) = (Free (id, ty), tm) in

  1152 map mk_sub subs end;

  1154 val atomthm = atomt o #prop o Thm.rep_thm;

  1156 (*.instantiate #prop thm with bound variables (as Free).*)

  1157 fun inst_bdv [] t = t : term

  1158   | inst_bdv (instl: (term*term) list) t =

  1159       let fun subst (v as Var((s,_),T)) =

  1160 	      (case Symbol.explode s of

  1161 		   "b"::"d"::"v"::_ =>

  1162 		   if_none (assoc(instl,Free(s,T))) (Free(s,T))

  1163 		 | _ => v)

  1164             | subst (Abs(a,T,body)) = Abs(a, T, subst body)

  1165             | subst (f$t') = subst f $ subst t'

  1166             | subst t = if_none (assoc(instl,t)) t

  1167       in  subst t  end;

  1170 (*WN050829 caution: is_atom (str2term"q_0/2 * L * x") = true !!!

  1171   use length (vars term) = 1 instead*)

  1172 fun is_atom (Const ("Float.Float",_) $ _) = true

  1173   | is_atom (Const ("ComplexI.I'_'_",_)) = true

  1174   | is_atom (Const ("Groups.times_class.times",_) $ t $ Const ("ComplexI.I'_'_",_)) = is_atom t

  1175   | is_atom (Const ("Groups.plus_class.plus",_) $ t1 $ Const ("ComplexI.I'_'_",_)) = is_atom t1

  1176   | is_atom (Const ("Groups.plus_class.plus",_) $ t1 $

  1177 		   (Const ("Groups.times_class.times",_) $ t2 $ Const ("ComplexI.I'_'_",_))) =

  1178     is_atom t1 andalso is_atom t2

  1179   | is_atom (Const _) = true

  1180   | is_atom (Free _) = true

  1181   | is_atom (Var _) = true

  1182   | is_atom _ = false;

  1183 (* val t = str2term "q_0/2 * L * x";

  1186 *)

  1187 (*val t = str2term "Float ((1,2),(0,0))";

  1188 > is_atom t;

  1189 val it = true : bool

  1190 > val t = str2term "Float ((1,2),(0,0)) * I__";

  1191 > is_atom t;

  1192 val it = true : bool

  1193 > val t = str2term "Float ((1,2),(0,0)) + Float ((3,4),(0,0)) * I__";

  1194 > is_atom t;

  1195 val it = true : bool

  1196 > val t = str2term "1 + 2*I__";

  1197 > val Const ("Groups.plus_class.plus",_) $ t1 $ (Const ("Groups.times_class.times",_) $ t2 $ Const ("ComplexI.I'_'_",_)) = t;

  1198 *)

  1200 (*.adaption from Isabelle/src/Pure/term.ML; reports if ALL Free's

  1201    have found a substitution (required for evaluating the preconditions

  1202    of _incomplete_ models).*)

  1203 fun subst_atomic_all [] t = (false, (*TODO may be 'true' for some terms ?*)

  1204 			     t : term)

  1205   | subst_atomic_all (instl: (term*term) list) t =

  1206       let fun subst (Abs(a,T,body)) =

  1207 	      let val (all, body') = subst body

  1208 	      in (all, Abs(a, T, body')) end

  1209             | subst (f$tt) =

  1210 	      let val (all1, f') = subst f

  1211 		  val (all2, tt') = subst tt

  1212 	      in (all1 andalso all2, f' $ tt') end

  1213             | subst (t as Free _) =

  1214 	      if is_num t then (true, t) (*numerals cannot be subst*)

  1215 	      else (case assoc(instl,t) of

  1216 					 SOME t' => (true, t')

  1217 				       | NONE => (false, t))

  1218             | subst t = (true, if_none (assoc(instl,t)) t)

  1219       in  subst t  end;

  1221 (*.add two terms with a type given.*)

  1222 fun mk_add t1 t2 =

  1223     let val T1 = type_of t1

  1224 	val T2 = type_of t2

  1225     in if T1 <> T2 then raise TYPE ("mk_add gets ",[T1, T2],[t1,t2])

  1226        else (Const ("Groups.plus_class.plus", [T1, T2] ---> T1) $ t1 $ t2)

  1227     end;

author	Walther Neuper <wneuper@ist.tugraz.at>
	Fri, 09 Feb 2018 11:16:05 +0100
changeset 59360	729c3ca4e5fc
parent 59352	172b53399454
child 59365	f771be3b6628
permissions	-rw-r--r--