diff -r 20231cdf39e7 -r 67a110289e4e src/Tools/isac/ProgLang/term.sml --- a/src/Tools/isac/ProgLang/term.sml Mon Sep 27 13:35:06 2010 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,1219 +0,0 @@ -(* extends Isabelle/src/Pure/term.ML - (c) Walther Neuper 1999 - -use"ProgLang/term.sml"; -use"term.sml"; -*) - -(* -> (cterm_of thy) a_term; -val it = "empty" : cterm *) - -(*2003 fun match thy t pat = - (snd (Pattern.match (Sign.tsig_of (sign_of thy)) (pat, t))) - handle _ => []; -fn : theory -> - Term.term -> Term.term -> (Term.indexname * Term.term) list*) -(*see src/Tools/eqsubst.ML fun clean_match*) -(*2003 fun matches thy tm pa = if match thy tm pa = [] then false else true;*) -fun matches thy tm pa = - (Pattern.match thy (pa, tm) (Vartab.empty, Vartab.empty); true) - handle _ => false - -fun atomtyp t = (*WN10 see raw_pp_typ*) - let - fun ato n (Type (s,[])) = - ("\n*** "^indent n^"Type ("^s^",[])") - | ato n (Type (s,Ts)) = - ("\n*** "^indent n^"Type ("^s^",["^ atol (n+1) Ts) - - | ato n (TFree (s,sort)) = - ("\n*** "^indent n^"TFree ("^s^",["^ strs2str' sort) - - | ato n (TVar ((s,i),sort)) = - ("\n*** "^indent n^"TVar (("^s^","^ - string_of_int i ^ strs2str' sort) - and atol n [] = - ("\n*** "^indent n^"]") - | atol n (T::Ts) = (ato n T ^ atol n Ts) -(*in print (ato 0 t ^ "\n") end; TODO TUM10*) -in tracing (ato 0 t) end; -(* -> val T = (type_of o term_of o the o (parse thy)) "a::[real,int] => nat"; -> atomtyp T; -*** Type (fun,[ -*** Type (RealDef.real,[]) -*** Type (fun,[ -*** Type (IntDef.int,[]) -*** Type (nat,[]) -*** ] -*** ] -*) - -(*Prog.Tutorial.p.34, Makarius 1005 does the above like this..*) -local - fun pp_pair (x, y) = Pretty.list "(" ")" [x, y] - fun pp_list xs = Pretty.list "[" "]" xs - fun pp_str s = Pretty.str s - fun pp_qstr s = Pretty.quote (pp_str s) - fun pp_int i = pp_str (string_of_int i) - fun pp_sort S = pp_list (map pp_qstr S) - fun pp_constr a args = Pretty.block [pp_str a, Pretty.brk 1, args] -in -fun raw_pp_typ (TVar ((a, i), S)) = - pp_constr "TVar" (pp_pair (pp_pair (pp_qstr a, pp_int i), pp_sort S)) - | raw_pp_typ (TFree (a, S)) = - pp_constr "TFree" (pp_pair (pp_qstr a, pp_sort S)) - | raw_pp_typ (Type (a, tys)) = - pp_constr "Type" (pp_pair (pp_qstr a, pp_list (map raw_pp_typ tys))) -end -(* install -PolyML.addPrettyPrinter - (fn _ => fn _ => ml_pretty o Pretty.to_ML o raw_pp_typ); -de-install -PolyML.addPrettyPrinter - (fn _ => fn _ => ml_pretty o Pretty.to_ML o Proof_Display.pp_typ Pure.thy); -*) - -fun atomt t = - let fun ato (Const (a, _)) n = - "\n*** " ^ indent n ^ "Const (" ^ a ^ ", _)" - | ato (Free (a, _)) n = - "\n*** " ^ indent n ^ "Free (" ^ a ^ ", _)" - | ato (Var ((a, i), _)) n = - "\n*** " ^ indent n ^ "Var (" ^ a ^ ", " ^ - string_of_int i ^ "), _)" - | ato (Bound i) n = - "\n*** " ^ indent n ^ "Bound " ^ string_of_int i - | ato (Abs (a, _, body)) n = - "\n*** " ^ indent n ^ "Abs(" ^ a ^ ", _" ^ ato body (n+1) - | ato (f $ t) n = (ato f n ^ ato t (n + 1)) - in tracing ("\n*** -------------" ^ ato t 0 ^ "\n***") end; - -fun term_detail2str t = - let fun ato (Const (a, T)) n = - "\n*** " ^ indent n ^ "Const (" ^ a ^ ", " ^ string_of_typ T ^ ")" - | ato (Free (a, T)) n = - "\n*** " ^ indent n ^ "Free (" ^ a ^ ", " ^ string_of_typ T ^ ")" - | ato (Var ((a, i), T)) n = - "\n*** " ^ indent n ^ "Var ((" ^ a ^ ", " ^ string_of_int i ^ "), "^ - string_of_typ T ^ ")" - | ato (Bound i) n = - "\n*** " ^ indent n ^ "Bound " ^ string_of_int i - | ato (Abs(a, T, body)) n = - "\n*** " ^ indent n ^ "Abs (" ^ a ^ ", " ^ string_of_typ T ^ ",.." - ^ ato body (n + 1) - | ato (f $ t) n = ato f n ^ ato t (n + 1) - in "\n*** " ^ ato t 0 ^ "\n***" end; -fun atomty t = (tracing o term_detail2str) t; (*WN100907 broken*) - -fun term_str thy (Const(s,_)) = s - | term_str thy (Free(s,_)) = s - | term_str thy (Var((s,i),_)) = s^(string_of_int i) - | term_str thy (Bound i) = "B."^(string_of_int i) - | term_str thy (Abs(s,_,_)) = s - | term_str thy t = raise error("term_str not for "^term2str t); - -(*.contains the fst argument the second argument (a leave! of term).*) -fun contains_term (Abs(_,_,body)) t = contains_term body t - | contains_term (f $ f') t = - contains_term f t orelse contains_term f' t - | contains_term s t = t = s; -(*.contains the term a VAR(("*",_),_) ?.