src/Pure/drule.ML
author wenzelm
Tue Oct 25 13:15:34 1994 +0100 (1994-10-25)
changeset 655 9748dbcd4157
parent 641 49fc43cd6a35
child 668 0d0923eb0f0d
permissions -rw-r--r--
minor change of occs_const in dest_defn;
     1 (*  Title:      Pure/drule.ML
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1993  University of Cambridge
     5 
     6 Derived rules and other operations on theorems and theories
     7 *)
     8 
     9 infix 0 RS RSN RL RLN MRS MRL COMP;
    10 
    11 signature DRULE =
    12   sig
    13   structure Thm : THM
    14   local open Thm  in
    15   val add_defs: (string * string) list -> theory -> theory
    16   val add_defs_i: (string * term) list -> theory -> theory
    17   val asm_rl: thm
    18   val assume_ax: theory -> string -> thm
    19   val COMP: thm * thm -> thm
    20   val compose: thm * int * thm -> thm list
    21   val cterm_instantiate: (cterm*cterm)list -> thm -> thm
    22   val cut_rl: thm
    23   val equal_abs_elim: cterm  -> thm -> thm
    24   val equal_abs_elim_list: cterm list -> thm -> thm
    25   val eq_thm: thm * thm -> bool
    26   val eq_thm_sg: thm * thm -> bool
    27   val flexpair_abs_elim_list: cterm list -> thm -> thm
    28   val forall_intr_list: cterm list -> thm -> thm
    29   val forall_intr_frees: thm -> thm
    30   val forall_elim_list: cterm list -> thm -> thm
    31   val forall_elim_var: int -> thm -> thm
    32   val forall_elim_vars: int -> thm -> thm
    33   val implies_elim_list: thm -> thm list -> thm
    34   val implies_intr_list: cterm list -> thm -> thm
    35   val MRL: thm list list * thm list -> thm list
    36   val MRS: thm list * thm -> thm
    37   val pprint_cterm: cterm -> pprint_args -> unit
    38   val pprint_ctyp: ctyp -> pprint_args -> unit
    39   val pprint_theory: theory -> pprint_args -> unit
    40   val pprint_thm: thm -> pprint_args -> unit
    41   val pretty_thm: thm -> Sign.Syntax.Pretty.T
    42   val print_cterm: cterm -> unit
    43   val print_ctyp: ctyp -> unit
    44   val print_goals: int -> thm -> unit
    45   val print_goals_ref: (int -> thm -> unit) ref
    46   val print_syntax: theory -> unit
    47   val print_sign: theory -> unit
    48   val print_axioms: theory -> unit
    49   val print_theory: theory -> unit
    50   val print_thm: thm -> unit
    51   val prth: thm -> thm
    52   val prthq: thm Sequence.seq -> thm Sequence.seq
    53   val prths: thm list -> thm list
    54   val read_instantiate: (string*string)list -> thm -> thm
    55   val read_instantiate_sg: Sign.sg -> (string*string)list -> thm -> thm
    56   val read_insts:
    57           Sign.sg -> (indexname -> typ option) * (indexname -> sort option)
    58                   -> (indexname -> typ option) * (indexname -> sort option)
    59                   -> (string*string)list
    60                   -> (indexname*ctyp)list * (cterm*cterm)list
    61   val reflexive_thm: thm
    62   val revcut_rl: thm
    63   val rewrite_goal_rule: bool*bool -> (meta_simpset -> thm -> thm option)
    64         -> meta_simpset -> int -> thm -> thm
    65   val rewrite_goals_rule: thm list -> thm -> thm
    66   val rewrite_rule: thm list -> thm -> thm
    67   val RS: thm * thm -> thm
    68   val RSN: thm * (int * thm) -> thm
    69   val RL: thm list * thm list -> thm list
    70   val RLN: thm list * (int * thm list) -> thm list
    71   val show_hyps: bool ref
    72   val size_of_thm: thm -> int
    73   val standard: thm -> thm
    74   val string_of_cterm: cterm -> string
    75   val string_of_ctyp: ctyp -> string
