src/Pure/drule.ML
author paulson
Mon Apr 02 11:31:08 2007 +0200 (2007-04-02)
changeset 22561 705d4fb9e628
parent 22360 26ead7ed4f4b
child 22681 9d42e5365ad1
permissions -rw-r--r--
optimizing the null instantiation case
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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.
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*)
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infix 0 RS RSN RL RLN MRS MRL OF COMP INCR_COMP COMP_INCR;
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signature BASIC_DRULE =
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sig
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  val mk_implies: cterm * cterm -> cterm
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  val list_implies: cterm list * cterm -> cterm
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  val dest_implies: cterm -> cterm * cterm
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  val dest_equals: cterm -> cterm * cterm
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  val dest_equals_lhs: cterm -> cterm
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  val dest_equals_rhs: cterm -> cterm
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  val strip_imp_prems: cterm -> cterm list
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  val strip_imp_concl: cterm -> cterm
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  val cprems_of: thm -> cterm list
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  val cterm_fun: (term -> term) -> (cterm -> cterm)
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  val ctyp_fun: (typ -> typ) -> (ctyp -> ctyp)
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  val read_insts: theory -> (indexname -> typ option) * (indexname -> sort option) ->
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    (indexname -> typ option) * (indexname -> sort option) -> string list ->
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    (indexname * string) list -> (ctyp * ctyp) list * (cterm * cterm) list
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  val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
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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_intr_vars: 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 gen_all: thm -> thm
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  val lift_all: cterm -> thm -> thm
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  val freeze_thaw: thm -> thm * (thm -> thm)
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  val freeze_thaw_robust: thm -> thm * (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 instantiate: (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm
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  val zero_var_indexes_list: thm list -> thm list
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  val zero_var_indexes: thm -> thm
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  val implies_intr_hyps: thm -> thm
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  val standard: thm -> thm
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  val standard': thm -> thm
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  val rotate_prems: int -> thm -> thm
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  val rearrange_prems: int list -> thm -> thm
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  val RSN: thm * (int * thm) -> thm
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  val RS: thm * thm -> thm
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  val RLN: thm list * (int * thm list) -> thm list
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  val RL: thm list * thm list -> thm list
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  val MRS: thm list * thm -> thm
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  val MRL: thm list list * thm list -> thm list
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  val OF: thm * thm list -> thm
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  val compose: thm * int * thm -> thm list
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  val COMP: thm * thm -> thm
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  val INCR_COMP: thm * thm -> thm
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  val COMP_INCR: thm * thm -> thm
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  val read_instantiate_sg: theory -> (string*string)list -> thm -> thm
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  val read_instantiate: (string*string)list -> thm -> thm
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  val cterm_instantiate: (cterm*cterm)list -> thm -> thm
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  val size_of_thm: thm -> int
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  val reflexive_thm: thm
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  val symmetric_thm: thm
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  val transitive_thm: thm
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  val symmetric_fun: thm -> thm
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  val extensional: thm -> thm
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  val equals_cong: thm
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  val imp_cong: thm
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  val swap_prems_eq: thm
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  val asm_rl: thm
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  val cut_rl: thm
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  val revcut_rl: thm
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  val thin_rl: thm
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  val triv_forall_equality: thm