*) -fun contains_Var (Abs(_,_,body)) = contains_Var body - | contains_Var (f $ f') = contains_Var f orelse contains_Var f' - | contains_Var (Var _) = true - | contains_Var _ = false; -(* contains_Var (str2term "?z = 3") (*true*); - contains_Var (str2term "z = 3") (*false*); - *) - -(*fun int_of_str str = - let val ss = explode str - val str' = case ss of - "("::s => drop_last s | _ => ss - in case BasisLibrary.Int.fromString (implode str') of - SOME i => SOME i - | NONE => NONE end;*) -fun int_of_str str = - let val ss = explode str - val str' = case ss of - "("::s => drop_last s | _ => ss - in (SOME (Thy_Output.integer (implode str'))) handle _ => NONE end; -(* -> int_of_str "123"; -val it = SOME 123 : int option -> int_of_str "(-123)"; -val it = SOME 123 : int option -> int_of_str "#123"; -val it = NONE : int option -> int_of_str "-123"; -val it = SOME ~123 : int option -*) -fun int_of_str' str = - case int_of_str str of - SOME i => i - | NONE => raise TERM ("int_of_string: no int-string",[]); -val str2int = int_of_str'; - -fun is_numeral str = case int_of_str str of - SOME _ => true - | NONE => false; -val is_no = is_numeral; -fun is_num (Free (s,_)) = if is_numeral s then true else false - | is_num _ = false; -(*> -> is_num ((term_of o the o (parse thy)) "#1"); -val it = true : bool -> is_num ((term_of o the o (parse thy)) "#-1"); -val it = true : bool -> is_num ((term_of o the o (parse thy)) "a123"); -val it = false : bool -*) - -(*fun int_of_Free (Free (intstr, _)) = - (case BasisLibrary.Int.fromString intstr of - SOME i => i - | NONE => raise error ("int_of_Free ( "^ intstr ^", _)")) - | int_of_Free t = raise error ("int_of_Free ( "^ term2str t ^" )");*) -fun int_of_Free (Free (intstr, _)) = (Thy_Output.integer intstr - handle _ => raise error ("int_of_Free ( "^ intstr ^", _)")) - | int_of_Free t = raise error ("int_of_Free ( "^ term2str t ^" )"); - -fun vars t = - let - fun scan vs (Const(s,T)) = vs - | scan vs (t as Free(s,T)) = if is_no s then vs else t::vs - | scan vs (t as Var((s,i),T)) = t::vs - | scan vs (Bound i) = vs - | scan vs (Abs(s,T,t)) = scan vs t - | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2) - in (distinct o (scan [])) t end; - -fun is_Free (Free _) = true - | is_Free _ = false; -fun is_fun_id (Const _) = true - | is_fun_id (Free _) = true - | is_fun_id _ = false; -fun is_f_x (f $ x) = is_fun_id f andalso is_Free x - | is_f_x _ = false; -(* is_f_x (str2term "q_0/2 * L * x") (*false*); - is_f_x (str2term "M_b x") (*true*); - *) -fun vars_str t = - let - fun scan vs (Const(s,T)) = vs - | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs - | scan vs (t as Var((s,i),T)) = (s^"_"^(string_of_int i))::vs - | scan vs (Bound i) = vs - | scan vs (Abs(s,T,t)) = scan vs t - | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2) - in (distinct o (scan [])) t end; - -fun ids2str t = - let - fun scan vs (Const(s,T)) = if is_no s then vs else s::vs - | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs - | scan vs (t as Var((s,i),T)) = (s^"_"^(string_of_int i))::vs - | scan vs (Bound i) = vs - | scan vs (Abs(s,T,t)) = scan (s::vs) t - | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2) - in (distinct o (scan [])) t end; -fun is_bdv str = - case explode str of - "b"::"d"::"v"::_ => true - | _ => false; -fun is_bdv_ (Free (s,_)) = is_bdv s - | is_bdv_ _ = false; - -fun free2str (Free (s,_)) = s - | free2str t = raise error ("free2str not for "^ term2str t); -fun free2int (t as Free (s, _)) = ((str2int s) - handle _ => raise error ("free2int: "^term_detail2str t)) - | free2int t = raise error ("free2int: "^term_detail2str t); - -(*27.8.01: unused*) -fun var2free (t as Const(s,T)) = t - | var2free (t as Free(s,T)) = t - | var2free (Var((s,i),T)) = Free(s,T) - | var2free (t as Bound i) = t - | var2free (Abs(s,T,t)) = Abs(s,T,var2free t) - | var2free (t1 $ t2) = (var2free t1) $ (var2free t2); - -(*27.8.01: doesn't find some subterm ???!???*) -(*2010 Logic.varify !!!*) -fun free2var (t as Const(s,T)) = t - | free2var (t as Free(s,T)) = if is_no s then t else Var((s,0),T) - | free2var (t as Var((s,i),T)) = t - | free2var (t as Bound i) = t - | free2var (Abs(s,T,t)) = Abs(s,T,free2var t) - | free2var (t1 $ t2) = (free2var t1) $ (free2var t2); - - -fun mk_listT T = Type ("List.list", [T]); -fun list_const T = - Const("List.list.Cons", [T, mk_listT T] ---> mk_listT T); -(*28.8.01: TODO: get type from head of list: 1 arg less!!!*) -fun list2isalist T [] = Const("List.list.Nil",mk_listT T) - | list2isalist T (t::ts) = (list_const T) $ t $ (list2isalist T ts); -(* -> val tt = (term_of o the o (parse thy)) "R=(R::real)"; -> val TT = type_of tt; -> val ss = list2isalist TT [tt,tt,tt]; -> (cterm_of thy) ss; -val it = "[R = R, R = R, R = R]" : cterm *) - -fun isapair2pair (Const ("Pair",_) $ a $ b) = (a,b) - | isapair2pair t = - raise error ("isapair2pair called with "^term2str t); - -val listType = Type ("List.list",[Type ("bool",[])]); -fun isalist2list ls = - let - fun get es (Const("List.list.Cons",_) $ t $ ls) = get (t::es) ls - | get es (Const("List.list.Nil",_)) = es - | get _ t = - raise error ("isalist2list applied to NON-list '"^term2str t^"'") - in (rev o (get [])) ls end; -(* -> val il = str2term "[a=b,c=d,e=f]"; -> val l = isalist2list il; -> (tracing o terms2str) l; -["a = b","c = d","e = f"] - -> val il = str2term "ss___::bool list"; -> val l = isalist2list il; -[Free ("ss___", "bool List.list")] -*) - - -(*review Isabelle2009/src/HOL/Tools/hologic.ML*) -val prop = Type ("prop",[]); (* ~/Diss.99/Integers-Isa/tools.sml*) -val bool = Type ("bool",[]); (* 2002 Integ.int *) -val Trueprop = Const("Trueprop",bool-->prop); -fun mk_prop t = Trueprop $ t; -val true_as_term = Const("True",bool); -val false_as_term = Const("False",bool); -val true_as_cterm = cterm_of (theory "HOL") true_as_term; -val false_as_cterm = cterm_of (theory "HOL") false_as_term; - -infixr 5 -->; (*2002 /Pure/term.ML *) -infixr --->; (*2002 /Pure/term.ML *) -fun S --> T = Type("fun",[S,T]); (*2002 /Pure/term.ML *) -val op ---> = foldr (op -->); (*2002 /Pure/term.ML *) -fun list_implies ([], B) = B : term (*2002 /term.ML *) - | list_implies (A::AS, B) = Logic.implies $ A $ list_implies(AS,B); - - - -(** substitution **) - -fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = (* = thm.ML *) - match_bvs(s, t, if x="" orelse y="" then al - else (x,y)::al) - | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al)) - | match_bvs(_,_,al) = al; -fun ren_inst(insts,prop,pat,obj) = (* = thm.ML *) - let val ren = match_bvs(pat,obj,[]) - fun renAbs(Abs(x,T,b)) = - Abs(case assoc_string(ren,x) of NONE => x - | SOME(y) => y, T, renAbs(b)) - | renAbs(f$t) = renAbs(f) $ renAbs(t) - | renAbs(t) = t - in subst_vars insts (if null(ren) then prop else renAbs(prop)) end; - - - - - - -fun dest_equals' (Const("op =",_) $ t $ u) = (t,u)(* logic.ML: Const("=="*) - | dest_equals' t = raise TERM("dest_equals'", [t]); -val lhs_ = (fst o dest_equals'); -val rhs_ = (snd o dest_equals'); - -fun is_equality (Const("op =",_) $ t $ u) = true (* logic.ML: Const("=="*) - | is_equality _ = false; -fun mk_equality (t,u) = (Const("op =",[type_of t,type_of u]--->bool) $ t $ u); -fun is_expliceq (Const("op =",_) $ (Free _) $ u) = true - | is_expliceq _ = false; -fun strip_trueprop (Const("Trueprop",_) $ t) = t - | strip_trueprop t = t; -(* | strip_trueprop t = raise TERM("strip_trueprop", [t]); -*) - -(*.(A1==>...An==>B) goes to (A1==>...An==>).*) -fun strip_imp_prems' (Const("==>", T) $ A $ t) = - let fun coll_prems As (Const("==>", _) $ A $ t) = - coll_prems (As $ (Logic.implies $ A)) t - | coll_prems As _ = SOME As - in coll_prems (Logic.implies $ A) t end - | strip_imp_prems' _ = NONE; (* logic.ML: term -> term list*) -(* - val thm = real_mult_div_cancel1; - val prop = (#prop o rep_thm) thm; - atomt prop; -*** ------------- -*** Const ( ==>) -*** . Const ( Trueprop) -*** . . Const ( Not) -*** . . . Const ( op =) -*** . . . . Var ((k, 0), ) -*** . . . . Const ( 0) -*** . Const ( Trueprop) -*** . . Const ( op =) *** ............. - val SOME t = strip_imp_prems' ((#prop o rep_thm) thm); - atomt t; -*** ------------- -*** Const ( ==>) -*** . Const ( Trueprop) -*** . . Const ( Not) -*** . . . Const ( op =) -*** . . . . Var ((k, 0), ) -*** . . . . Const ( 0) - - val thm = real_le_anti_sym; - val prop = (#prop o rep_thm) thm; - atomt prop; -*** ------------- -*** Const ( ==>) -*** . Const ( Trueprop) -*** . . Const ( op <=) -*** . . . Var ((z, 0), ) -*** . . . Var ((w, 0), ) -*** . Const ( ==>) -*** . . Const ( Trueprop) -*** . . . Const ( op <=) -*** . . . . Var ((w, 0), ) -*** . . . . Var ((z, 0), ) -*** . . Const ( Trueprop) -*** . . . Const ( op =) -*** ............. - val SOME t = strip_imp_prems' ((#prop o rep_thm) thm); - atomt t; -*** ------------- -*** Const ( ==>) -*** . Const ( Trueprop) -*** . . Const ( op <=) -*** . . . Var ((z, 0), ) -*** . . . Var ((w, 0), ) -*** . Const ( ==>) -*** . . Const ( Trueprop) -*** . . . Const ( op <=) -*** . . . . Var ((w, 0), ) -*** . . . . Var ((z, 0), ) -*) - -(*. (A1==>...An==>) (B) goes to (A1==>...An==>B), where B is lowest branch.*) -fun ins_concl (Const("==>", T) $ A $ t) B = Logic.implies $ A $ (ins_concl t B) - | ins_concl (Const("==>", T) $ A ) B = Logic.implies $ A $ B - | ins_concl t B = raise TERM("ins_concl", [t, B]); -(* - val thm = real_le_anti_sym; - val prop = (#prop o rep_thm) thm; - val concl = Logic.strip_imp_concl prop; - val SOME prems = strip_imp_prems' prop; - val prop' = ins_concl prems concl; - prop = prop'; - atomt prop; - atomt prop'; -*) - - -fun vperm (Var _, Var _) = true (*2002 Pure/thm.ML *) - | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t) - | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2) - | vperm (t, u) = (t = u); - -(*2002 cp from Pure/term.ML --- since 2009 in Pure/old_term.ML*) -fun mem_term (_, []) = false - | mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts); -fun subset_term ([], ys) = true - | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys); -fun eq_set_term (xs, ys) = - xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs)); -(*a total, irreflexive ordering on index names*) -fun xless ((a,i), (b,j): indexname) = i insert_aterm(t,vars) - | Abs (_,_,body) => add_term_vars(body,vars) - | f$t => add_term_vars (f, add_term_vars(t, vars)) - | _ => vars; -fun term_vars t = add_term_vars(t,[]); - - -fun var_perm (t, u) = (*2002 Pure/thm.ML *) - vperm (t, u) andalso eq_set_term (term_vars t, term_vars u); - -(*2002 fun decomp_simp, Pure/thm.ML *) -fun perm lhs rhs = var_perm (lhs, rhs) andalso not (lhs aconv rhs) - andalso not (is_Var lhs); - - -fun str_of_int n = - if n < 0 then "-"^((string_of_int o abs) n) - else string_of_int n; -(* -> str_of_int 1; -val it = "1" : string > str_of_int ~1; -val it = "-1" : string -*) - - -fun power b 0 = 1 - | power b n = - if n>0 then b*(power b (n-1)) - else raise error ("power "^(str_of_int b)^" "^(str_of_int n)); -(* -> power 2 3; -val it = 8 : int -> power ~2 3; -val it = ~8 : int -> power ~3 2; -val it = 9 : int -> power 3 ~2; -*) -fun gcd 0 b = b - | gcd a b = if a < b then gcd (b mod a) a - else gcd (a mod b) b; -fun sign n = if n < 0 then ~1 - else if n = 0 then 0 else 1; -fun sign2 n1 n2 = (sign n1) * (sign n2); - -infix dvd; -fun d dvd n = n mod d = 0; - -fun divisors n = - let fun pdiv ds d n = - if d=n then d::ds - else if d dvd n then pdiv (d::ds) d (n div d) - else pdiv ds (d+1) n - in pdiv [] 2 n end; - -divisors 30; -divisors 32; -divisors 60; -divisors 11; - -fun doubles ds = (* ds is ordered *) - let fun dbls ds [] = ds - | dbls ds [i] = ds - | dbls ds (i::i'::is) = if i=i' then dbls (i::ds) is - else dbls ds (i'::is) - in dbls [] ds end; -(*> doubles [2,3,4]; -val it = [] : int list -> doubles [2,3,3,5,5,7]; -val it = [5,3] : int list*) - -fun squfact 0 = 0 - | squfact 1 = 1 - | squfact n = foldl op* (1, (doubles o divisors) n); -(*> squfact 30; -val it = 1 : int -> squfact 32; -val it = 4 : int -> squfact 60; -val it = 2 : int -> squfact 11; -val it = 1 : int*) - - -fun dest_type (Type(T,[])) = T - | dest_type T = - (atomtyp T; - raise error ("... dest_type: not impl. for this type")); - -fun term_of_num ntyp n = Free (str_of_int n, ntyp); - -fun pairT T1 T2 = Type ("*", [T1, T2]); -(*> val t = str2term "(1,2)"; -> type_of t = pairT HOLogic.realT HOLogic.realT; -val it = true : bool -*) -fun PairT T1 T2 = ([T1, T2] ---> Type ("*", [T1, T2])); -(*> val t = str2term "(1,2)"; -> val Const ("Pair",pT) $ _ $ _ = t; -> pT = PairT HOLogic.realT HOLogic.realT; -val it = true : bool -*) -fun pairt t1 t2 = - Const ("Pair", PairT (type_of t1) (type_of t2)) $ t1 $ t2; -(*> val t = str2term "(1,2)"; -> val (t1, t2) = (str2term "1", str2term "2"); -> t = pairt t1 t2; -val it = true : bool*) - - -fun num_of_term (t as Free (s,_)) = - (case int_of_str s of - SOME s' => s' - | NONE => raise error ("num_of_term not for "^ term2str t)) - | num_of_term t = raise error ("num_of_term not for "^term2str t); - -fun mk_factroot op_(*=thy.sqrt*) T fact root = - Const ("op *", [T, T] ---> T) $ (term_of_num T fact) $ - (Const (op_, T --> T) $ term_of_num T root); -(* -val T = (type_of o term_of o the) (parse thy "#12::real"); -val t = mk_factroot "SqRoot.sqrt" T 2 3; -(cterm_of thy) t; -val it = "#2 * sqrt #3 " : cterm -*) -fun var_op_num v op_ optype ntyp n = - Const (op_, optype) $ v $ - Free (str_of_int n, ntyp); - -fun num_op_var v op_ optype ntyp n = - Const (op_,optype) $ - Free (str_of_int n, ntyp) $ v; - -fun num_op_num T1 T2 (op_,Top) n1 n2 = - Const (op_,Top) $ - Free (str_of_int n1, T1) $ Free (str_of_int n2, T2); -(* -> val t = num_op_num "Int" 3 4; -> atomty t; -> string_of_cterm ((cterm_of thy) t); -*) - -fun const_in str (Const _) = false - | const_in str (Free (s,_)) = if strip_thy s = str then true else false - | const_in str (Bound _) = false - | const_in str (Var _) = false - | const_in str (Abs (_,_,body)) = const_in str body - | const_in str (f$u) = const_in str f orelse const_in str u; -(* -> val t = (term_of o the o (parse thy)) "6 + 5 * sqrt 4 + 3"; -> const_in "sqrt" t; -val it = true : bool -> val t = (term_of o the o (parse thy)) "6 + 5 * 4 + 3"; -> const_in "sqrt" t; -val it = false : bool -*) - -(*used for calculating built in binary operations in Isabelle2002->Float.ML*) -(*fun calc "Groups.plus_class.plus" (n1, n2) = n1+n2 - | calc "Groups.minus_class.minus" (n1, n2) = n1-n2 - | calc "op *" (n1, n2) = n1*n2 - | calc "Rings.inverse_class.divide"(n1, n2) = n1 div n2 - | calc "Atools.pow"(n1, n2) = power n1 n2 - | calc op_ _ = raise error ("calc: operator = "^op_^" not defined");-----*) -fun calc_equ "op <" (n1, n2) = n1 < n2 - | calc_equ "op <=" (n1, n2) = n1 <= n2 - | calc_equ op_ _ = - raise error ("calc_equ: operator = "^op_^" not defined"); -fun sqrt (n:int) = if n < 0 then 0 - (*FIXME ~~~*) else (trunc o Math.sqrt o Real.fromInt) n; - -fun mk_thmid thmid op_ n1 n2 = - thmid ^ (strip_thy n1) ^ "_" ^ (strip_thy n2); - -fun dest_binop_typ (Type("fun",[range,Type("fun",[arg2,arg1])])) = - (arg1,arg2,range) - | dest_binop_typ _ = raise error "dest_binop_typ: not