src/Pure/drule.ML
author nipkow
Mon Mar 13 09:38:10 1995 +0100 (1995-03-13)
changeset 949 83c588d6fee9
parent 922 196ca0973a6d
child 952 9e10962866b0
permissions -rw-r--r--
Changed treatment of during type inference internally generated type
variables.

1. They are renamed to 'a, 'b, 'c etc away from a given set of used names.
2. They are either frozen (turned into TFrees) or left schematic (TVars)
depending on a parameter. In goals they are frozen, for instantiations they
are left schematic.
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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 add_defs		: (string * string) list -> theory -> theory
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  val add_defs_i	: (string * term) list -> theory -> theory
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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 cprems_of		: thm -> cterm list
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  val cskip_flexpairs	: cterm -> cterm
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  val cstrip_imp_prems	: cterm -> cterm 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_syntax	: 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 list -> (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 thin_rl		: 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 Syntax = Sign.Syntax;
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structure Pretty = 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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(**** Extend Theories ****)
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(** add constant definitions **)
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(* all_axioms_of *)
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(*results may contain duplicates!*)
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fun ancestry_of thy =
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  thy :: flat (map ancestry_of (parents_of thy));
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val all_axioms_of = 
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  flat o map (Symtab.dest o #new_axioms o rep_theory) o ancestry_of;
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(* clash_types, clash_consts *)
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(*check if types have common instance (ignoring sorts)*)
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fun clash_types ty1 ty2 =
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  let
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    val ty1' = Type.varifyT ty1;
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    val ty2' = incr_tvar (maxidx_of_typ ty1' + 1) (Type.varifyT ty2);
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  in
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    Type.raw_unify (ty1', ty2')
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  end;
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fun clash_consts (c1, ty1) (c2, ty2) =
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  c1 = c2 andalso clash_types ty1 ty2;
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(* clash_defns *)
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fun clash_defn c_ty (name, tm) =
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  let val (c, ty') = dest_Const (head_of (fst (Logic.dest_equals tm))) in
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    if clash_consts c_ty (c, ty') then Some (name, ty') else None
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  end handle TERM _ => None;
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fun clash_defns c_ty axms =
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  distinct (mapfilter (clash_defn c_ty) axms);
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(* dest_defn *)
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fun dest_defn tm =
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  let
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    fun err msg = raise_term msg [tm];
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    val (lhs, rhs) = Logic.dest_equals tm
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      handle TERM _ => err "Not a meta-equality (==)";
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    val (head, args) = strip_comb lhs;
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    val (c, ty) = dest_Const head
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      handle TERM _ => err "Head of lhs not a constant";
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    fun occs_const (Const c_ty') = (c_ty' = (c, ty))
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      | occs_const (Abs (_, _, t)) = occs_const t
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      | occs_const (t $ u) = occs_const t orelse occs_const u
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      | occs_const _ = false;
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    val show_frees = commas_quote o map (fst o dest_Free);
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    val show_tfrees = commas_quote o map fst;
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    val lhs_dups = duplicates args;