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  val distinct_prems_rl: thm
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  val swap_prems_rl: thm
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  val equal_intr_rule: thm
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  val equal_elim_rule1: thm
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  val equal_elim_rule2: thm
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  val instantiate': ctyp option list -> cterm option list -> thm -> thm
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end;
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signature DRULE =
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sig
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  include BASIC_DRULE
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  val generalize: string list * string list -> thm -> thm
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  val list_comb: cterm * cterm list -> cterm
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  val strip_comb: cterm -> cterm * cterm list
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  val strip_type: ctyp -> ctyp list * ctyp
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  val lhs_of: thm -> cterm
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  val rhs_of: thm -> cterm
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  val beta_conv: cterm -> cterm -> cterm
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  val plain_prop_of: thm -> term
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  val fold_terms: (term -> 'a -> 'a) -> thm -> 'a -> 'a
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  val add_used: thm -> string list -> string list
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  val flexflex_unique: thm -> thm
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  val close_derivation: thm -> thm
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  val store_thm: bstring -> thm -> thm
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  val store_standard_thm: bstring -> thm -> thm
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  val store_thm_open: bstring -> thm -> thm
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  val store_standard_thm_open: bstring -> thm -> thm
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  val compose_single: thm * int * thm -> thm
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  val add_rule: thm -> thm list -> thm list
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  val del_rule: thm -> thm list -> thm list
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  val merge_rules: thm list * thm list -> thm list
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  val imp_cong_rule: thm -> thm -> thm
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  val beta_eta_conversion: cterm -> thm
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  val eta_long_conversion: cterm -> thm
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  val eta_contraction_rule: thm -> thm
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  val forall_conv: int -> (cterm -> thm) -> cterm -> thm
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  val concl_conv: int -> (cterm -> thm) -> cterm -> thm
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  val prems_conv: int -> (int -> cterm -> thm) -> cterm -> thm
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  val goals_conv: (int -> bool) -> (cterm -> thm) -> cterm -> thm
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  val fconv_rule: (cterm -> thm) -> thm -> thm
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  val norm_hhf_eq: thm
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  val is_norm_hhf: term -> bool
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  val norm_hhf: theory -> term -> term
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  val norm_hhf_cterm: cterm -> cterm
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  val unvarify: thm -> thm
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  val protect: cterm -> cterm
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  val protectI: thm
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  val protectD: thm
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  val protect_cong: thm
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  val implies_intr_protected: cterm list -> thm -> thm
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  val termI: thm
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  val mk_term: cterm -> thm
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  val dest_term: thm -> cterm
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  val cterm_rule: (thm -> thm) -> cterm -> cterm
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  val term_rule: theory -> (thm -> thm) -> term -> term
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  val sort_triv: theory -> typ * sort -> thm list
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  val unconstrainTs: thm -> thm
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  val rename_bvars: (string * string) list -> thm -> thm
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  val rename_bvars': string option list -> thm -> thm
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  val incr_indexes: thm -> thm -> thm
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  val incr_indexes2: thm -> thm -> thm -> thm
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  val remdups_rl: thm
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  val multi_resolve: thm list -> thm -> thm Seq.seq
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  val multi_resolves: thm list -> thm list -> thm Seq.seq
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  val abs_def: thm -> thm