binary"; -(* ----- -> val t = (term_of o the o (parse thy)) "#3^#4"; -> val hT = type_of (head_of t); -> dest_binop_typ hT; -val it = ("'a","nat","'a") : typ * typ * typ - ----- *) - - -(** transform binary numeralsstrings **) -(*Makarius 100308, hacked by WN*) -val numbers_to_string = - let - fun dest_num t = - (case try HOLogic.dest_number t of - SOME (T, i) => - (*if T = @{typ int} orelse T = @{typ real} then WN*) - SOME (Free (signed_string_of_int i, T)) - (*else NONE WN*) - | NONE => NONE); - - fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b) - | to_str (t as (u1 $ u2)) = - (case dest_num t of - SOME t' => t' - | NONE => to_str u1 $ to_str u2) - | to_str t = perhaps dest_num t; - in to_str end - -(*.make uminus uniform: - Const ("uminus", _) $ Free ("2", "RealDef.real") --> Free ("-2", _) -to be used immediately before evaluation of numerals; -see Scripts/calculate.sml .*) -(*2002 fun(*app_num_tr'2 (Const("0",T)) = Free("0",T) - | app_num_tr'2 (Const("1",T)) = Free("1",T) - |*)app_num_tr'2 (t as Const("uminus",_) $ Free(s,T)) = - (case int_of_str s of SOME i => - if i > 0 then Free("-"^s,T) else Free(s,T) - | NONE => t) -(*| app_num_tr'2 (t as Const(s,T)) = t - | app_num_tr'2 (Const("Numeral.number_of",Type ("fun", [_, T])) $ t) = - Free(NumeralSyntax.dest_bin_str t, T) - | app_num_tr'2 (t as Free(s,T)) = t - | app_num_tr'2 (t as Var(n,T)) = t - | app_num_tr'2 (t as Bound i) = t -*)| app_num_tr'2 (Abs(s,T,body)) = Abs(s,T, app_num_tr'2 body) - | app_num_tr'2 (t1 $ t2) = (app_num_tr'2 t1) $ (app_num_tr'2 t2) - | app_num_tr'2 t = t; -*) -val uminus_to_string = - let - fun dest_num t = - (case t of - (Const ("HOL.uminus_class.uminus", _) $ Free (s, T)) => - (case int_of_str s of - SOME i => - SOME (Free (signed_string_of_int (~1 * i), T)) - | NONE => NONE) - | _ => NONE); - - fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b) - | to_str (t as (u1 $ u2)) = - (case dest_num t of - SOME t' => t' - | NONE => to_str u1 $ to_str u2) - | to_str t = perhaps dest_num t; - in to_str end; - - -(*2002 fun num_str thm = - let - val {sign_ref = sign_ref, der = der, maxidx = maxidx, - shyps = shyps, hyps = hyps, (*tpairs = tpairs,*) prop = prop} = - rep_thm_G thm; - val prop' = app_num_tr'1 prop; - in assbl_thm sign_ref der maxidx shyps hyps (*tpairs*) prop' end;*) -fun num_str thm = - let val (deriv, - {thy_ref = thy_ref, tags = tags, maxidx = maxidx, shyps = shyps, - hyps = hyps, tpairs = tpairs, prop = prop}) = rep_thm_G thm - val prop' = numbers_to_string prop; - in assbl_thm deriv thy_ref tags maxidx shyps hyps tpairs prop' end; - -fun get_thm' xstring = (*?covers 2009 Thm?!, replaces 2002 fun get_thm : -val it = fn : theory -> xstring -> Thm.thm*) - Thm (xstring, - num_str (ProofContext.get_thm (thy2ctxt' "Isac") xstring)); - -(** get types of Free and Abs for parse' **) -(*11.1.00: not used, fix-typed +,*,-,^ instead *) - -val dummyT = Type ("dummy",[]); -val dummyT = TVar (("DUMMY",0),[]); - -(* assumes only 1 type for numerals - and different identifiers for Const, Free and Abs *) -fun get_types t = - let - fun get ts (Const(s,T)) = (s,T)::ts - | get ts (Free(s,T)) = if is_no s - then ("#",T)::ts else (s,T)::ts - | get ts (Var(n,T)) = ts - | get ts (Bound i) = ts - | get ts (Abs(s,T,body)) = get ((s,T)::ts) body - | get ts (t1 $ t2) = (get ts t1) @ (get ts t2) - in distinct (get [] t) end; -(* -val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)"; -get_types t; -*) - -(*11.1.00: not used, fix-typed +,*,-,^ instead *) -fun set_types al (Const(s,T)) = - (case assoc (al,s) of - SOME T' => Const(s,T') - | NONE => (warning ("set_types: no type for "^s); Const(s,dummyT))) - | set_types al (Free(s,T)) = - if is_no s then - (case assoc (al,"#") of - SOME T' => Free(s,T') - | NONE => (warning ("set_types: no type for numerals"); Free(s,T))) - else (case assoc (al,s) of - SOME T' => Free(s,T') - | NONE => (warning ("set_types: no type for "^s); Free(s,T))) - | set_types al (Var(n,T)) = Var(n,T) - | set_types al (Bound i) = Bound i - | set_types al (Abs(s,T,body)) = - (case assoc (al,s) of - SOME T' => Abs(s,T', set_types al body) - | NONE => (warning ("set_types: no type for "^s); - Abs(s,T, set_types al body))) - | set_types al (t1 $ t2) = (set_types al t1) $ (set_types al t2); -(* -val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)"; -val al = get_types t; - -val t = (term_of o the o (parse thy)) "x = #0 + #-1 * #-4"; -atomty t; (* 'a *) -val t' = set_types al t; -atomty t'; (*real*) -(cterm_of thy) t'; -val it = "x = #0 + #-1 * #-4" : cterm - -val t = (term_of o the o (parse thy)) - "#5 * x + x ^^^ #2 = (#2 + x) ^^^ #2"; -atomty t; -val t' = set_types al t; -atomty t'; -(cterm_of thy) t'; -uncaught exception TYPE (*^^^ is new, NOT in al*) -*) - - -(** from Descript.ML **) - -(** decompose an isa-list to an ML-list - i.e. [] belong to the