src/Pure/drule.ML
author wenzelm
Thu May 26 16:43:48 1994 +0200 (1994-05-26)
changeset 400 3c2c40c87112
parent 385 921f87897a76
child 561 95225e63ef02
permissions -rw-r--r--
replaced ext_axtab by new_axioms;
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(*  Title:      Pure/drule.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1993  University of Cambridge
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Derived rules and other operations on theorems and theories
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*)
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infix 0 RS RSN RL RLN MRS MRL COMP;
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signature DRULE =
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  sig
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  structure Thm : THM
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  local open Thm  in
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  val asm_rl: thm
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  val assume_ax: theory -> string -> thm
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  val COMP: thm * thm -> thm
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  val compose: thm * int * thm -> thm list
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  val cterm_instantiate: (cterm*cterm)list -> thm -> thm
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  val cut_rl: thm
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  val equal_abs_elim: cterm  -> thm -> thm
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  val equal_abs_elim_list: cterm list -> thm -> thm
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  val eq_thm: thm * thm -> bool
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  val eq_thm_sg: thm * thm -> bool
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  val flexpair_abs_elim_list: cterm list -> thm -> thm
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  val forall_intr_list: cterm list -> thm -> thm
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  val forall_intr_frees: thm -> thm
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  val forall_elim_list: cterm list -> thm -> thm
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  val forall_elim_var: int -> thm -> thm
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  val forall_elim_vars: int -> thm -> thm
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  val implies_elim_list: thm -> thm list -> thm
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  val implies_intr_list: cterm list -> thm -> thm
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  val MRL: thm list list * thm list -> thm list
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  val MRS: thm list * thm -> thm
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  val pprint_cterm: cterm -> pprint_args -> unit
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  val pprint_ctyp: ctyp -> pprint_args -> unit
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  val pprint_theory: theory -> pprint_args -> unit
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  val pprint_thm: thm -> pprint_args -> unit
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  val pretty_thm: thm -> Sign.Syntax.Pretty.T
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  val print_cterm: cterm -> unit
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  val print_ctyp: ctyp -> unit
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  val print_goals: int -> thm -> unit
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  val print_goals_ref: (int -> thm -> unit) ref
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  val print_sign: theory -> unit
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  val print_axioms: theory -> unit
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  val print_theory: theory -> unit
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  val print_thm: thm -> unit
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  val prth: thm -> thm
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  val prthq: thm Sequence.seq -> thm Sequence.seq
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  val prths: thm list -> thm list
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  val read_instantiate: (string*string)list -> thm -> thm
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  val read_instantiate_sg: Sign.sg -> (string*string)list -> thm -> thm
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  val read_insts:
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          Sign.sg -> (indexname -> typ option) * (indexname -> sort option)
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                  -> (indexname -> typ option) * (indexname -> sort option)
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                  -> (string*string)list
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                  -> (indexname*ctyp)list * (cterm*cterm)list
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  val reflexive_thm: thm
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  val revcut_rl: thm
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  val rewrite_goal_rule: bool*bool -> (meta_simpset -> thm -> thm option)
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        -> meta_simpset -> int -> thm -> thm
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  val rewrite_goals_rule: thm list -> thm -> thm
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  val rewrite_rule: thm list -> thm -> thm
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  val RS: thm * thm -> thm
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  val RSN: thm * (int * thm) -> thm
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  val RL: thm list * thm list -> thm list
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  val RLN: thm list * (int * thm list) -> thm list
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  val show_hyps: bool ref
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  val size_of_thm: thm -> int
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  val standard: thm -> thm
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  val string_of_cterm: cterm -> string
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  val string_of_ctyp: ctyp -> string
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  val string_of_thm: thm -> string
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  val symmetric_thm: thm
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  val transitive_thm: thm
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  val triv_forall_equality: thm
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  val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
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  val zero_var_indexes: thm -> thm
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  end
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  end;
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functor DruleFun (structure Logic: LOGIC and Thm: THM): DRULE =
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struct
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structure Thm = Thm;
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structure Sign = Thm.Sign;
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structure Type = Sign.Type;
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structure Pretty = Sign.Syntax.Pretty
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structure Symtab = Sign.Symtab;
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local open Thm
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in
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(**** More derived rules and operations on theorems ****)
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(** reading of instantiations **)
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fun indexname cs = case Syntax.scan_varname cs of (v,[]) => v
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        | _ => error("Lexical error in variable name " ^ quote (implode cs));
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fun absent ixn =
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  error("No such variable in term: " ^ Syntax.string_of_vname ixn);
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fun inst_failure ixn =
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  error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails");
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fun read_insts sign (rtypes,rsorts) (types,sorts) insts =
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let val {tsig,...} = Sign.rep_sg sign
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    fun split([],tvs,vs) = (tvs,vs)