    76   val string_of_thm: thm -> string
    77   val symmetric_thm: thm
    78   val transitive_thm: thm
    79   val triv_forall_equality: thm
    80   val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
    81   val zero_var_indexes: thm -> thm
    82   end
    83   end;
    84 
    85 functor DruleFun (structure Logic: LOGIC and Thm: THM): DRULE =
    86 struct
    87 structure Thm = Thm;
    88 structure Sign = Thm.Sign;
    89 structure Type = Sign.Type;
    90 structure Syntax = Sign.Syntax;
    91 structure Pretty = Syntax.Pretty
    92 structure Symtab = Sign.Symtab;
    93 
    94 local open Thm
    95 in
    96 
    97 (**** Extend Theories ****)
    98 
    99 (** add constant definitions **)
   100 
   101 (* all_axioms_of *)
   102 
   103 (*results may contain duplicates!*)
   104 
   105 fun ancestry_of thy =
   106   thy :: flat (map ancestry_of (parents_of thy));
   107 
   108 val all_axioms_of = flat o map axioms_of o ancestry_of;
   109 
   110 
   111 (* clash_types, clash_consts *)
   112 
   113 (*check if types have common instance (ignoring sorts)*)
   114 
   115 fun clash_types ty1 ty2 =
   116   let
   117     val ty1' = Type.varifyT ty1;
   118     val ty2' = incr_tvar (maxidx_of_typ ty1' + 1) (Type.varifyT ty2);
   119   in
   120     Type.raw_unify (ty1', ty2')
   121   end;
   122 
   123 fun clash_consts (c1, ty1) (c2, ty2) =
   124   c1 = c2 andalso clash_types ty1 ty2;
   125 
   126 
   127 (* clash_defns *)
   128 
   129 fun clash_defn c_ty (name, tm) =
   130   let val (c, ty') = dest_Const (head_of (fst (Logic.dest_equals tm))) in
   131     if clash_consts c_ty (c, ty') then Some (name, ty') else None
   132   end handle TERM _ => None;
   133 
   134 fun clash_defns c_ty axms =
   135   distinct (mapfilter (clash_defn c_ty) axms);
   136 
   137 
   138 (* dest_defn *)
   139 
   140 fun dest_defn tm =
   141   let
   142     fun err msg = raise_term msg [tm];
   143 
   144     val (lhs, rhs) = Logic.dest_equals tm
   145       handle TERM _ => err "Not a meta-equality (==)";
   146     val (head, args) = strip_comb lhs;
   147     val (c, ty) = dest_Const head
   148       handle TERM _ => err "Head of lhs not a constant";
   149 
   150     fun occs_const (Const c_ty') = (c_ty' = (c, ty))
   151       | occs_const (Abs (_, _, t)) = occs_const t
   152       | occs_const (t $ u) = occs_const t orelse occs_const u
   153       | occs_const _ = false;
   154 
   155     val show_frees = commas_quote o map (fst o dest_Free);
   156     val show_tfrees = commas_quote o map fst;
   157 
   158     val lhs_dups = duplicates args;
   159     val rhs_extras = gen_rems (op =) (term_frees rhs, args);
   160     val rhs_extrasT = gen_rems (op =) (term_tfrees rhs, typ_tfrees ty);
   161   in
   162     if not (forall is_Free args) then
   163       err "Arguments of lhs have to be variables"
   164     else if not (null lhs_dups) then
   165       err ("Duplicate variables on lhs: " ^ show_frees lhs_dups)
   166     else if not (null rhs_extras) then
   167       err ("Extra variables on rhs: " ^ show_frees rhs_extras)
   168     else if not (null rhs_extrasT) then
   169       err ("Extra type variables on rhs: " ^ show_tfrees rhs_extrasT)
   170     else if occs_const rhs then
   171       err ("Constant to be defined occurs on rhs")
   172     else (c, ty)
   173   end;
   174 
   175 
   176 (* check_defn *)
   177 
   178 fun err_in_defn name msg =
   179   (writeln msg; error ("The error(s) above occurred in definition " ^ quote name));
   180 
   181 fun check_defn sign (axms, (name, tm)) =
   182   let