meta-language, too **) - -fun is_list ((Const("List.list.Cons",_)) $ _ $ _) = true - | is_list _ = false; -(* val (SOME ct) = parse thy "lll::real list"; -> val ty = (#t o rep_cterm) ct; -> is_list ty; -val it = false : bool -> val (SOME ct) = parse thy "[lll]"; -> val ty = (#t o rep_cterm) ct; -> is_list ty; -val it = true : bool *) - - - -fun mk_Free (s,T) = Free(s,T); -fun mk_free T s = Free(s,T); - -(*Special case: one argument cp from Isabelle2002/src/Pure/term.ML*) -fun subst_bound (arg, t) : term = (*WN100908 neglects 'raise Same.SAME'*) - let fun subst (t as Bound i, lev) = - if i val ttt = (term_of o the o (parse thy)) scr; -> tracing(term2str ttt); -> atomt ttt; -*** ------------- -*** Const ( DiffApp.Make'_fun'_by'_explicit) -*** . Free ( f_, ) -*** . Free ( v_, ) -*** . Free ( eqs_, ) -*** . Const ( Let) -*** . . Const ( Fun.op o) -*** . . . Const ( List.hd) -*** . . . Const ( DiffApp.filterVar) -*** . . . . Free ( f_, ) -*** . . . Free ( eqs_, ) -*** . . Abs( h_,.. -*** . . . Const ( Let) -*** . . . . Const ( List.hd) -*** . . . . . Const ( List.dropWhile) -*** . . . . . . Const ( Atools.ident) -*** . . . . . . . Bound 0 <---- Free ( h_, ) -*** . . . . . . Free ( eqs_, ) -*** . . . . Abs( e_1,.. -*** . . . . . Const ( Let) -*** . . . . . . Const ( List.dropWhile) -*** . . . . . . . Const ( Atools.ident) -*** . . . . . . . . Free ( f_, ) -*** . . . . . . . Const ( Tools.Vars) -*** . . . . . . . . Bound 1 <---- Free ( h_, ) -*** . . . . . . Abs( vs_,.. -*** . . . . . . . Const ( Let) -*** . . . . . . . . Const ( List.hd) -*** . . . . . . . . . Const ( List.dropWhile) -*** . . . . . . . . . . Const ( Atools.ident) -*** . . . . . . . . . . . Free ( v_, ) -*** . . . . . . . . . . Bound 0 <---- Free ( vs_, ) -*** . . . . . . . . Abs( v_1,.. -*** . . . . . . . . . Const ( Let) -*** . . . . . . . . . . Const ( Script.SubProblem) -*** . . . . . . . . . . . Const ( Pair) -*** . . . . . . . . . . . . Free ( DiffApp_, ) -*** . . . . . . . . . . . . Const ( Pair) -*** . . . . . . . . . . . . . Const ( List.list.Cons) -*** . . . . . . . . . . . . . . Free ( univar, ) -*** . . . . . . . . . . . . . . Const ( List.list.Cons) -*** . . . . . . . . . . . . . . . Free ( equation, ) -*** . . . . . . . . . . . . . . . Const ( List.list.Nil) -*** . . . . . . . . . . . . . Const ( List.list.Cons) -*** . . . . . . . . . . . . . . Free ( no_met, ) -*** . . . . . . . . . . . . . . Const ( List.list.Nil) -*** . . . . . . . . . . . Const ( List.list.Cons) -*** . . . . . . . . . . . . Const ( Script.BOOL) -*** . . . . . . . . . . . . . Bound 2 <----- Free ( e_1, ) -*** . . . . . . . . . . . . Const ( List.list.Cons) -*** . . . . . . . . . . . . . Const ( Script.real_) -*** . . . . . . . . . . . . . . Bound 0 <----- Free ( v_1, ) -*** . . . . . . . . . . . . . Const ( List.list.Nil) -*** . . . . . . . . . . Abs( s_1,.. -*** . . . . . . . . . . . Const ( Script.Substitute) -*** . . . . . . . . . . . . Const ( List.list.Cons) -*** . . . . . . . . . . . . . Const ( Pair) -*** . . . . . . . . . . . . . . Bound 1 <----- Free ( v_1, ) -*** . . . . . . . . . . . . . . Const ( Fun.op o) -*** . . . . . . . . . . . . . . . Const ( Tools.rhs) -*** . . . . . . . . . . . . . . . Const ( List.hd) -*** . . . . . . . . . . . . . . . Bound 0 <----- Free ( s_1, ) -*** . . . . . . . . . . . . . Const ( List.list.Nil) -*** . . . . . . . . . . . . Bound 4 <----- Free ( h_, ) - -> val ttt' = inst_abs thy ttt; -> tracing(term2str ttt'); -Script Make_fun_by_explicit f_ v_ eqs_ = - ... as above ... -> atomt ttt'; -*** ------------- -*** Const ( DiffApp.Make'_fun'_by'_explicit) -*** . Free ( f_, ) -*** . Free ( v_, ) -*** . Free ( eqs_, ) -*** . Const ( Let) -*** . . Const ( Fun.op o) -*** . . . Const ( List.hd) -*** . . . Const ( DiffApp.filterVar) -*** . . . . Free ( f_, ) -*** . . . Free ( eqs_, ) -*** . . Abs( h_,.. -*** . . . Const ( Let) -*** . . . . Const ( List.hd) -*** . . . . . Const ( List.dropWhile) -*** . . . . . . Const ( Atools.ident) -*** . . . . . . . Free ( h_, ) <---- Bound 0 -*** . . . . . . Free ( eqs_, ) -*** . . . . Abs( e_1,.. -*** . . . . . Const ( Let) -*** . . . . . . Const ( List.dropWhile) -*** . . . . . . . Const ( Atools.ident) -*** . . . . . . . . Free ( f_, ) -*** . . . . . . . Const ( Tools.Vars) -*** . . . . . . . . Free ( h_, ) <---- Bound 1 -*** . . . . . . Abs( vs_,.. -*** . . . . . . . Const ( Let) -*** . . . . . . . . Const ( List.hd) -*** . . . . . . . . . Const ( List.dropWhile) -*** . . . . . . . . . . Const ( Atools.ident) -*** . . . . . . . . . . . Free ( v_, ) -*** . . . . . . . . . . Free ( vs_, ) <---- Bound 0 -*** . . . . . . . . Abs( v_1,.. -*** . . . . . . . . . Const ( Let) -*** . . . . . . . . . . Const ( Script.SubProblem) -*** . . . . . . . . . . . Const ( Pair) -*** . . . . . . . . . . . . Free ( DiffApp_, ) -*** . . . . . . . . . . . . Const ( Pair) -*** . . . . . . . . . . . . . Const ( List.list.Cons) -*** . . . . . . . . . . . . . . Free ( univar, ) -*** . . . . . . . . . . . . . . Const ( List.list.Cons) -*** . . . . . . . . . . . . . . . Free ( equation, ) -*** . . . . . . . . . . . . . . . Const ( List.list.Nil) -*** . . . . . . . . . . . . . Const ( List.list.Cons) -*** . . . . . . . . . . . . . . Free ( no_met, ) -*** . . . . . . . . . . . . . . Const ( List.list.Nil) -*** . . . . . . . . . . . Const ( List.list.Cons) -*** . . . . . . . . . . . . Const ( Script.BOOL) -*** . . . . . . . . . . . . . Free ( e_1, ) <----- Bound 2 -*** . . . . . . . . . . . . Const ( List.list.Cons) -*** . . . . . . . . . . . . . Const ( Script.real_) -*** . . . . . . . . . . . . . . Free ( v_1, ) <----- Bound 0 -*** . . . . . . . . . . . . . Const ( List.list.Nil) -*** . . . . . . . . . . Abs( s_1,.. -*** . . . . . . . . . . . Const ( Script.Substitute) -*** . . . . . . . . . . . . Const ( List.list.Cons) -*** . . . . . . . . . . . . . Const ( Pair) -*** . . . . . . . . . . . . . . Free ( v_1, ) <----- Bound 1 -*** . . . . . . . . . . . . . . Const ( Fun.op o) -*** . . . . . . . . . . . . . . . Const ( Tools.rhs) -*** . . . . . . . . . . . . . . . Const ( List.hd) -*** . . . . . . . . . . . . . . . Free ( s_1, ) <----- Bound 0 -*** . . . . . . . . . . . . . Const ( List.list.Nil) -*** . . . . . . . . . . . . Free ( h_, ) <----- Bound 4 - -Note numbering of de Bruijn indexes ! - -Script Make_fun_by_explicit f_ v_ eqs_ = - let h_ = (hd o filterVar f_) eqs_; - e_1 = hd (dropWhile (ident h_ BOUND_0) eqs_); - vs_ = dropWhile (ident f_) (Vars h_ BOUND_1); - v_1 = hd (dropWhile (ident v_) vs_ BOUND_0); - s_1 = - SubProblem (DiffApp_, [univar, equation], [no_met]) - [BOOL e_1 BOUND_2, REAL v_1 BOUND_0] - in Substitute [(v_1 BOUND_1 = (rhs o hd) s_1 BOUND_0)] h_ BOUND_4 -*) - - -fun T_a2real (Type (s, [])) = - if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else Type (s, []) - | T_a2real (Type (s, Ts)) = Type (s, map T_a2real Ts) - | T_a2real (TFree (s, srt)) = - if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else TFree (s, srt) - | T_a2real (TVar (("DUMMY",_),srt)) = HOLogic.realT; - -(*FIXME .. fixes the type (+see Typefix.thy*) -fun typ_a2real (Const( s, T)) = (Const( s, T_a2real T)) - | typ_a2real (Free( s, T)) = (Free( s, T_a2real T)) - | typ_a2real (Var( n, T)) = (Var( n, T_a2real T)) - | typ_a2real (Bound i) = (Bound i) - | typ_a2real (Abs(s,T,t)) = Abs(s, T, typ_a2real t) - | typ_a2real (t1 $ t2) = (typ_a2real t1) $ (typ_a2real t2); -(* -----------------6.8.02--------------------------------------------------- - val str = "1"; - val t = read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[]))); - atomty (term_of t); -*** ------------- -*** Const ( 1, 'a) - val t = (app_num_tr' o term_of) t; - atomty t; -*** ------------- -*** Const ( 1, 'a) - val t = typ_a2real t; - atomty t; -*** ------------- -*** Const ( 1, real) - - val str = "2"; - val t = read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[]))); - atomty (term_of t); -*** ------------- -*** Const ( Numeral.number_of, bin => 'a) -*** . Const ( Numeral.bin.Bit, [bin, bool] => bin) -*** . . Const ( Numeral.bin.Bit, [bin, bool] => bin) -*** . . . Const ( Numeral.bin.Pls, bin) -*** . . . Const ( True, bool) -*** . . Const ( False, bool) - val t = (app_num_tr' o term_of) t; - atomty t; -*** ------------- -*** Free ( 2, 'a) - val t = typ_a2real t; - atomty t; -*** ------------- -*** Free ( 2, real) -----------------6.8.02--------------------------------------------------- - - -> val str = "R"; -> val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[])))); -val t = Free ("R","?DUMMY") : term -> val t' = typ_a2real t; -> (cterm_of thy) t'; -val it = "R::RealDef.real" : cterm - -> val str = "R=R"; -> val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[])))); -> atomty (typ_a2real t); -*** ------------- -*** Const ( op =, [RealDef.real, RealDef.real] => bool) -*** Free ( R, RealDef.real) -*** Free ( R, RealDef.real) -> val t' = typ_a2real t; -> (cterm_of thy) t'; -val it = "(R::RealDef.real) = R" : cterm - -> val str = "fixed_values [R=R]"; -> val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[])))); -> val t' = typ_a2real t; -> (cterm_of thy) t'; -val it = "fixed_values [(R::RealDef.real) = R]" : cterm -*) - -(*TODO.WN0609: parse should return a term or a string - (or even more comprehensive datastructure for error-messages) - i.e. in wrapping with SOME term or NONE the latter is not sufficient*) -(*2002 fun parseold thy str = - (let - val sgn = sign_of thy; - val t = ((*typ_a2real o*) app_num_tr'1 o term_of) - (read_cterm sgn (str,(TVar(("DUMMY",0),[])))); - in SOME (cterm_of sgn t) end) - handle _ => NONE;*) - - - -fun parseold thy str = - (let val t = ((*typ_a2real o*) numbers_to_string) - (Syntax.read_term_global thy str) - in SOME (cterm_of thy t) end) - handle _ => NONE; -(*2002 fun parseN thy str = - (let - val sgn = sign_of thy; - val t = ((*typ_a2real o app_num_tr'1 o*) term_of) - (read_cterm sgn (str,(TVar(("DUMMY",0),[])))); - in SOME (cterm_of sgn t) end) - handle _ => NONE;*) -fun parseN thy str = - (let val t = (*(typ_a2real o numbers_to_string)*) - (Syntax.read_term_global thy str) - in SOME (cterm_of thy t) end) - handle _ => NONE; -(*2002 fun parse thy str = - (let - val sgn = sign_of thy; - val t = (typ_a2real o app_num_tr'1 o term_of) - (read_cterm sgn (str,(TVar(("DUMMY",0),[])))); - in SOME (cterm_of sgn t) end) (*FIXXXXME 10.8.02: return term !!!