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  val read_instantiate_sg': theory -> (indexname * string) list -> thm -> thm
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  val read_instantiate': (indexname * string) list -> thm -> thm
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end;
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structure Drule: DRULE =
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struct
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(** some cterm->cterm operations: faster than calling cterm_of! **)
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fun dest_implies ct =
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  (case Thm.term_of ct of
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    Const ("==>", _) $ _ $ _ => Thm.dest_binop ct
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  | _ => raise TERM ("dest_implies", [Thm.term_of ct]));
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fun dest_equals ct =
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  (case Thm.term_of ct of
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    Const ("==", _) $ _ $ _ => Thm.dest_binop ct
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  | _ => raise TERM ("dest_equals", [Thm.term_of ct]));
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fun dest_equals_lhs ct =
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  (case Thm.term_of ct of
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    Const ("==", _) $ _ $ _ => #1 (Thm.dest_binop ct)
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  | _ => raise TERM ("dest_equals_lhs", [Thm.term_of ct]));
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fun dest_equals_rhs ct =
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  (case Thm.term_of ct of
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    Const ("==", _) $ _ $ _ => Thm.dest_arg ct
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  | _ => raise TERM ("dest_equals_rhs", [Thm.term_of ct]));
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val lhs_of = dest_equals_lhs o Thm.cprop_of;
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val rhs_of = dest_equals_rhs o Thm.cprop_of;
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(* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
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fun strip_imp_prems ct =
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  let val (cA, cB) = dest_implies ct
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  in cA :: strip_imp_prems cB end
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  handle TERM _ => [];
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(* A1==>...An==>B  goes to B, where B is not an implication *)
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fun strip_imp_concl ct =
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  (case Thm.term_of ct of
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    Const ("==>", _) $ _ $ _ => strip_imp_concl (Thm.dest_arg ct)
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  | _ => ct);
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(*The premises of a theorem, as a cterm list*)
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val cprems_of = strip_imp_prems o cprop_of;
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fun cterm_fun f ct =
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  let val {t, thy, ...} = Thm.rep_cterm ct
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  in Thm.cterm_of thy (f t) end;
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fun ctyp_fun f cT =
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  let val {T, thy, ...} = Thm.rep_ctyp cT
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  in Thm.ctyp_of thy (f T) end;
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val cert = cterm_of ProtoPure.thy;
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val implies = cert Term.implies;
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fun mk_implies (A, B) = Thm.capply (Thm.capply implies A) B;
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(*cterm version of list_implies: [A1,...,An], B  goes to [|A1;==>;An|]==>B *)
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fun list_implies([], B) = B
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  | list_implies(A::AS, B) = mk_implies (A, list_implies(AS,B));
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(*cterm version of list_comb: maps  (f, [t1,...,tn])  to  f(t1,...,tn) *)
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fun list_comb (f, []) = f
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  | list_comb (f, t::ts) = list_comb (Thm.capply f t, ts);
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(*cterm version of strip_comb: maps  f(t1,...,tn)  to  (f, [t1,...,tn]) *)
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fun strip_comb ct =
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  let
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    fun stripc (p as (ct, cts)) =
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      let val (ct1, ct2) = Thm.dest_comb ct
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      in stripc (ct1, ct2 :: cts) end handle CTERM _ => p
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  in stripc (ct, []) end;
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(* cterm version of strip_type: maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T) *)
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fun strip_type cT = (case Thm.typ_of cT of
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    Type ("fun", _) =>
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      let