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    val rhs_extras = gen_rems (op =) (term_frees rhs, args);
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    val rhs_extrasT = gen_rems (op =) (term_tfrees rhs, typ_tfrees ty);
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  in
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    if not (forall is_Free args) then
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      err "Arguments of lhs have to be variables"
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    else if not (null lhs_dups) then
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      err ("Duplicate variables on lhs: " ^ show_frees lhs_dups)
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    else if not (null rhs_extras) then
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      err ("Extra variables on rhs: " ^ show_frees rhs_extras)
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    else if not (null rhs_extrasT) then
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      err ("Extra type variables on rhs: " ^ show_tfrees rhs_extrasT)
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    else if occs_const rhs then
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      err ("Constant to be defined occurs on rhs")
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    else (c, ty)
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  end;
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(* check_defn *)
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fun err_in_defn name msg =
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  (writeln msg; error ("The error(s) above occurred in definition " ^ quote name));
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fun check_defn sign (axms, (name, tm)) =
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  let
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    fun show_const (c, ty) = quote (Pretty.string_of (Pretty.block
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      [Pretty.str (c ^ " ::"), Pretty.brk 1, Sign.pretty_typ sign ty]));
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    fun show_defn c (dfn, ty') = show_const (c, ty') ^ " in " ^ dfn;
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    fun show_defns c = commas o map (show_defn c);
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    val (c, ty) = dest_defn tm
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      handle TERM (msg, _) => err_in_defn name msg;
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    val defns = clash_defns (c, ty) axms;
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  in
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    if not (null defns) then
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      err_in_defn name ("Definition of " ^ show_const (c, ty) ^
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        " clashes with " ^ show_defns c defns)
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    else (name, tm) :: axms
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  end;
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(* add_defs *)
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fun ext_defns prep_axm raw_axms thy =
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  let
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    val axms = map (prep_axm (sign_of thy)) raw_axms;
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    val all_axms = all_axioms_of thy;
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  in
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    foldl (check_defn (sign_of thy)) (all_axms, axms);
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    add_axioms_i axms thy
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  end;
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val add_defs_i = ext_defns cert_axm;
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val add_defs = ext_defns read_axm;
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(**** More derived rules and operations on theorems ****)
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(** some cterm->cterm operations: much faster than calling cterm_of! **)
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(*Discard flexflex pairs; return a cterm*)
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fun cskip_flexpairs ct =
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    case term_of ct of
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	(Const("==>", _) $ (Const("=?=",_)$_$_) $ _) =>
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	    cskip_flexpairs (#2 (dest_cimplies ct))
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      | _ => ct;
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(* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
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fun cstrip_imp_prems ct =
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    let val (cA,cB) = dest_cimplies ct
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    in  cA :: cstrip_imp_prems cB  end
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    handle TERM _ => [];