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      | split((sv,st)::l,tvs,vs) = (case explode sv of
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                  "'"::cs => split(l,(indexname cs,st)::tvs,vs)
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                | cs => split(l,tvs,(indexname cs,st)::vs));
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    val (tvs,vs) = split(insts,[],[]);
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    fun readT((a,i),st) =
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        let val ixn = ("'" ^ a,i);
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            val S = case rsorts ixn of Some S => S | None => absent ixn;
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            val T = Sign.read_typ (sign,sorts) st;
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        in if Type.typ_instance(tsig,T,TVar(ixn,S)) then (ixn,T)
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           else inst_failure ixn
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        end
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    val tye = map readT tvs;
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    fun add_cterm ((cts,tye), (ixn,st)) =
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        let val T = case rtypes ixn of
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                      Some T => typ_subst_TVars tye T
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                    | None => absent ixn;
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            val (ct,tye2) = read_def_cterm (sign,types,sorts) (st,T);
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            val cv = cterm_of sign (Var(ixn,typ_subst_TVars tye2 T))
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        in ((cv,ct)::cts,tye2 @ tye) end
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    val (cterms,tye') = foldl add_cterm (([],tye), vs);
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in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) tye', cterms) end;
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(*** Printing of theories, theorems, etc. ***)
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(*If false, hypotheses are printed as dots*)
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val show_hyps = ref true;
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fun pretty_thm th =
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let val {sign, hyps, prop,...} = rep_thm th
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    val hsymbs = if null hyps then []
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                 else if !show_hyps then
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                      [Pretty.brk 2,
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                       Pretty.lst("[","]") (map (Sign.pretty_term sign) hyps)]
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                 else Pretty.str" [" :: map (fn _ => Pretty.str".") hyps @
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                      [Pretty.str"]"];
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in Pretty.blk(0, Sign.pretty_term sign prop :: hsymbs) end;
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val string_of_thm = Pretty.string_of o pretty_thm;
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val pprint_thm = Pretty.pprint o Pretty.quote o pretty_thm;
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(** Top-level commands for printing theorems **)
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val print_thm = writeln o string_of_thm;
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fun prth th = (print_thm th; th);
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(*Print and return a sequence of theorems, separated by blank lines. *)
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fun prthq thseq =
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  (Sequence.prints (fn _ => print_thm) 100000 thseq; thseq);
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(*Print and return a list of theorems, separated by blank lines. *)
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fun prths ths = (print_list_ln print_thm ths; ths);
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(* other printing commands *)
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fun pprint_ctyp cT =
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  let val {sign, T} = rep_ctyp cT in Sign.pprint_typ sign T end;
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fun string_of_ctyp cT =
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  let val {sign, T} = rep_ctyp cT in Sign.string_of_typ sign T end;
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val print_ctyp = writeln o string_of_ctyp;
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fun pprint_cterm ct =
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  let val {sign, t, ...} = rep_cterm ct in Sign.pprint_term sign t end;
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fun string_of_cterm ct =
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  let val {sign, t, ...} = rep_cterm ct in Sign.string_of_term sign t end;
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val print_cterm = writeln o string_of_cterm;
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(* print theory *)
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val pprint_theory = Sign.pprint_sg o sign_of;
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val print_sign = Sign.print_sg o sign_of;
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fun print_axioms thy =
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  let
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    val {sign, new_axioms, ...} = rep_theory thy;
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    val axioms = Symtab.dest new_axioms;
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    fun prt_axm (a, t) = Pretty.block [Pretty.str (a ^ ":"), Pretty.brk 1,
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      Pretty.quote (Sign.pretty_term sign t)];
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  in
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    Pretty.writeln (Pretty.big_list "additional axioms:" (map prt_axm axioms))
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  end;
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fun print_theory thy = (print_sign thy; print_axioms thy);
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(** Print thm A1,...,An/B in "goal style" -- premises as numbered subgoals **)
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fun prettyprints es = writeln(Pretty.string_of(Pretty.blk(0,es)));
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fun print_goals maxgoals th : unit =
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let val {sign, hyps, prop,...} = rep_thm th;
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    fun printgoals (_, []) = ()
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      | printgoals (n, A::As) =
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        let val prettyn = Pretty.str(" " ^ string_of_int n ^ ". ");
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            val prettyA = Sign.pretty_term sign A
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        in prettyprints[prettyn,prettyA];
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           printgoals (n+1,As)
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        end;
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    fun prettypair(t,u) =
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        Pretty.blk(0, [Sign.pretty_term sign t, Pretty.str" =?=", Pretty.brk 1,
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                       Sign.pretty_term sign u]);
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    fun printff [] = ()
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      | printff tpairs =
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         writeln("\nFlex-flex pairs:\n" ^
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                 Pretty.string_of(Pretty.lst("","") (map prettypair tpairs)))
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    val (tpairs,As,B) = Logic.strip_horn(prop);
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    val ngoals = length As
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in
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   writeln (Sign.string_of_term sign B);
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   if ngoals=0 then writeln"No subgoals!"