*) - handle _ => NONE;*) -(*2010 fun parse thy str = - (let val t = (typ_a2real o app_num_tr'1) (Syntax.read_term_global thy str) - in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*) - handle _ => NONE;*) -fun parse thy str = - (let val t = (typ_a2real o numbers_to_string) - (Syntax.read_term_global thy str) - in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*) - handle _ => NONE; -(* -> val (SOME ct) = parse thy "(-#5)^^^#3"; -> atomty (term_of ct); -*** ------------- -*** Const ( Nat.op ^, ['a, nat] => 'a) -*** Const ( uminus, 'a => 'a) -*** Free ( #5, 'a) -*** Free ( #3, nat) -> val (SOME ct) = parse thy "R=R"; -> atomty (term_of ct); -*** ------------- -*** Const ( op =, [real, real] => bool) -*** Free ( R, real) -*** Free ( R, real) - -THIS IS THE OUTPUT FOR VERSION (3) above at typ_a2real !!!!! -*** ------------- -*** Const ( op =, [RealDef.real, RealDef.real] => bool) -*** Free ( R, RealDef.real) -*** Free ( R, RealDef.real) *) - -fun parse_patt thy str = - ProofContext.read_term_pattern (thy2ctxt thy) str; - -(*version for testing local to theories*) -fun str2term_ thy str = (term_of o the o (parse thy)) str; -fun str2term str = (term_of o the o (parse (theory "Isac"))) str; -fun strs2terms ss = map str2term ss; -fun str2termN str = (term_of o the o (parseN (theory "Isac"))) str; - -(*+ makes a substitution from the output of Pattern.match +*) -(*fun mk_subs ((id, _):indexname, t:term) = (Free (id,type_of t), t);*) -fun mk_subs (subs: ((string * int) * (Term.typ * Term.term)) list) = -let fun mk_sub ((id, _), (ty, tm)) = (Free (id, ty), tm) in -map mk_sub subs end; - -val atomthm = atomt o #prop o rep_thm; - -(*.instantiate #prop thm with bound variables (as Free).*) -fun inst_bdv [] t = t : term - | inst_bdv (instl: (term*term) list) t = - let fun subst (v as Var((s,_),T)) = - (case explode s of - "b"::"d"::"v"::_ => - if_none (assoc(instl,Free(s,T))) (Free(s,T)) - | _ => v) - | subst (Abs(a,T,body)) = Abs(a, T, subst body) - | subst (f$t') = subst f $ subst t' - | subst t = if_none (assoc(instl,t)) t - in subst t end; - - -(*WN050829 caution: is_atom (str2term"q_0/2 * L * x") = true !!! - use length (vars term) = 1 instead*) -fun is_atom (Const ("Float.Float",_) $ _) = true - | is_atom (Const ("ComplexI.I'_'_",_)) = true - | is_atom (Const ("op *",_) $ t $ Const ("ComplexI.I'_'_",_)) = is_atom t - | is_atom (Const ("Groups.plus_class.plus",_) $ t1 $ Const ("ComplexI.I'_'_",_)) = is_atom t1 - | is_atom (Const ("Groups.plus_class.plus",_) $ t1 $ - (Const ("op *",_) $ t2 $ Const ("ComplexI.I'_'_",_))) = - is_atom t1 andalso is_atom t2 - | is_atom (Const _) = true - | is_atom (Free _) = true - | is_atom (Var _) = true - | is_atom _ = false; -(* val t = str2term "q_0/2 * L * x"; - - -*) -(*val t = str2term "Float ((1,2),(0,0))"; -> is_atom t; -val it = true : bool -> val t = str2term "Float ((1,2),(0,0)) * I__"; -> is_atom t; -val it = true : bool -> val t = str2term "Float ((1,2),(0,0)) + Float ((3,4),(0,0)) * I__"; -> is_atom t; -val it = true : bool -> val t = str2term "1 + 2*I__"; -> val Const ("Groups.plus_class.plus",_) $ t1 $ (Const ("op *",_) $ t2 $ Const ("ComplexI.I'_'_",_)) = t; -*) - -(*.adaption from Isabelle/src/Pure/term.ML; reports if ALL Free's - have found a substitution (required for evaluating the preconditions - of _incomplete_ models).*) -fun subst_atomic_all [] t = (false, (*TODO may be 'true' for some terms ?*) - t : term) - | subst_atomic_all (instl: (term*term) list) t = - let fun subst (Abs(a,T,body)) = - let val (all, body') = subst body - in (all, Abs(a, T, body')) end - | subst (f$tt) = - let val (all1, f') = subst f - val (all2, tt') = subst tt - in (all1 andalso all2, f' $ tt') end - | subst (t as Free _) = - if is_num t then (true, t) (*numerals cannot be subst*) - else (case assoc(instl,t) of - SOME t' => (true, t') - | NONE => (false, t)) - | subst t = (true, if_none (assoc(instl,t)) t) - in subst t end; - -(*.add two terms with a type given.*) -fun mk_add t1 t2 = - let val T1 = type_of t1 - val T2 = type_of t2 - in if T1 <> T2 then raise TYPE ("mk_add gets ",[T1, T2],[t1,t2]) - else (Const ("Groups.plus_class.plus", [T1, T2] ---> T1) $ t1 $ t2) - end; -