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        val [cT1, cT2] = Thm.dest_ctyp cT;
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        val (cTs, cT') = strip_type cT2
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      in (cT1 :: cTs, cT') end
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  | _ => ([], cT));
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(*Beta-conversion for cterms, where x is an abstraction. Simply returns the rhs
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  of the meta-equality returned by the beta_conversion rule.*)
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fun beta_conv x y =
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  Thm.dest_arg (cprop_of (Thm.beta_conversion false (Thm.capply x y)));
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fun plain_prop_of raw_thm =
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  let
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    val thm = Thm.strip_shyps raw_thm;
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    fun err msg = raise THM ("plain_prop_of: " ^ msg, 0, [thm]);
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    val {hyps, prop, tpairs, ...} = Thm.rep_thm thm;
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  in
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    if not (null hyps) then
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      err "theorem may not contain hypotheses"
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    else if not (null (Thm.extra_shyps thm)) then
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      err "theorem may not contain sort hypotheses"
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    else if not (null tpairs) then
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      err "theorem may not contain flex-flex pairs"
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    else prop
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  end;
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fun fold_terms f th =
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  let val {tpairs, prop, hyps, ...} = Thm.rep_thm th
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  in fold (fn (t, u) => f t #> f u) tpairs #> f prop #> fold f hyps end;
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(** reading of instantiations **)
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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 thy (rtypes,rsorts) (types,sorts) used insts =
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let
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    fun is_tv ((a, _), _) =
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      (case Symbol.explode a of "'" :: _ => true | _ => false);
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    val (tvs, vs) = List.partition is_tv insts;
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    fun sort_of ixn = case rsorts ixn of SOME S => S | NONE => absent ixn;
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    fun readT (ixn, st) =
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        let val S = sort_of ixn;
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            val T = Sign.read_typ (thy,sorts) st;
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        in if Sign.typ_instance thy (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 mkty(ixn,st) = (case rtypes ixn of
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                          SOME T => (ixn,(st,typ_subst_TVars tye T))
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                        | NONE => absent ixn);
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    val ixnsTs = map mkty vs;
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    val ixns = map fst ixnsTs
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    and sTs  = map snd ixnsTs
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    val (cts,tye2) = read_def_cterms(thy,types,sorts) used false sTs;
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    fun mkcVar(ixn,T) =
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        let val U = typ_subst_TVars tye2 T
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        in cterm_of thy (Var(ixn,U)) end
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    val ixnTs = ListPair.zip(ixns, map snd sTs)
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in (map (fn (ixn, T) => (ctyp_of thy (TVar (ixn, sort_of ixn)),
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      ctyp_of thy T)) (tye2 @ tye),
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    ListPair.zip(map mkcVar ixnTs,cts))
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end;
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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
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    val vars = fold_terms Term.add_vars thm [];
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    val frees = fold_terms Term.add_frees thm [];
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    val tvars = fold_terms Term.add_tvars thm [];
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    val tfrees = fold_terms Term.add_tfrees thm [];
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    fun types (a, i) =
wenzelm@20329
   304
      if i < 0 then AList.lookup (op =) frees a else AList.lookup (op =) vars (a, i);
wenzelm@20329
   305
    fun sorts (a, i) =
wenzelm@20329
   306
      if i < 0 then AList.lookup (op =) tfrees a else AList.lookup (op =) tvars (a, i);
wenzelm@20329
   307
  in (types, sorts) end;
clasohm@0
   308
wenzelm@20329
   309
val add_used =
wenzelm@20329
   310
  (fold_terms o fold_types o fold_atyps)
wenzelm@20329
   311
    (fn TFree (a, _) => insert (op =) a
wenzelm@20329