   183     fun show_const (c, ty) = quote (Pretty.string_of (Pretty.block
   184       [Pretty.str (c ^ " ::"), Pretty.brk 1, Sign.pretty_typ sign ty]));
   185 
   186     fun show_defn c (dfn, ty') = show_const (c, ty') ^ " in " ^ dfn;
   187     fun show_defns c = commas o map (show_defn c);
   188 
   189     val (c, ty) = dest_defn tm
   190       handle TERM (msg, _) => err_in_defn name msg;
   191     val defns = clash_defns (c, ty) axms;
   192   in
   193     if not (null defns) then
   194       err_in_defn name ("Definition of " ^ show_const (c, ty) ^
   195         " clashes with " ^ show_defns c defns)
   196     else (name, tm) :: axms
   197   end;
   198 
   199 
   200 (* add_defs *)
   201 
   202 fun ext_defns prep_axm raw_axms thy =
   203   let
   204     val axms = map (prep_axm (sign_of thy)) raw_axms;
   205     val all_axms = all_axioms_of thy;
   206   in
   207     foldl (check_defn (sign_of thy)) (all_axms, axms);
   208     add_axioms_i axms thy
   209   end;
   210 
   211 val add_defs_i = ext_defns cert_axm;
   212 val add_defs = ext_defns read_axm;
   213 
   214 
   215 
   216 (**** More derived rules and operations on theorems ****)
   217 
   218 (** reading of instantiations **)
   219 
   220 fun indexname cs = case Syntax.scan_varname cs of (v,[]) => v
   221         | _ => error("Lexical error in variable name " ^ quote (implode cs));
   222 
   223 fun absent ixn =
   224   error("No such variable in term: " ^ Syntax.string_of_vname ixn);
   225 
   226 fun inst_failure ixn =
   227   error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails");
   228 
   229 fun read_insts sign (rtypes,rsorts) (types,sorts) insts =
   230 let val {tsig,...} = Sign.rep_sg sign
   231     fun split([],tvs,vs) = (tvs,vs)
   232       | split((sv,st)::l,tvs,vs) = (case explode sv of
   233                   "'"::cs => split(l,(indexname cs,st)::tvs,vs)
   234                 | cs => split(l,tvs,(indexname cs,st)::vs));
   235     val (tvs,vs) = split(insts,[],[]);
   236     fun readT((a,i),st) =
   237         let val ixn = ("'" ^ a,i);
   238             val S = case rsorts ixn of Some S => S | None => absent ixn;
   239             val T = Sign.read_typ (sign,sorts) st;
   240         in if Type.typ_instance(tsig,T,TVar(ixn,S)) then (ixn,T)
   241            else inst_failure ixn
   242         end
   243     val tye = map readT tvs;
   244     fun add_cterm ((cts,tye), (ixn,st)) =
   245         let val T = case rtypes ixn of
   246                       Some T => typ_subst_TVars tye T
   247                     | None => absent ixn;
   248             val (ct,tye2) = read_def_cterm (sign,types,sorts) (st,T);
   249             val cv = cterm_of sign (Var(ixn,typ_subst_TVars tye2 T))
   250         in ((cv,ct)::cts,tye2 @ tye) end
   251     val (cterms,tye') = foldl add_cterm (([],tye), vs);
   252 in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) tye', cterms) end;
   253 
   254 
   255 
   256 (*** Printing of theories, theorems, etc. ***)
   257 
   258 (*If false, hypotheses are printed as dots*)
   259 val show_hyps = ref true;
   260 
   261 fun pretty_thm th =
   262 let val {sign, hyps, prop,...} = rep_thm th
   263     val hsymbs = if null hyps then []
   264                  else if !show_hyps then
   265                       [Pretty.brk 2,
   266                        Pretty.lst("[","]") (map (Sign.pretty_term sign) hyps)]
   267                  else Pretty.str" [" :: map (fn _ => Pretty.str".") hyps @
   268                       [Pretty.str"]"];