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(*The premises of a theorem, as a cterm list*)
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val cprems_of = cstrip_imp_prems o cskip_flexpairs o cprop_of;
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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) used 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,used), (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) used false (st,T);
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            val cv = cterm_of sign (Var(ixn,typ_subst_TVars tye2 T))
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            val used' = add_term_tvarnames(term_of ct,used);
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        in ((cv,ct)::cts,tye2 @ tye,used') end
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    val (cterms,tye',_) = foldl add_cterm (([],tye,used), 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_syntax = Syntax.print_syntax o syn_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,
wenzelm@385
   344
      Pretty.quote (Sign.pretty_term sign t)];
wenzelm@252
   345
  in
wenzelm@385
   346
    Pretty.writeln (Pretty.big_list "additional axioms:" (map prt_axm axioms))
wenzelm@252
   347
  end;
lcp@229
   348
wenzelm@843
   349
fun print_theory thy = (Sign.print_sg (sign_of thy); print_axioms thy);
wenzelm@385
   350
lcp@229
   351
lcp@229
   352
lcp@229
   353
(** Print thm A1,...,An/B in "goal style" -- premises as numbered subgoals **)
lcp@229
   354
wenzelm@641
   355
(* get type_env, sort_env of term *)
wenzelm@641
   356
wenzelm@641
   357
local
wenzelm@641
   358
  open Syntax;
wenzelm@641
   359
wenzelm@641
   360
  fun ins_entry (x, y) [] = [(x, [y])]
wenzelm@641
   361
    | ins_entry (x, y) ((pair as (x', ys')) :: pairs) =
wenzelm@641
   362
        if x = x' then (x', y ins ys') :: pairs
wenzelm@641
   363
        else pair :: ins_entry (x, y) pairs;
wenzelm@641
   364
wenzelm@641
   365
  fun add_type_env (Free (x, T), env) = ins_entry (T, x) env
wenzelm@641
   366
    | add_type_env (Var (xi, T), env) = ins_entry (T, string_of_vname xi) env
wenzelm@641
   367
    | add_type_env (Abs (_, _, t), env) = add_type_env (t, env)
wenzelm@641
   368
    | add_type_env (t $ u, env) = add_type_env (u, add_type_env (t, env))
wenzelm@641
   369
    | add_type_env (_, env) = env;
wenzelm@641
   370
wenzelm@641
   371
  fun add_sort_env (Type (_, Ts), env) = foldr add_sort_env (Ts, env)
wenzelm@641
   372
    | add_sort_env (TFree (x, S), env) = ins_entry (S, x) env
wenzelm@641
   373
    | add_sort_env (TVar (xi, S), env) = ins_entry (S, string_of_vname xi) env;
wenzelm@641
   374
wenzelm@641
   375
  val sort = map (apsnd sort_strings);
wenzelm@641
   376
in
wenzelm@641
   377
  fun type_env t = sort (add_type_env (t, []));
wenzelm@641
   378
  fun sort_env t = rev (sort (it_term_types add_sort_env (t, [])));
wenzelm@641
   379
end;
wenzelm@641
   380
wenzelm@641
   381
wenzelm@641
   382
(* print_goals *)
wenzelm@641
   383
wenzelm@641
   384
fun print_goals maxgoals state =
wenzelm@641
   385
  let
wenzelm@641
   386
    open Syntax;
wenzelm@641
   387
wenzelm@641
   388
    val {sign, prop, ...} = rep_thm state;
wenzelm@641
   389
wenzelm@641
   390
    val pretty_term = Sign.pretty_term sign;
wenzelm@641
   391
    val pretty_typ = Sign.pretty_typ sign;
wenzelm@641
   392
    val pretty_sort = Sign.pretty_sort;
wenzelm@641
   393
wenzelm@641
   394
    fun pretty_vars prtf (X, vs) = Pretty.block
wenzelm@641
   395
      [Pretty.block (Pretty.commas (map Pretty.str vs)),
wenzelm@641
   396
        Pretty.str " ::", Pretty.brk 1, prtf X];
lcp@229
   397
wenzelm@641
   398
    fun print_list _ _ [] = ()
wenzelm@641
   399
      | print_list name prtf lst =
wenzelm@641
   400
          (writeln ""; Pretty.writeln (Pretty.big_list name (map prtf lst)));
wenzelm@641
   401
wenzelm@641
   402
wenzelm@641
   403
    fun print_goals (_, []) = ()
wenzelm@641
   404
      | print_goals (n, A :: As) = (Pretty.writeln (Pretty.blk (0,
wenzelm@641
   405
          [Pretty.str (" " ^ string_of_int n ^ ". "), pretty_term A]));
wenzelm@641
   406
            print_goals (n + 1, As));
wenzelm@641
   407
wenzelm@641
   408
    val print_ffpairs =
wenzelm@641
   409
      print_list "Flex-flex pairs:" (pretty_term o Logic.mk_flexpair);
wenzelm@641
   410
wenzelm@641
   411
    val print_types = print_list "Types:" (pretty_vars pretty_typ) o type_env;
wenzelm@641
   412
    val print_sorts = print_list "Sorts:" (pretty_vars pretty_sort) o sort_env;
wenzelm@641
   413
wenzelm@641
   414
wenzelm@641
   415
    val (tpairs, As, B) = Logic.strip_horn prop;
wenzelm@641
   416
    val ngoals = length As;
wenzelm@641
   417
wenzelm@641
   418
    val orig_no_freeTs = ! show_no_free_types;
wenzelm@641
   419
    val orig_sorts = ! show_sorts;
wenzelm@641
   420
wenzelm@641
   421
    fun restore () =
wenzelm@641
   422
      (show_no_free_types := orig_no_freeTs; show_sorts := orig_sorts);
wenzelm@641
   423
  in
wenzelm@641
   424
    (show_no_free_types := true; show_sorts := false;
wenzelm@641
   425
      Pretty.writeln (pretty_term B);
wenzelm@641
   426
      if ngoals = 0 then writeln "No subgoals!"