   312
      | TVar ((a, _), _) => insert (op =) a
wenzelm@20329
   313
      | _ => I);
wenzelm@15669
   314
wenzelm@7636
   315
wenzelm@9455
   316
clasohm@0
   317
(** Standardization of rules **)
clasohm@0
   318
wenzelm@19523
   319
(* type classes and sorts *)
wenzelm@19523
   320
wenzelm@19523
   321
fun sort_triv thy (T, S) =
wenzelm@19523
   322
  let
wenzelm@19523
   323
    val certT = Thm.ctyp_of thy;
wenzelm@19523
   324
    val cT = certT T;
wenzelm@19523
   325
    fun class_triv c =
wenzelm@19523
   326
      Thm.class_triv thy c
wenzelm@19523
   327
      |> Thm.instantiate ([(certT (TVar (("'a", 0), [c])), cT)], []);
wenzelm@19523
   328
  in map class_triv S end;
wenzelm@19523
   329
wenzelm@19504
   330
fun unconstrainTs th =
wenzelm@20298
   331
  fold (Thm.unconstrainT o Thm.ctyp_of (Thm.theory_of_thm th) o TVar)
wenzelm@20298
   332
    (fold_terms Term.add_tvars th []) th;
wenzelm@19504
   333
wenzelm@19730
   334
(*Generalization over a list of variables*)
wenzelm@19730
   335
val forall_intr_list = fold_rev forall_intr;
clasohm@0
   336
clasohm@0
   337
(*Generalization over all suitable Free variables*)
clasohm@0
   338
fun forall_intr_frees th =
wenzelm@19730
   339
    let
wenzelm@19730
   340
      val {prop, hyps, tpairs, thy,...} = rep_thm th;
wenzelm@19730
   341
      val fixed = fold Term.add_frees (Thm.terms_of_tpairs tpairs @ hyps) [];
wenzelm@19730
   342
      val frees = Term.fold_aterms (fn Free v =>
wenzelm@19730
   343
        if member (op =) fixed v then I else insert (op =) v | _ => I) prop [];
wenzelm@19730
   344
    in fold (forall_intr o cterm_of thy o Free) frees th end;
clasohm@0
   345
wenzelm@18535
   346
(*Generalization over Vars -- canonical order*)
wenzelm@18535
   347
fun forall_intr_vars th =
wenzelm@20298
   348
  fold forall_intr
wenzelm@20298
   349
    (map (Thm.cterm_of (Thm.theory_of_thm th) o Var) (fold_terms Term.add_vars th [])) th;
wenzelm@18535
   350
wenzelm@7898
   351
val forall_elim_var = PureThy.forall_elim_var;
wenzelm@7898
   352
val forall_elim_vars = PureThy.forall_elim_vars;
clasohm@0
   353
wenzelm@18025
   354
fun outer_params t =
wenzelm@20077
   355
  let val vs = Term.strip_all_vars t
wenzelm@20077
   356
  in Name.variant_list [] (map (Name.clean o #1) vs) ~~ map #2 vs end;
wenzelm@18025
   357
wenzelm@18025
   358
(*generalize outermost parameters*)
wenzelm@18025
   359
fun gen_all th =
wenzelm@12719
   360
  let
wenzelm@18025
   361
    val {thy, prop, maxidx, ...} = Thm.rep_thm th;
wenzelm@18025
   362
    val cert = Thm.cterm_of thy;
wenzelm@18025
   363
    fun elim (x, T) = Thm.forall_elim (cert (Var ((x, maxidx + 1), T)));
wenzelm@18025
   364
  in fold elim (outer_params prop) th end;
wenzelm@18025
   365
wenzelm@18025
   366
(*lift vars wrt. outermost goal parameters
wenzelm@18118
   367
  -- reverses the effect of gen_all modulo higher-order unification*)
wenzelm@18025
   368
fun lift_all goal th =
wenzelm@18025
   369
  let
wenzelm@18025
   370
    val thy = Theory.merge (Thm.theory_of_cterm goal, Thm.theory_of_thm th);
wenzelm@18025
   371
    val cert = Thm.cterm_of thy;
wenzelm@19421
   372
    val maxidx = Thm.maxidx_of th;
wenzelm@18025
   373
    val ps = outer_params (Thm.term_of goal)
wenzelm@18025
   374
      |> map (fn (x, T) => Var ((x, maxidx + 1), Logic.incr_tvar (maxidx + 1) T));
wenzelm@18025
   375
    val Ts = map Term.fastype_of ps;
wenzelm@20298
   376
    val inst = fold_terms Term.add_vars th [] |> map (fn (xi, T) =>
wenzelm@18025
   377
      (cert (Var (xi, T)), cert (Term.list_comb (Var (xi, Ts ---> T), ps))));
wenzelm@18025
   378
  in
wenzelm@18025
   379
    th |> Thm.instantiate ([], inst)
wenzelm@18025
   380
    |> fold_rev (Thm.forall_intr o cert) ps
wenzelm@18025
   381
  end;
wenzelm@18025
   382
wenzelm@19999
   383
(*direct generalization*)
wenzelm@19999
   384
fun generalize names th = Thm.generalize names (Thm.maxidx_of th + 1) th;
wenzelm@9554
   385
wenzelm@16949
   386
(*specialization over a list of cterms*)
wenzelm@16949
   387
val forall_elim_list = fold forall_elim;
clasohm@0
   388
wenzelm@16949
   389
(*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
wenzelm@16949
   390
val implies_intr_list = fold_rev implies_intr;
clasohm@0
   391
wenzelm@16949
   392
(*maps [| A1;...;An |] ==> B and [A1,...,An]  to  B*)
skalberg@15570
   393
fun implies_elim_list impth ths = Library.foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   394
clasohm@0
   395
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@21603
   396
fun zero_var_indexes_list [] = []
wenzelm@21603
   397
  | zero_var_indexes_list ths =
wenzelm@21603
   398
      let
wenzelm@21603
   399
        val thy = Theory.merge_list (map Thm.theory_of_thm ths);
wenzelm@21603
   400
        val certT = Thm.ctyp_of thy and cert = Thm.cterm_of thy;
wenzelm@21603
   401
        val (instT, inst) = TermSubst.zero_var_indexes_inst (map Thm.full_prop_of ths);
wenzelm@21603
   402
        val cinstT = map (fn (v, T) => (certT (TVar v), certT T)) instT;
wenzelm@21603
   403
        val cinst = map (fn (v, t) => (cert (Var v), cert t)) inst;
wenzelm@21603
   404
      in map (Thm.adjust_maxidx_thm ~1 o Thm.instantiate (cinstT, cinst)) ths end;
wenzelm@21603
   405
wenzelm@21603
   406
val zero_var_indexes = singleton zero_var_indexes_list;
clasohm@0
   407
clasohm@0
   408
paulson@14394
   409
(** Standard form of object-rule: no hypotheses, flexflex constraints,
paulson@14394
   410
    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
wenzelm@10515
   411
wenzelm@16595
   412
(*Discharge all hypotheses.*)
wenzelm@16595
   413
fun implies_intr_hyps th =
wenzelm@16595
   414
  fold Thm.implies_intr (#hyps (Thm.crep_thm th)) th;
wenzelm@16595
   415
paulson@14394
   416
(*Squash a theorem's flexflex constraints provided it can be done uniquely.