   269 in Pretty.blk(0, Sign.pretty_term sign prop :: hsymbs) end;
   270 
   271 val string_of_thm = Pretty.string_of o pretty_thm;
   272 
   273 val pprint_thm = Pretty.pprint o Pretty.quote o pretty_thm;
   274 
   275 
   276 (** Top-level commands for printing theorems **)
   277 val print_thm = writeln o string_of_thm;
   278 
   279 fun prth th = (print_thm th; th);
   280 
   281 (*Print and return a sequence of theorems, separated by blank lines. *)
   282 fun prthq thseq =
   283   (Sequence.prints (fn _ => print_thm) 100000 thseq; thseq);
   284 
   285 (*Print and return a list of theorems, separated by blank lines. *)
   286 fun prths ths = (print_list_ln print_thm ths; ths);
   287 
   288 
   289 (* other printing commands *)
   290 
   291 fun pprint_ctyp cT =
   292   let val {sign, T} = rep_ctyp cT in Sign.pprint_typ sign T end;
   293 
   294 fun string_of_ctyp cT =
   295   let val {sign, T} = rep_ctyp cT in Sign.string_of_typ sign T end;
   296 
   297 val print_ctyp = writeln o string_of_ctyp;
   298 
   299 fun pprint_cterm ct =
   300   let val {sign, t, ...} = rep_cterm ct in Sign.pprint_term sign t end;
   301 
   302 fun string_of_cterm ct =
   303   let val {sign, t, ...} = rep_cterm ct in Sign.string_of_term sign t end;
   304 
   305 val print_cterm = writeln o string_of_cterm;
   306 
   307 
   308 (* print theory *)
   309 
   310 val pprint_theory = Sign.pprint_sg o sign_of;
   311 
   312 val print_syntax = Syntax.print_syntax o syn_of;
   313 
   314 val print_sign = Sign.print_sg o sign_of;
   315 
   316 fun print_axioms thy =
   317   let
   318     val {sign, new_axioms, ...} = rep_theory thy;
   319     val axioms = Symtab.dest new_axioms;
   320 
   321     fun prt_axm (a, t) = Pretty.block [Pretty.str (a ^ ":"), Pretty.brk 1,
   322       Pretty.quote (Sign.pretty_term sign t)];
   323   in
   324     Pretty.writeln (Pretty.big_list "additional axioms:" (map prt_axm axioms))
   325   end;
   326 
   327 fun print_theory thy = (print_sign thy; print_axioms thy);
   328 
   329 
   330 
   331 (** Print thm A1,...,An/B in "goal style" -- premises as numbered subgoals **)
   332 
   333 (* get type_env, sort_env of term *)
   334 
   335 local
   336   open Syntax;
   337 
   338   fun ins_entry (x, y) [] = [(x, [y])]
   339     | ins_entry (x, y) ((pair as (x', ys')) :: pairs) =
   340         if x = x' then (x', y ins ys') :: pairs
   341         else pair :: ins_entry (x, y) pairs;
   342 
   343   fun add_type_env (Free (x, T), env) = ins_entry (T, x) env
   344     | add_type_env (Var (xi, T), env) = ins_entry (T, string_of_vname xi) env
   345     | add_type_env (Abs (_, _, t), env) = add_type_env (t, env)
   346     | add_type_env (t $ u, env) = add_type_env (u, add_type_env (t, env))
   347     | add_type_env (_, env) = env;
   348 
   349   fun add_sort_env (Type (_, Ts), env) = foldr add_sort_env (Ts, env)
   350     | add_sort_env (TFree (x, S), env) = ins_entry (S, x) env
   351     | add_sort_env (TVar (xi, S), env) = ins_entry (S, string_of_vname xi) env;
   352 
   353   val sort = map (apsnd sort_strings);
   354 in
   355   fun type_env t = sort (add_type_env (t, []));
   356   fun sort_env t = rev (sort (it_term_types add_sort_env (t, [])));
   357 end;
   358 
   359 
   360 (* print_goals *)
   361 
   362 fun print_goals maxgoals state =
   363   let
   364     open Syntax;
   365 
   366     val {sign, prop, ...} = rep_thm state;
   367 
   368     val pretty_term = Sign.pretty_term sign;
   369     val pretty_typ = Sign.pretty_typ sign;
   370     val pretty_sort = Sign.pretty_sort;
   371 