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   else if ngoals>maxgoals
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        then (printgoals (1, take(maxgoals,As));
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              writeln("A total of " ^ string_of_int ngoals ^ " subgoals..."))
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        else printgoals (1, As);
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   printff tpairs
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end;
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(*"hook" for user interfaces: allows print_goals to be replaced*)
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val print_goals_ref = ref print_goals;
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(*** Find the type (sort) associated with a (T)Var or (T)Free in a term
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     Used for establishing default types (of variables) and sorts (of
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     type variables) when reading another term.
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     Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
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***)
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fun types_sorts thm =
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    let val {prop,hyps,...} = rep_thm thm;
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        val big = list_comb(prop,hyps); (* bogus term! *)
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        val vars = map dest_Var (term_vars big);
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        val frees = map dest_Free (term_frees big);
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        val tvars = term_tvars big;
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        val tfrees = term_tfrees big;
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        fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i));
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        fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i));
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    in (typ,sort) end;
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(** Standardization of rules **)
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(*Generalization over a list of variables, IGNORING bad ones*)
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fun forall_intr_list [] th = th
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  | forall_intr_list (y::ys) th =
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        let val gth = forall_intr_list ys th
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        in  forall_intr y gth   handle THM _ =>  gth  end;
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(*Generalization over all suitable Free variables*)
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fun forall_intr_frees th =
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    let val {prop,sign,...} = rep_thm th
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    in  forall_intr_list
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         (map (cterm_of sign) (sort atless (term_frees prop)))
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         th
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    end;
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(*Replace outermost quantified variable by Var of given index.
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    Could clash with Vars already present.*)
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fun forall_elim_var i th =
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    let val {prop,sign,...} = rep_thm th
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    in case prop of
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          Const("all",_) $ Abs(a,T,_) =>
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              forall_elim (cterm_of sign (Var((a,i), T)))  th
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        | _ => raise THM("forall_elim_var", i, [th])
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    end;
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(*Repeat forall_elim_var until all outer quantifiers are removed*)
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fun forall_elim_vars i th =
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    forall_elim_vars i (forall_elim_var i th)
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        handle THM _ => th;
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(*Specialization over a list of cterms*)
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fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
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(* maps [A1,...,An], B   to   [| A1;...;An |] ==> B  *)
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fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
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(* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
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fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
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(*Reset Var indexes to zero, renaming to preserve distinctness*)
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fun zero_var_indexes th =
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    let val {prop,sign,...} = rep_thm th;
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        val vars = term_vars prop
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        val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
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        val inrs = add_term_tvars(prop,[]);
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        val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
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        val tye = map (fn ((v,rs),a) => (v, TVar((a,0),rs))) (inrs ~~ nms')
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        val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye;
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        fun varpairs([],[]) = []
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          | varpairs((var as Var(v,T)) :: vars, b::bs) =
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                let val T' = typ_subst_TVars tye T
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                in (cterm_of sign (Var(v,T')),
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                    cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
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                end
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          | varpairs _ = raise TERM("varpairs", []);
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    in instantiate (ctye, varpairs(vars,rev bs)) th end;
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(*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers;
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    all generality expressed by Vars having index 0.*)
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fun standard th =
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    let val {maxidx,...} = rep_thm th
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    in  varifyT (zero_var_indexes (forall_elim_vars(maxidx+1)
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                         (forall_intr_frees(implies_intr_hyps th))))
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    end;
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(*Assume a new formula, read following the same conventions as axioms.