wenzelm@641
   427
      else if ngoals > maxgoals then
wenzelm@641
   428
        (print_goals (1, take (maxgoals, As));
wenzelm@641
   429
          writeln ("A total of " ^ string_of_int ngoals ^ " subgoals..."))
wenzelm@641
   430
      else print_goals (1, As);
wenzelm@641
   431
wenzelm@641
   432
      print_ffpairs tpairs;
wenzelm@641
   433
wenzelm@641
   434
      if orig_sorts then
wenzelm@641
   435
        (print_types prop; print_sorts prop)
wenzelm@641
   436
      else if ! show_types then
wenzelm@641
   437
        print_types prop
wenzelm@641
   438
      else ())
wenzelm@641
   439
    handle exn => (restore (); raise exn);
wenzelm@641
   440
    restore ()
wenzelm@641
   441
  end;
wenzelm@641
   442
lcp@229
   443
lcp@229
   444
(*"hook" for user interfaces: allows print_goals to be replaced*)
lcp@229
   445
val print_goals_ref = ref print_goals;
lcp@229
   446
wenzelm@252
   447
(*** Find the type (sort) associated with a (T)Var or (T)Free in a term
clasohm@0
   448
     Used for establishing default types (of variables) and sorts (of
clasohm@0
   449
     type variables) when reading another term.
clasohm@0
   450
     Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
clasohm@0
   451
***)
clasohm@0
   452
clasohm@0
   453
fun types_sorts thm =
clasohm@0
   454
    let val {prop,hyps,...} = rep_thm thm;
wenzelm@252
   455
        val big = list_comb(prop,hyps); (* bogus term! *)
wenzelm@252
   456
        val vars = map dest_Var (term_vars big);
wenzelm@252
   457
        val frees = map dest_Free (term_frees big);
wenzelm@252
   458
        val tvars = term_tvars big;
wenzelm@252
   459
        val tfrees = term_tfrees big;
wenzelm@252
   460
        fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i));
wenzelm@252
   461
        fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i));
clasohm@0
   462
    in (typ,sort) end;
clasohm@0
   463
clasohm@0
   464
(** Standardization of rules **)
clasohm@0
   465
clasohm@0
   466
(*Generalization over a list of variables, IGNORING bad ones*)
clasohm@0
   467
fun forall_intr_list [] th = th
clasohm@0
   468
  | forall_intr_list (y::ys) th =
wenzelm@252
   469
        let val gth = forall_intr_list ys th
wenzelm@252
   470
        in  forall_intr y gth   handle THM _ =>  gth  end;
clasohm@0
   471
clasohm@0
   472
(*Generalization over all suitable Free variables*)
clasohm@0
   473
fun forall_intr_frees th =
clasohm@0
   474
    let val {prop,sign,...} = rep_thm th
clasohm@0
   475
    in  forall_intr_list
wenzelm@252
   476
         (map (cterm_of sign) (sort atless (term_frees prop)))
clasohm@0
   477
         th
clasohm@0
   478
    end;
clasohm@0
   479
clasohm@0
   480
(*Replace outermost quantified variable by Var of given index.