   372     fun pretty_vars prtf (X, vs) = Pretty.block
   373       [Pretty.block (Pretty.commas (map Pretty.str vs)),
   374         Pretty.str " ::", Pretty.brk 1, prtf X];
   375 
   376     fun print_list _ _ [] = ()
   377       | print_list name prtf lst =
   378           (writeln ""; Pretty.writeln (Pretty.big_list name (map prtf lst)));
   379 
   380 
   381     fun print_goals (_, []) = ()
   382       | print_goals (n, A :: As) = (Pretty.writeln (Pretty.blk (0,
   383           [Pretty.str (" " ^ string_of_int n ^ ". "), pretty_term A]));
   384             print_goals (n + 1, As));
   385 
   386     val print_ffpairs =
   387       print_list "Flex-flex pairs:" (pretty_term o Logic.mk_flexpair);
   388 
   389     val print_types = print_list "Types:" (pretty_vars pretty_typ) o type_env;
   390     val print_sorts = print_list "Sorts:" (pretty_vars pretty_sort) o sort_env;
   391 
   392 
   393     val (tpairs, As, B) = Logic.strip_horn prop;
   394     val ngoals = length As;
   395 
   396     val orig_no_freeTs = ! show_no_free_types;
   397     val orig_sorts = ! show_sorts;
   398 
   399     fun restore () =
   400       (show_no_free_types := orig_no_freeTs; show_sorts := orig_sorts);
   401   in
   402     (show_no_free_types := true; show_sorts := false;
   403 
   404       Pretty.writeln (pretty_term B);
   405 
   406       if ngoals = 0 then writeln "No subgoals!"
   407       else if ngoals > maxgoals then
   408         (print_goals (1, take (maxgoals, As));
   409           writeln ("A total of " ^ string_of_int ngoals ^ " subgoals..."))
   410       else print_goals (1, As);
   411 
   412       print_ffpairs tpairs;
   413 
   414       if orig_sorts then
   415         (print_types prop; print_sorts prop)
   416       else if ! show_types then
   417         print_types prop
   418       else ())
   419     handle exn => (restore (); raise exn);
   420     restore ()
   421   end;
   422 
   423 
   424 (*"hook" for user interfaces: allows print_goals to be replaced*)
   425 val print_goals_ref = ref print_goals;
   426 
   427 (*** Find the type (sort) associated with a (T)Var or (T)Free in a term
   428      Used for establishing default types (of variables) and sorts (of
   429      type variables) when reading another term.
   430      Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
   431 ***)
   432 
   433 fun types_sorts thm =
   434     let val {prop,hyps,...} = rep_thm thm;
   435         val big = list_comb(prop,hyps); (* bogus term! *)
   436         val vars = map dest_Var (term_vars big);
   437         val frees = map dest_Free (term_frees big);
   438         val tvars = term_tvars big;
   439         val tfrees = term_tfrees big;
   440         fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i));
   441         fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i));
   442     in (typ,sort) end;
   443 
   444 (** Standardization of rules **)
   445 
   446 (*Generalization over a list of variables, IGNORING bad ones*)
   447 fun forall_intr_list [] th = th
   448   | forall_intr_list (y::ys) th =
   449         let val gth = forall_intr_list ys th
   450         in  forall_intr y gth   handle THM _ =>  gth  end;
   451 
   452 (*Generalization over all suitable Free variables*)
   453 fun forall_intr_frees th =
   454     let val {prop,sign,...} = rep_thm th
   455     in  forall_intr_list
   456          (map (cterm_of sign) (sort atless (term_frees prop)))
   457          th
   458     end;
   459 
   460 (*Replace outermost quantified variable by Var of given index.