paulson@14394
   417
  This step can lose information.*)
paulson@14387
   418
fun flexflex_unique th =
berghofe@17713
   419
  if null (tpairs_of th) then th else
wenzelm@19861
   420
    case Seq.chop 2 (flexflex_rule th) of
paulson@14387
   421
      ([th],_) => th
paulson@14387
   422
    | ([],_)   => raise THM("flexflex_unique: impossible constraints", 0, [th])
paulson@14387
   423
    |      _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   424
wenzelm@10515
   425
fun close_derivation thm =
wenzelm@21646
   426
  if Thm.get_name thm = "" then Thm.put_name "" thm
wenzelm@10515
   427
  else thm;
wenzelm@10515
   428
wenzelm@21603
   429
wenzelm@21603
   430
(* legacy standard operations *)
wenzelm@21603
   431
wenzelm@16949
   432
val standard' =
wenzelm@16949
   433
  implies_intr_hyps
wenzelm@16949
   434
  #> forall_intr_frees
wenzelm@19421
   435
  #> `Thm.maxidx_of
wenzelm@16949
   436
  #-> (fn maxidx =>
wenzelm@16949
   437
    forall_elim_vars (maxidx + 1)
wenzelm@20904
   438
    #> Thm.strip_shyps
wenzelm@16949
   439
    #> zero_var_indexes
wenzelm@16949
   440
    #> Thm.varifyT
wenzelm@21600
   441
    #> Thm.compress);
wenzelm@1218
   442
wenzelm@16949
   443
val standard =
wenzelm@21600
   444
  flexflex_unique
wenzelm@16949
   445
  #> standard'
wenzelm@16949
   446
  #> close_derivation;
berghofe@11512
   447
clasohm@0
   448
wenzelm@8328
   449
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   450
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   451
  Similar code in type/freeze_thaw*)
paulson@15495
   452
paulson@15495
   453
fun freeze_thaw_robust th =
wenzelm@19878
   454
 let val fth = Thm.freezeT th
wenzelm@16425
   455
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@15495
   456
 in
skalberg@15574
   457
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@15495
   458
       [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
paulson@15495
   459
     | vars =>
paulson@19753
   460
         let fun newName (Var(ix,_)) = (ix, gensym (string_of_indexname ix))
paulson@19753
   461
             val alist = map newName vars
paulson@15495
   462
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   463
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   464
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
paulson@15495
   465
             val insts = map mk_inst vars
paulson@15495
   466
             fun thaw i th' = (*i is non-negative increment for Var indexes*)
paulson@15495
   467
                 th' |> forall_intr_list (map #2 insts)
paulson@15495
   468
                     |> forall_elim_list (map (Thm.cterm_incr_indexes i o #1) insts)
paulson@15495
   469
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@15495
   470
 end;
paulson@15495
   471
paulson@15495
   472
(*Basic version of the function above. No option to rename Vars apart in thaw.