clasohm@0
   481
    Could clash with Vars already present.*)
wenzelm@252
   482
fun forall_elim_var i th =
clasohm@0
   483
    let val {prop,sign,...} = rep_thm th
clasohm@0
   484
    in case prop of
wenzelm@252
   485
          Const("all",_) $ Abs(a,T,_) =>
wenzelm@252
   486
              forall_elim (cterm_of sign (Var((a,i), T)))  th
wenzelm@252
   487
        | _ => raise THM("forall_elim_var", i, [th])
clasohm@0
   488
    end;
clasohm@0
   489
clasohm@0
   490
(*Repeat forall_elim_var until all outer quantifiers are removed*)
wenzelm@252
   491
fun forall_elim_vars i th =
clasohm@0
   492
    forall_elim_vars i (forall_elim_var i th)
wenzelm@252
   493
        handle THM _ => th;
clasohm@0
   494
clasohm@0
   495
(*Specialization over a list of cterms*)
clasohm@0
   496
fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
clasohm@0
   497
clasohm@0
   498
(* maps [A1,...,An], B   to   [| A1;...;An |] ==> B  *)
clasohm@0
   499
fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
clasohm@0
   500
clasohm@0
   501
(* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
clasohm@0
   502
fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   503
clasohm@0
   504
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@252
   505
fun zero_var_indexes th =
clasohm@0
   506
    let val {prop,sign,...} = rep_thm th;
clasohm@0
   507
        val vars = term_vars prop
clasohm@0
   508
        val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
wenzelm@252
   509
        val inrs = add_term_tvars(prop,[]);
wenzelm@252
   510
        val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
wenzelm@252
   511
        val tye = map (fn ((v,rs),a) => (v, TVar((a,0),rs))) (inrs ~~ nms')
wenzelm@252
   512
        val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye;
wenzelm@252
   513
        fun varpairs([],[]) = []
wenzelm@252
   514
          | varpairs((var as Var(v,T)) :: vars, b::bs) =
wenzelm@252
   515
                let val T' = typ_subst_TVars tye T
wenzelm@252
   516
                in (cterm_of sign (Var(v,T')),
wenzelm@252
   517
                    cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
wenzelm@252
   518
                end
wenzelm@252
   519
          | varpairs _ = raise TERM("varpairs", []);
clasohm@0
   520
    in instantiate (ctye, varpairs(vars,rev bs)) th end;
clasohm@0
   521
clasohm@0
   522
clasohm@0
   523
(*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers;
clasohm@0
   524
    all generality expressed by Vars having index 0.*)
clasohm@0
   525
fun standard th =
clasohm@0
   526
    let val {maxidx,...} = rep_thm th
wenzelm@252
   527
    in  varifyT (zero_var_indexes (forall_elim_vars(maxidx+1)
clasohm@0
   528
                         (forall_intr_frees(implies_intr_hyps th))))
clasohm@0
   529
    end;
clasohm@0
   530
wenzelm@252
   531
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   532
  Generalizes over Free variables,
clasohm@0
   533
  creates the assumption, and then strips quantifiers.
clasohm@0
   534
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   535
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   536
fun assume_ax thy sP =
clasohm@0
   537
    let val sign = sign_of thy
wenzelm@252
   538
        val prop = Logic.close_form (term_of (read_cterm sign
wenzelm@252
   539
                         (sP, propT)))
lcp@229
   540
    in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
clasohm@0
   541
wenzelm@252
   542
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   543
fun tha RSN (i,thb) =
clasohm@0
   544
  case Sequence.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   545
      ([th],_) => th
clasohm@0
   546
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   547
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   548
clasohm@0
   549
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   550