   461     Could clash with Vars already present.*)
   462 fun forall_elim_var i th =
   463     let val {prop,sign,...} = rep_thm th
   464     in case prop of
   465           Const("all",_) $ Abs(a,T,_) =>
   466               forall_elim (cterm_of sign (Var((a,i), T)))  th
   467         | _ => raise THM("forall_elim_var", i, [th])
   468     end;
   469 
   470 (*Repeat forall_elim_var until all outer quantifiers are removed*)
   471 fun forall_elim_vars i th =
   472     forall_elim_vars i (forall_elim_var i th)
   473         handle THM _ => th;
   474 
   475 (*Specialization over a list of cterms*)
   476 fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
   477 
   478 (* maps [A1,...,An], B   to   [| A1;...;An |] ==> B  *)
   479 fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
   480 
   481 (* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
   482 fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
   483 
   484 (*Reset Var indexes to zero, renaming to preserve distinctness*)
   485 fun zero_var_indexes th =
   486     let val {prop,sign,...} = rep_thm th;
   487         val vars = term_vars prop
   488         val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
   489         val inrs = add_term_tvars(prop,[]);
   490         val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
   491         val tye = map (fn ((v,rs),a) => (v, TVar((a,0),rs))) (inrs ~~ nms')
   492         val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye;
   493         fun varpairs([],[]) = []
   494           | varpairs((var as Var(v,T)) :: vars, b::bs) =
   495                 let val T' = typ_subst_TVars tye T
   496                 in (cterm_of sign (Var(v,T')),
   497                     cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
   498                 end
   499           | varpairs _ = raise TERM("varpairs", []);
   500     in instantiate (ctye, varpairs(vars,rev bs)) th end;
   501 
   502 
   503 (*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers;
   504     all generality expressed by Vars having index 0.*)
   505 fun standard th =
   506     let val {maxidx,...} = rep_thm th
   507     in  varifyT (zero_var_indexes (forall_elim_vars(maxidx+1)
   508                          (forall_intr_frees(implies_intr_hyps th))))
   509     end;
   510 
   511 (*Assume a new formula, read following the same conventions as axioms.
   512   Generalizes over Free variables,
   513   creates the assumption, and then strips quantifiers.
   514   Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
   515              [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
   516 fun assume_ax thy sP =
   517     let val sign = sign_of thy
   518         val prop = Logic.close_form (term_of (read_cterm sign
   519                          (sP, propT)))
   520     in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
   521 
   522 (*Resolution: exactly one resolvent must be produced.*)
   523 fun tha RSN (i,thb) =
   524   case Sequence.chop (2, biresolution false [(false,tha)] i thb) of
   525       ([th],_) => th
   526     | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
   527     |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
   528 
   529 (*resolution: P==>Q, Q==>R gives P==>R. *)
   530 fun tha RS thb = tha RSN (1,thb);
   531 
   532 (*For joining lists of rules*)
   533 fun thas RLN (i,thbs) =
   534   let val resolve = biresolution false (map (pair false) thas) i
   535       fun resb thb = Sequence.list_of_s (resolve thb) handle THM _ => []
   536   in  flat (map resb thbs)  end;
   537 
   538 fun thas RL thbs = thas RLN (1,thbs);
   539 
   540 (*Resolve a list of rules against bottom_rl from right to left;
   541   makes proof trees*)
   542 fun rls MRS bottom_rl =
   543   let fun rs_aux i [] = bottom_rl
   544         | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
   545   in  rs_aux 1 rls  end;
   546 
   547 (*As above, but for rule lists*)
   548 fun rlss MRL bottom_rls =
   549   let fun rs_aux i [] = bottom_rls
   550         | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
   551   in  rs_aux 1 rlss  end;
   552 
   553 (*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
   554   with no lifting or renaming!  Q may contain ==> or meta-quants
   555   ALWAYS deletes premise i *)
   556 fun compose(tha,i,thb) =
   557     Sequence.list_of_s (bicompose false (false,tha,0) i thb);
   558 
   559 (*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
   560 fun tha COMP thb =
   561     case compose(tha,1,thb) of
   562         [th] => th
   563       | _ =>   raise THM("COMP", 1, [tha,thb]);
   564 
   565 (*Instantiate theorem th, reading instantiations under signature sg*)
   566 fun read_instantiate_sg sg sinsts th =
   567     let val ts = types_sorts th;
   568     in  instantiate (read_insts sg ts ts sinsts) th  end;
   569 
   570 (*Instantiate theorem th, reading instantiations under theory of th*)
   571 fun read_instantiate sinsts th =
   572     read_instantiate_sg (#sign (rep_thm th)) sinsts th;
   573 
   574 
   575 (*Left-to-right replacements: tpairs = [...,(vi,ti),...].