wenzelm@19999
   473
  The Frees created from Vars have nice names. FIXME: does not check for
paulson@19753
   474
  clashes with variables in the assumptions, so delete and use freeze_thaw_robust instead?*)
paulson@4610
   475
fun freeze_thaw th =
wenzelm@19878
   476
 let val fth = Thm.freezeT th
wenzelm@16425
   477
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@7248
   478
 in
skalberg@15574
   479
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@7248
   480
       [] => (fth, fn x => x)
paulson@7248
   481
     | vars =>
wenzelm@8328
   482
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@20077
   483
                   let val v = Name.variant used (string_of_indexname ix)
wenzelm@8328
   484
                   in  ((ix,v)::pairs, v::used)  end;
skalberg@15574
   485
             val (alist, _) = foldr newName ([], Library.foldr add_term_names
skalberg@15574
   486
               (prop :: Thm.terms_of_tpairs tpairs, [])) vars
wenzelm@8328
   487
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   488
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   489
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
wenzelm@8328
   490
             val insts = map mk_inst vars
wenzelm@8328
   491
             fun thaw th' =
wenzelm@8328
   492
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   493
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   494
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   495
 end;
paulson@4610
   496
paulson@7248
   497
(*Rotates a rule's premises to the left by k*)
paulson@7248
   498
val rotate_prems = permute_prems 0;
paulson@4610
   499
oheimb@11163
   500
(* permute prems, where the i-th position in the argument list (counting from 0)
oheimb@11163
   501
   gives the position within the original thm to be transferred to position i.
oheimb@11163
   502
   Any remaining trailing positions are left unchanged. *)
oheimb@11163
   503
val rearrange_prems = let
oheimb@11163
   504
  fun rearr new []      thm = thm
wenzelm@11815
   505
  |   rearr new (p::ps) thm = rearr (new+1)
oheimb@11163
   506
     (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
oheimb@11163
   507
     (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
oheimb@11163
   508
  in rearr 0 end;
paulson@4610
   509
wenzelm@252
   510
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   511
fun tha RSN (i,thb) =
wenzelm@19861
   512
  case Seq.chop 2 (biresolution false [(false,tha)] i thb) of
clasohm@0
   513
      ([th],_) => th
clasohm@0
   514
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   515
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   516
clasohm@0
   517
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   518
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   519
clasohm@0
   520
(*For joining lists of rules*)
wenzelm@252
   521
fun thas RLN (i,thbs) =
clasohm@0
   522
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   523
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
wenzelm@19482
   524
  in maps resb thbs end;
clasohm@0
   525
clasohm@0
   526
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   527
lcp@11
   528
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   529
  makes proof trees*)
wenzelm@252
   530
fun rls MRS bottom_rl =
lcp@11
   531
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   532
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   533
  in  rs_aux 1 rls  end;
lcp@11
   534
lcp@11
   535
(*As above, but for rule lists*)
wenzelm@252
   536
fun rlss MRL bottom_rls =
lcp@11
   537
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   538
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   539
  in  rs_aux 1 rlss  end;
lcp@11
   540
wenzelm@9288
   541
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   542
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   543
wenzelm@252
   544
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   545
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   546
  ALWAYS deletes premise i *)
wenzelm@252
   547
fun compose(tha,i,thb) =
wenzelm@4270
   548
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   549
wenzelm@6946
   550
fun compose_single (tha,i,thb) =
wenzelm@6946
   551
  (case compose (tha,i,thb) of
wenzelm@6946
   552
    [th] => th
wenzelm@6946
   553
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   554
clasohm@0
   555
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   556
fun tha COMP thb =
wenzelm@22360
   557
    case distinct Thm.eq_thm (compose(tha,1,thb)) of
wenzelm@252
   558
        [th] => th
clasohm@0
   559
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   560
wenzelm@13105
   561
wenzelm@4016
   562
(** theorem equality **)
clasohm@0
   563
clasohm@0
   564
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   565
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   566
wenzelm@9829
   567
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@22360
   568
val del_rule = remove Thm.eq_thm_prop;
wenzelm@18922
   569
fun add_rule th = cons th o del_rule th;
wenzelm@22360
   570