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   551
clasohm@0
   552
(*For joining lists of rules*)
wenzelm@252
   553
fun thas RLN (i,thbs) =
clasohm@0
   554
  let val resolve = biresolution false (map (pair false) thas) i
clasohm@0
   555
      fun resb thb = Sequence.list_of_s (resolve thb) handle THM _ => []
clasohm@0
   556
  in  flat (map resb thbs)  end;
clasohm@0
   557
clasohm@0
   558
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   559
lcp@11
   560
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   561
  makes proof trees*)
wenzelm@252
   562
fun rls MRS bottom_rl =
lcp@11
   563
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   564
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   565
  in  rs_aux 1 rls  end;
lcp@11
   566
lcp@11
   567
(*As above, but for rule lists*)
wenzelm@252
   568
fun rlss MRL bottom_rls =
lcp@11
   569
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   570
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   571
  in  rs_aux 1 rlss  end;
lcp@11
   572
wenzelm@252
   573
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   574
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   575
  ALWAYS deletes premise i *)
wenzelm@252
   576
fun compose(tha,i,thb) =
clasohm@0
   577
    Sequence.list_of_s (bicompose false (false,tha,0) i thb);
clasohm@0
   578
clasohm@0
   579
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   580
fun tha COMP thb =
clasohm@0
   581
    case compose(tha,1,thb) of
wenzelm@252
   582
        [th] => th
clasohm@0
   583
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   584
clasohm@0
   585
(*Instantiate theorem th, reading instantiations under signature sg*)
clasohm@0
   586
fun read_instantiate_sg sg sinsts th =
clasohm@0
   587
    let val ts = types_sorts th;
nipkow@949
   588
    in  instantiate (read_insts sg ts ts [] sinsts) th  end;
clasohm@0
   589
clasohm@0
   590
(*Instantiate theorem th, reading instantiations under theory of th*)
clasohm@0
   591
fun read_instantiate sinsts th =
clasohm@0
   592
    read_instantiate_sg (#sign (rep_thm th)) sinsts th;
clasohm@0
   593
clasohm@0
   594
clasohm@0
   595
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
clasohm@0
   596
  Instantiates distinct Vars by terms, inferring type instantiations. *)
clasohm@0
   597
local
clasohm@0
   598
  fun add_types ((ct,cu), (sign,tye)) =
lcp@229
   599
    let val {sign=signt, t=t, T= T, ...} = rep_cterm ct
lcp@229
   600
        and {sign=signu, t=u, T= U, ...} = rep_cterm cu
clasohm@0
   601
        val sign' = Sign.merge(sign, Sign.merge(signt, signu))
wenzelm@252
   602
        val tye' = Type.unify (#tsig(Sign.rep_sg sign')) ((T,U), tye)
wenzelm@252
   603
          handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u])
clasohm@0
   604
    in  (sign', tye')  end;
clasohm@0
   605
in
wenzelm@252
   606
fun cterm_instantiate ctpairs0 th =
clasohm@0
   607
  let val (sign,tye) = foldr add_types (ctpairs0, (#sign(rep_thm th),[]))
clasohm@0
   608
      val tsig = #tsig(Sign.rep_sg sign);
clasohm@0
   609
      fun instT(ct,cu) = let val inst = subst_TVars tye
wenzelm@252
   610
                         in (cterm_fun inst ct, cterm_fun inst cu) end
lcp@229
   611
      fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
clasohm@0
   612
  in  instantiate (map ctyp2 tye, map instT ctpairs0) th  end
wenzelm@252
   613
  handle TERM _ =>
clasohm@0
   614
           raise THM("cterm_instantiate: incompatible signatures",0,[th])
clasohm@0
   615
       | TYPE _ => raise THM("cterm_instantiate: types", 0, [th])
clasohm@0
   616
end;
clasohm@0
   617
clasohm@0
   618
clasohm@0
   619
(** theorem equality test is exported and used by BEST_FIRST **)
clasohm@0
   620
wenzelm@252
   621
(*equality of theorems uses equality of signatures and
clasohm@0
   622
  the a-convertible test for terms*)