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  Generalizes over Free variables,
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  creates the assumption, and then strips quantifiers.
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  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
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             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
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   330
fun assume_ax thy sP =
clasohm@0
   331
    let val sign = sign_of thy
wenzelm@252
   332
        val prop = Logic.close_form (term_of (read_cterm sign
wenzelm@252
   333
                         (sP, propT)))
lcp@229
   334
    in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
clasohm@0
   335
wenzelm@252
   336
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   337
fun tha RSN (i,thb) =
clasohm@0
   338
  case Sequence.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   339
      ([th],_) => th
clasohm@0
   340
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   341
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   342
clasohm@0
   343
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   344
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   345
clasohm@0
   346
(*For joining lists of rules*)
wenzelm@252
   347
fun thas RLN (i,thbs) =
clasohm@0
   348
  let val resolve = biresolution false (map (pair false) thas) i
clasohm@0
   349
      fun resb thb = Sequence.list_of_s (resolve thb) handle THM _ => []
clasohm@0
   350
  in  flat (map resb thbs)  end;
clasohm@0
   351
clasohm@0
   352
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   353
lcp@11
   354
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   355
  makes proof trees*)
wenzelm@252
   356
fun rls MRS bottom_rl =
lcp@11
   357
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   358
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   359
  in  rs_aux 1 rls  end;
lcp@11
   360
lcp@11
   361
(*As above, but for rule lists*)
wenzelm@252
   362
fun rlss MRL bottom_rls =
lcp@11
   363
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   364
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   365
  in  rs_aux 1 rlss  end;
lcp@11
   366
wenzelm@252
   367
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   368
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   369
  ALWAYS deletes premise i *)
wenzelm@252
   370
fun compose(tha,i,thb) =
clasohm@0
   371
    Sequence.list_of_s (bicompose false (false,tha,0) i thb);
clasohm@0
   372
clasohm@0
   373
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   374
fun tha COMP thb =
clasohm@0
   375
    case compose(tha,1,thb) of
wenzelm@252
   376
        [th] => th
clasohm@0
   377
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   378
clasohm@0
   379
(*Instantiate theorem th, reading instantiations under signature sg*)
clasohm@0
   380
fun read_instantiate_sg sg sinsts th =
clasohm@0
   381
    let val ts = types_sorts th;
lcp@229
   382
    in  instantiate (read_insts sg ts ts sinsts) th  end;
clasohm@0
   383
clasohm@0
   384
(*Instantiate theorem th, reading instantiations under theory of th*)
clasohm@0
   385
fun read_instantiate sinsts th =
clasohm@0
   386
    read_instantiate_sg (#sign (rep_thm th)) sinsts th;
clasohm@0
   387
clasohm@0
   388
clasohm@0
   389
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
clasohm@0
   390
  Instantiates distinct Vars by terms, inferring type instantiations. *)
clasohm@0
   391
local
clasohm@0
   392
  fun add_types ((ct,cu), (sign,tye)) =
lcp@229
   393
    let val {sign=signt, t=t, T= T, ...} = rep_cterm ct
lcp@229
   394
        and {sign=signu, t=u, T= U, ...} = rep_cterm cu
clasohm@0
   395
        val sign' = Sign.merge(sign, Sign.merge(signt, signu))
wenzelm@252
   396
        val tye' = Type.unify (#tsig(Sign.rep_sg sign')) ((T,U), tye)
wenzelm@252
   397
          handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u])
clasohm@0
   398
    in  (sign', tye')  end;
clasohm@0
   399
in
wenzelm@252
   400
fun cterm_instantiate ctpairs0 th =