   576   Instantiates distinct Vars by terms, inferring type instantiations. *)
   577 local
   578   fun add_types ((ct,cu), (sign,tye)) =
   579     let val {sign=signt, t=t, T= T, ...} = rep_cterm ct
   580         and {sign=signu, t=u, T= U, ...} = rep_cterm cu
   581         val sign' = Sign.merge(sign, Sign.merge(signt, signu))
   582         val tye' = Type.unify (#tsig(Sign.rep_sg sign')) ((T,U), tye)
   583           handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u])
   584     in  (sign', tye')  end;
   585 in
   586 fun cterm_instantiate ctpairs0 th =
   587   let val (sign,tye) = foldr add_types (ctpairs0, (#sign(rep_thm th),[]))
   588       val tsig = #tsig(Sign.rep_sg sign);
   589       fun instT(ct,cu) = let val inst = subst_TVars tye
   590                          in (cterm_fun inst ct, cterm_fun inst cu) end
   591       fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
   592   in  instantiate (map ctyp2 tye, map instT ctpairs0) th  end
   593   handle TERM _ =>
   594            raise THM("cterm_instantiate: incompatible signatures",0,[th])
   595        | TYPE _ => raise THM("cterm_instantiate: types", 0, [th])
   596 end;
   597 
   598 
   599 (** theorem equality test is exported and used by BEST_FIRST **)
   600 
   601 (*equality of theorems uses equality of signatures and
   602   the a-convertible test for terms*)
   603 fun eq_thm (th1,th2) =
   604     let val {sign=sg1, hyps=hyps1, prop=prop1, ...} = rep_thm th1
   605         and {sign=sg2, hyps=hyps2, prop=prop2, ...} = rep_thm th2
   606     in  Sign.eq_sg (sg1,sg2) andalso
   607         aconvs(hyps1,hyps2) andalso
   608         prop1 aconv prop2
   609     end;
   610 
   611 (*Do the two theorems have the same signature?*)
   612 fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2));
   613 
   614 (*Useful "distance" function for BEST_FIRST*)
   615 val size_of_thm = size_of_term o #prop o rep_thm;
   616 
   617 
   618 (*** Meta-Rewriting Rules ***)
   619 
   620 
   621 val reflexive_thm =
   622   let val cx = cterm_of Sign.pure (Var(("x",0),TVar(("'a",0),logicS)))
   623   in Thm.reflexive cx end;
   624 
   625 val symmetric_thm =
   626   let val xy = read_cterm Sign.pure ("x::'a::logic == y",propT)
   627   in standard(Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy))) end;
   628 
   629 val transitive_thm =
   630   let val xy = read_cterm Sign.pure ("x::'a::logic == y",propT)
   631       val yz = read_cterm Sign.pure ("y::'a::logic == z",propT)
   632       val xythm = Thm.assume xy and yzthm = Thm.assume yz
   633   in standard(Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
   634 
   635 (** Below, a "conversion" has type cterm -> thm **)
   636 
   637 val refl_cimplies = reflexive (cterm_of Sign.pure implies);
   638 
   639 (*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
   640 (*Do not rewrite flex-flex pairs*)
   641 fun goals_conv pred cv =
   642   let fun gconv i ct =
   643         let val (A,B) = Thm.dest_cimplies ct
   644             val (thA,j) = case term_of A of
   645                   Const("=?=",_)$_$_ => (reflexive A, i)
   646                 | _ => (if pred i then cv A else reflexive A, i+1)
   647         in  combination (combination refl_cimplies thA) (gconv j B) end
   648         handle TERM _ => reflexive ct
   649   in gconv 1 end;
   650 
   651 (*Use a conversion to transform a theorem*)
   652 fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
   653 
   654 (*rewriting conversion*)
   655 fun rew_conv mode prover mss = rewrite_cterm mode mss prover;
   656 
   657 (*Rewrite a theorem*)
   658 fun rewrite_rule thms =