wenzelm@252
   623
fun eq_thm (th1,th2) =
clasohm@0
   624
    let val {sign=sg1, hyps=hyps1, prop=prop1, ...} = rep_thm th1
wenzelm@252
   625
        and {sign=sg2, hyps=hyps2, prop=prop2, ...} = rep_thm th2
wenzelm@252
   626
    in  Sign.eq_sg (sg1,sg2) andalso
wenzelm@252
   627
        aconvs(hyps1,hyps2) andalso
wenzelm@252
   628
        prop1 aconv prop2
clasohm@0
   629
    end;
clasohm@0
   630
clasohm@0
   631
(*Do the two theorems have the same signature?*)
wenzelm@252
   632
fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2));
clasohm@0
   633
clasohm@0
   634
(*Useful "distance" function for BEST_FIRST*)
clasohm@0
   635
val size_of_thm = size_of_term o #prop o rep_thm;
clasohm@0
   636
clasohm@0
   637
clasohm@0
   638
(*** Meta-Rewriting Rules ***)
clasohm@0
   639
clasohm@0
   640
clasohm@0
   641
val reflexive_thm =
clasohm@922
   642
  let val cx = cterm_of Sign.proto_pure (Var(("x",0),TVar(("'a",0),logicS)))
clasohm@0
   643
  in Thm.reflexive cx end;
clasohm@0
   644
clasohm@0
   645
val symmetric_thm =
clasohm@922
   646
  let val xy = read_cterm Sign.proto_pure ("x::'a::logic == y",propT)
clasohm@0
   647
  in standard(Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy))) end;
clasohm@0
   648
clasohm@0
   649
val transitive_thm =
clasohm@922
   650
  let val xy = read_cterm Sign.proto_pure ("x::'a::logic == y",propT)
clasohm@922
   651
      val yz = read_cterm Sign.proto_pure ("y::'a::logic == z",propT)
clasohm@0
   652
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
clasohm@0
   653
  in standard(Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   654
lcp@229
   655
(** Below, a "conversion" has type cterm -> thm **)
lcp@229
   656
clasohm@922
   657
val refl_cimplies = reflexive (cterm_of Sign.proto_pure implies);
clasohm@0
   658
clasohm@0
   659
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
nipkow@214
   660
(*Do not rewrite flex-flex pairs*)
wenzelm@252
   661
fun goals_conv pred cv =
lcp@229
   662
  let fun gconv i ct =
lcp@229
   663
        let val (A,B) = Thm.dest_cimplies ct
lcp@229
   664
            val (thA,j) = case term_of A of
lcp@229
   665
                  Const("=?=",_)$_$_ => (reflexive A, i)
lcp@229
   666
                | _ => (if pred i then cv A else reflexive A, i+1)
wenzelm@252
   667
        in  combination (combination refl_cimplies thA) (gconv j B) end
lcp@229
   668
        handle TERM _ => reflexive ct
clasohm@0
   669
  in gconv 1 end;
clasohm@0
   670
clasohm@0
   671
(*Use a conversion to transform a theorem*)
lcp@229
   672
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
clasohm@0
   673
clasohm@0
   674
(*rewriting conversion*)
lcp@229
   675
fun rew_conv mode prover mss = rewrite_cterm mode mss prover;
clasohm@0
   676
clasohm@0
   677
(*Rewrite a theorem*)
nipkow@214
   678
fun rewrite_rule thms =
nipkow@214
   679
  fconv_rule (rew_conv (true,false) (K(K None)) (Thm.mss_of thms));
clasohm@0
   680
clasohm@0
   681
(*Rewrite the subgoals of a proof state (represented by a theorem) *)
clasohm@0
   682
fun rewrite_goals_rule thms =
nipkow@214
   683
  fconv_rule (goals_conv (K true) (rew_conv (true,false) (K(K None))
nipkow@214
   684
             (Thm.mss_of thms)));
clasohm@0
   685
clasohm@0
   686
(*Rewrite the subgoal of a proof state (represented by a theorem) *)
nipkow@214
   687
fun rewrite_goal_rule mode prover mss i thm =
nipkow@214
   688
  if 0 < i  andalso  i <= nprems_of thm
nipkow@214
   689
  then fconv_rule (goals_conv (fn j => j=i) (rew_conv mode prover mss)) thm
nipkow@214
   690
  else raise THM("rewrite_goal_rule",i,[thm]);
clasohm@0
   691
clasohm@0
   692
clasohm@0
   693
(** Derived rules mainly for METAHYPS **)
clasohm@0
   694
clasohm@0
   695
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
clasohm@0
   696
fun equal_abs_elim ca eqth =
lcp@229
   697