clasohm@0
   401
  let val (sign,tye) = foldr add_types (ctpairs0, (#sign(rep_thm th),[]))
clasohm@0
   402
      val tsig = #tsig(Sign.rep_sg sign);
clasohm@0
   403
      fun instT(ct,cu) = let val inst = subst_TVars tye
wenzelm@252
   404
                         in (cterm_fun inst ct, cterm_fun inst cu) end
lcp@229
   405
      fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
clasohm@0
   406
  in  instantiate (map ctyp2 tye, map instT ctpairs0) th  end
wenzelm@252
   407
  handle TERM _ =>
clasohm@0
   408
           raise THM("cterm_instantiate: incompatible signatures",0,[th])
clasohm@0
   409
       | TYPE _ => raise THM("cterm_instantiate: types", 0, [th])
clasohm@0
   410
end;
clasohm@0
   411
clasohm@0
   412
clasohm@0
   413
(** theorem equality test is exported and used by BEST_FIRST **)
clasohm@0
   414
wenzelm@252
   415
(*equality of theorems uses equality of signatures and
clasohm@0
   416
  the a-convertible test for terms*)
wenzelm@252
   417
fun eq_thm (th1,th2) =
clasohm@0
   418
    let val {sign=sg1, hyps=hyps1, prop=prop1, ...} = rep_thm th1
wenzelm@252
   419
        and {sign=sg2, hyps=hyps2, prop=prop2, ...} = rep_thm th2
wenzelm@252
   420
    in  Sign.eq_sg (sg1,sg2) andalso
wenzelm@252
   421
        aconvs(hyps1,hyps2) andalso
wenzelm@252
   422
        prop1 aconv prop2
clasohm@0
   423
    end;
clasohm@0
   424
clasohm@0
   425
(*Do the two theorems have the same signature?*)
wenzelm@252
   426
fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2));
clasohm@0
   427
clasohm@0
   428
(*Useful "distance" function for BEST_FIRST*)
clasohm@0
   429
val size_of_thm = size_of_term o #prop o rep_thm;
clasohm@0
   430
clasohm@0
   431
clasohm@0
   432
(*** Meta-Rewriting Rules ***)
clasohm@0
   433
clasohm@0
   434
clasohm@0
   435
val reflexive_thm =
wenzelm@385
   436
  let val cx = cterm_of Sign.pure (Var(("x",0),TVar(("'a",0),logicS)))
clasohm@0
   437
  in Thm.reflexive cx end;
clasohm@0
   438
clasohm@0
   439
val symmetric_thm =
lcp@229
   440
  let val xy = read_cterm Sign.pure ("x::'a::logic == y",propT)
clasohm@0
   441
  in standard(Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy))) end;
clasohm@0
   442
clasohm@0
   443
val transitive_thm =
lcp@229
   444
  let val xy = read_cterm Sign.pure ("x::'a::logic == y",propT)
lcp@229
   445
      val yz = read_cterm Sign.pure ("y::'a::logic == z",propT)
clasohm@0
   446
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
clasohm@0
   447
  in standard(Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   448
lcp@229
   449
(** Below, a "conversion" has type cterm -> thm **)
lcp@229
   450
lcp@229
   451
val refl_cimplies = reflexive (cterm_of Sign.pure implies);
clasohm@0
   452
clasohm@0
   453
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
nipkow@214
   454
(*Do not rewrite flex-flex pairs*)
wenzelm@252
   455
fun goals_conv pred cv =
lcp@229
   456
  let fun gconv i ct =
lcp@229
   457
        let val (A,B) = Thm.dest_cimplies ct
lcp@229
   458
            val (thA,j) = case term_of A of
lcp@229
   459
                  Const("=?=",_)$_$_ => (reflexive A, i)
lcp@229
   460
                | _ => (if pred i then cv A else reflexive A, i+1)
wenzelm@252
   461
        in  combination (combination refl_cimplies thA) (gconv j B) end
lcp@229
   462
        handle TERM _ => reflexive ct
clasohm@0
   463
  in gconv 1 end;
clasohm@0
   464
clasohm@0
   465
(*Use a conversion to transform a theorem*)
lcp@229
   466
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
clasohm@0
   467
clasohm@0
   468
(*rewriting conversion*)
lcp@229
   469
fun rew_conv mode prover mss = rewrite_cterm mode mss prover;
clasohm@0
   470
clasohm@0
   471
(*Rewrite a theorem*)
nipkow@214
   472
fun rewrite_rule thms =
nipkow@214
   473
  fconv_rule (rew_conv (true,false) (K(K None)) (Thm.mss_of thms));
clasohm@0
   474
clasohm@0
   475
(*Rewrite the subgoals of a proof state (represented by a theorem) *)
clasohm@0
   476
fun rewrite_goals_rule thms =
nipkow@214
   477
  fconv_rule (goals_conv (K true) (rew_conv (true,false) (K(K None))
nipkow@214
   478