   659   fconv_rule (rew_conv (true,false) (K(K None)) (Thm.mss_of thms));
   660 
   661 (*Rewrite the subgoals of a proof state (represented by a theorem) *)
   662 fun rewrite_goals_rule thms =
   663   fconv_rule (goals_conv (K true) (rew_conv (true,false) (K(K None))
   664              (Thm.mss_of thms)));
   665 
   666 (*Rewrite the subgoal of a proof state (represented by a theorem) *)
   667 fun rewrite_goal_rule mode prover mss i thm =
   668   if 0 < i  andalso  i <= nprems_of thm
   669   then fconv_rule (goals_conv (fn j => j=i) (rew_conv mode prover mss)) thm
   670   else raise THM("rewrite_goal_rule",i,[thm]);
   671 
   672 
   673 (** Derived rules mainly for METAHYPS **)
   674 
   675 (*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
   676 fun equal_abs_elim ca eqth =
   677   let val {sign=signa, t=a, ...} = rep_cterm ca
   678       and combth = combination eqth (reflexive ca)
   679       val {sign,prop,...} = rep_thm eqth
   680       val (abst,absu) = Logic.dest_equals prop
   681       val cterm = cterm_of (Sign.merge (sign,signa))
   682   in  transitive (symmetric (beta_conversion (cterm (abst$a))))
   683            (transitive combth (beta_conversion (cterm (absu$a))))
   684   end
   685   handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
   686 
   687 (*Calling equal_abs_elim with multiple terms*)
   688 fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
   689 
   690 local
   691   open Logic
   692   val alpha = TVar(("'a",0), [])     (*  type ?'a::{}  *)
   693   fun err th = raise THM("flexpair_inst: ", 0, [th])
   694   fun flexpair_inst def th =
   695     let val {prop = Const _ $ t $ u,  sign,...} = rep_thm th
   696         val cterm = cterm_of sign
   697         fun cvar a = cterm(Var((a,0),alpha))
   698         val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)]
   699                    def
   700     in  equal_elim def' th
   701     end
   702     handle THM _ => err th | bind => err th
   703 in
   704 val flexpair_intr = flexpair_inst (symmetric flexpair_def)
   705 and flexpair_elim = flexpair_inst flexpair_def
   706 end;
   707 
   708 (*Version for flexflex pairs -- this supports lifting.*)
   709 fun flexpair_abs_elim_list cts =
   710     flexpair_intr o equal_abs_elim_list cts o flexpair_elim;
   711 
   712 
   713 (*** Some useful meta-theorems ***)
   714 
   715 (*The rule V/V, obtains assumption solving for eresolve_tac*)
   716 val asm_rl = trivial(read_cterm Sign.pure ("PROP ?psi",propT));
   717 
   718 (*Meta-level cut rule: [| V==>W; V |] ==> W *)
   719 val cut_rl = trivial(read_cterm Sign.pure
   720         ("PROP ?psi ==> PROP ?theta", propT));
   721 
   722 (*Generalized elim rule for one conclusion; cut_rl with reversed premises:
   723      [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
   724 val revcut_rl =
   725   let val V = read_cterm Sign.pure ("PROP V", propT)
   726       and VW = read_cterm Sign.pure ("PROP V ==> PROP W", propT);
   727   in  standard (implies_intr V
   728                 (implies_intr VW
   729                  (implies_elim (assume VW) (assume V))))
   730   end;
   731 
   732 (* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
   733 val triv_forall_equality =
   734   let val V  = read_cterm Sign.pure ("PROP V", propT)
   735       and QV = read_cterm Sign.pure ("!!x::'a. PROP V", propT)
   736       and x  = read_cterm Sign.pure ("x", TFree("'a",logicS));
   737   in  standard (equal_intr (implies_intr QV (forall_elim x (assume QV)))
   738                            (implies_intr V  (forall_intr x (assume V))))
   739   end;
   740 
   741 end
   742 end;
   743