  let val {sign=signa, t=a, ...} = rep_cterm ca
clasohm@0
   698
      and combth = combination eqth (reflexive ca)
clasohm@0
   699
      val {sign,prop,...} = rep_thm eqth
clasohm@0
   700
      val (abst,absu) = Logic.dest_equals prop
lcp@229
   701
      val cterm = cterm_of (Sign.merge (sign,signa))
clasohm@0
   702
  in  transitive (symmetric (beta_conversion (cterm (abst$a))))
clasohm@0
   703
           (transitive combth (beta_conversion (cterm (absu$a))))
clasohm@0
   704
  end
clasohm@0
   705
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
clasohm@0
   706
clasohm@0
   707
(*Calling equal_abs_elim with multiple terms*)
clasohm@0
   708
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
clasohm@0
   709
clasohm@0
   710
local
clasohm@0
   711
  open Logic
clasohm@0
   712
  val alpha = TVar(("'a",0), [])     (*  type ?'a::{}  *)
clasohm@0
   713
  fun err th = raise THM("flexpair_inst: ", 0, [th])
clasohm@0
   714
  fun flexpair_inst def th =
clasohm@0
   715
    let val {prop = Const _ $ t $ u,  sign,...} = rep_thm th
wenzelm@252
   716
        val cterm = cterm_of sign
wenzelm@252
   717
        fun cvar a = cterm(Var((a,0),alpha))
wenzelm@252
   718
        val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)]
wenzelm@252
   719
                   def
clasohm@0
   720
    in  equal_elim def' th
clasohm@0
   721
    end
clasohm@0
   722
    handle THM _ => err th | bind => err th
clasohm@0
   723
in
clasohm@0
   724
val flexpair_intr = flexpair_inst (symmetric flexpair_def)
clasohm@0
   725
and flexpair_elim = flexpair_inst flexpair_def
clasohm@0
   726
end;
clasohm@0
   727
clasohm@0
   728
(*Version for flexflex pairs -- this supports lifting.*)
wenzelm@252
   729
fun flexpair_abs_elim_list cts =
clasohm@0
   730
    flexpair_intr o equal_abs_elim_list cts o flexpair_elim;
clasohm@0
   731
clasohm@0
   732
clasohm@0
   733
(*** Some useful meta-theorems ***)
clasohm@0
   734
clasohm@0
   735
(*The rule V/V, obtains assumption solving for eresolve_tac*)
clasohm@922
   736
val asm_rl = trivial(read_cterm Sign.proto_pure ("PROP ?psi",propT));
clasohm@0
   737
clasohm@0
   738
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
clasohm@922
   739
val cut_rl = trivial(read_cterm Sign.proto_pure
wenzelm@252
   740
        ("PROP ?psi ==> PROP ?theta", propT));
clasohm@0
   741
wenzelm@252
   742
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   743
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   744
val revcut_rl =
clasohm@922
   745
  let val V = read_cterm Sign.proto_pure ("PROP V", propT)
clasohm@922
   746
      and VW = read_cterm Sign.proto_pure ("PROP V ==> PROP W", propT);
wenzelm@252
   747
  in  standard (implies_intr V
wenzelm@252
   748
                (implies_intr VW
wenzelm@252
   749
                 (implies_elim (assume VW) (assume V))))
clasohm@0
   750
  end;
clasohm@0
   751
lcp@668
   752
(*for deleting an unwanted assumption*)
lcp@668
   753
val thin_rl =
clasohm@922
   754
  let val V = read_cterm Sign.proto_pure ("PROP V", propT)
clasohm@922
   755
      and W = read_cterm Sign.proto_pure ("PROP W", propT);
lcp@668
   756
  in  standard (implies_intr V (implies_intr W (assume W)))
lcp@668
   757
  end;
lcp@668
   758
clasohm@0
   759
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   760
val triv_forall_equality =
clasohm@922
   761
  let val V  = read_cterm Sign.proto_pure ("PROP V", propT)
clasohm@922
   762
      and QV = read_cterm Sign.proto_pure ("!!x::'a. PROP V", propT)
clasohm@922
   763
      and x  = read_cterm Sign.proto_pure ("x", TFree("'a",logicS));
clasohm@0
   764
  in  standard (equal_intr (implies_intr QV (forall_elim x (assume QV)))
wenzelm@252
   765
                           (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   766
  end;
clasohm@0
   767
clasohm@0
   768
end
clasohm@0
   769
end;
wenzelm@252
   770