             (Thm.mss_of thms)));
clasohm@0
   479
clasohm@0
   480
(*Rewrite the subgoal of a proof state (represented by a theorem) *)
nipkow@214
   481
fun rewrite_goal_rule mode prover mss i thm =
nipkow@214
   482
  if 0 < i  andalso  i <= nprems_of thm
nipkow@214
   483
  then fconv_rule (goals_conv (fn j => j=i) (rew_conv mode prover mss)) thm
nipkow@214
   484
  else raise THM("rewrite_goal_rule",i,[thm]);
clasohm@0
   485
clasohm@0
   486
clasohm@0
   487
(** Derived rules mainly for METAHYPS **)
clasohm@0
   488
clasohm@0
   489
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
clasohm@0
   490
fun equal_abs_elim ca eqth =
lcp@229
   491
  let val {sign=signa, t=a, ...} = rep_cterm ca
clasohm@0
   492
      and combth = combination eqth (reflexive ca)
clasohm@0
   493
      val {sign,prop,...} = rep_thm eqth
clasohm@0
   494
      val (abst,absu) = Logic.dest_equals prop
lcp@229
   495
      val cterm = cterm_of (Sign.merge (sign,signa))
clasohm@0
   496
  in  transitive (symmetric (beta_conversion (cterm (abst$a))))
clasohm@0
   497
           (transitive combth (beta_conversion (cterm (absu$a))))
clasohm@0
   498
  end
clasohm@0
   499
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
clasohm@0
   500
clasohm@0
   501
(*Calling equal_abs_elim with multiple terms*)
clasohm@0
   502
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
clasohm@0
   503
clasohm@0
   504
local
clasohm@0
   505
  open Logic
clasohm@0
   506
  val alpha = TVar(("'a",0), [])     (*  type ?'a::{}  *)
clasohm@0
   507
  fun err th = raise THM("flexpair_inst: ", 0, [th])
clasohm@0
   508
  fun flexpair_inst def th =
clasohm@0
   509
    let val {prop = Const _ $ t $ u,  sign,...} = rep_thm th
wenzelm@252
   510
        val cterm = cterm_of sign
wenzelm@252
   511
        fun cvar a = cterm(Var((a,0),alpha))
wenzelm@252
   512
        val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)]
wenzelm@252
   513
                   def
clasohm@0
   514
    in  equal_elim def' th
clasohm@0
   515
    end
clasohm@0
   516
    handle THM _ => err th | bind => err th
clasohm@0
   517
in
clasohm@0
   518
val flexpair_intr = flexpair_inst (symmetric flexpair_def)
clasohm@0
   519
and flexpair_elim = flexpair_inst flexpair_def
clasohm@0
   520
end;
clasohm@0
   521
clasohm@0
   522
(*Version for flexflex pairs -- this supports lifting.*)
wenzelm@252
   523
fun flexpair_abs_elim_list cts =
clasohm@0
   524
    flexpair_intr o equal_abs_elim_list cts o flexpair_elim;
clasohm@0
   525
clasohm@0
   526
clasohm@0
   527
(*** Some useful meta-theorems ***)
clasohm@0
   528
clasohm@0
   529
(*The rule V/V, obtains assumption solving for eresolve_tac*)
lcp@229
   530
val asm_rl = trivial(read_cterm Sign.pure ("PROP ?psi",propT));
clasohm@0
   531
clasohm@0
   532
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@252
   533
val cut_rl = trivial(read_cterm Sign.pure
wenzelm@252
   534
        ("PROP ?psi ==> PROP ?theta", propT));
clasohm@0
   535
wenzelm@252
   536
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   537
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   538
val revcut_rl =
lcp@229
   539
  let val V = read_cterm Sign.pure ("PROP V", propT)
lcp@229
   540
      and VW = read_cterm Sign.pure ("PROP V ==> PROP W", propT);
wenzelm@252
   541
  in  standard (implies_intr V
wenzelm@252
   542
                (implies_intr VW
wenzelm@252
   543
                 (implies_elim (assume VW) (assume V))))
clasohm@0
   544
  end;
clasohm@0
   545
clasohm@0
   546
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   547
val triv_forall_equality =
lcp@229
   548
  let val V  = read_cterm Sign.pure ("PROP V", propT)
lcp@229
   549
      and QV = read_cterm Sign.pure ("!!x::'a. PROP V", propT)
wenzelm@385
   550
      and x  = read_cterm Sign.pure ("x", TFree("'a",logicS));
clasohm@0
   551
  in  standard (equal_intr (implies_intr QV (forall_elim x (assume QV)))
wenzelm@252
   552
                           (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   553
  end;
clasohm@0
   554
clasohm@0
   555
end
clasohm@0
   556
end;
wenzelm@252
   557