val merge_rules = Library.merge Thm.eq_thm_prop;
wenzelm@9829
   571
lcp@1194
   572
lcp@1194
   573
clasohm@0
   574
(*** Meta-Rewriting Rules ***)
clasohm@0
   575
wenzelm@16425
   576
fun read_prop s = read_cterm ProtoPure.thy (s, propT);
paulson@4610
   577
wenzelm@9455
   578
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   579
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@12135
   580
fun store_thm_open name thm = hd (PureThy.smart_store_thms_open (name, [thm]));
wenzelm@12135
   581
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   582
clasohm@0
   583
val reflexive_thm =
wenzelm@19421
   584
  let val cx = cert (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   585
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   586
clasohm@0
   587
val symmetric_thm =
wenzelm@14854
   588
  let val xy = read_prop "x == y"
wenzelm@16595
   589
  in store_standard_thm_open "symmetric" (Thm.implies_intr xy (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   590
clasohm@0
   591
val transitive_thm =
wenzelm@14854
   592
  let val xy = read_prop "x == y"
wenzelm@14854
   593
      val yz = read_prop "y == z"
clasohm@0
   594
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   595
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   596
nipkow@4679
   597
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   598
berghofe@11512
   599
fun extensional eq =
berghofe@11512
   600
  let val eq' =
wenzelm@20579
   601
    abstract_rule "x" (Thm.dest_arg (fst (dest_equals (cprop_of eq)))) eq
berghofe@11512
   602
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   603
wenzelm@18820
   604
val equals_cong =
wenzelm@18820
   605
  store_standard_thm_open "equals_cong" (Thm.reflexive (read_prop "x == y"));
wenzelm@18820
   606
berghofe@10414
   607
val imp_cong =
berghofe@10414
   608
  let
berghofe@10414
   609
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   610
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   611
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   612
    val A = read_prop "PROP A"
berghofe@10414
   613
  in
wenzelm@12135
   614
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   615
      (implies_intr AB (implies_intr A
berghofe@10414
   616
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   617
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   618
      (implies_intr AC (implies_intr A
berghofe@10414
   619
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   620
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   621
  end;
berghofe@10414
   622
berghofe@10414
   623
val swap_prems_eq =
berghofe@10414
   624
  let
berghofe@10414
   625
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   626
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   627
    val A = read_prop "PROP A"
berghofe@10414
   628
    val B = read_prop "PROP B"
berghofe@10414
   629
  in
wenzelm@12135
   630
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   631
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   632
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   633
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   634
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   635
  end;
lcp@229
   636
wenzelm@18468
   637
val imp_cong_rule = combination o combination (reflexive implies);
clasohm@0
   638
skalberg@15001
   639
local
skalberg@15001
   640
  val dest_eq = dest_equals o cprop_of
skalberg@15001
   641
  val rhs_of = snd o dest_eq
skalberg@15001
   642
in
skalberg@15001
   643
fun beta_eta_conversion t =
skalberg@15001
   644
  let val thm = beta_conversion true t
skalberg@15001
   645
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   646
end;
skalberg@15001
   647
berghofe@15925
   648
fun eta_long_conversion ct = transitive (beta_eta_conversion ct)
berghofe@15925
   649
  (symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
berghofe@15925
   650
paulson@20861
   651
(*Contract all eta-redexes in the theorem, lest they give rise to needless abstractions*)
paulson@20861
   652
fun eta_contraction_rule th =
paulson@20861
   653
  equal_elim (eta_conversion (cprop_of th)) th;
paulson@20861
   654
wenzelm@18337
   655
val abs_def =
wenzelm@18337
   656
  let
wenzelm@18337
   657
    fun contract_lhs th =
wenzelm@18337
   658
      Thm.transitive (Thm.symmetric (beta_eta_conversion (fst (dest_equals (cprop_of th))))) th;
wenzelm@18777
   659
    fun abstract cx th = Thm.abstract_rule
wenzelm@18777
   660
        (case Thm.term_of cx of Var ((x, _), _) => x | Free (x, _) => x | _ => "x") cx th
wenzelm@18777
   661
      handle THM _ => raise THM ("Malformed definitional equation", 0, [th]);
wenzelm@18337
   662
  in
wenzelm@18337
   663
    contract_lhs
wenzelm@18337
   664
    #> `(snd o strip_comb o fst o dest_equals o cprop_of)
wenzelm@18337
   665
    #-> fold_rev abstract
wenzelm@18337
   666
    #> contract_lhs
wenzelm@18337
   667
  end;
wenzelm@18337
   668
wenzelm@18468
   669
(*rewrite B in !!x1 ... xn. B*)
wenzelm@18251
   670
fun forall_conv 0 cv ct = cv ct
wenzelm@18251
   671
  | forall_conv n cv ct =
wenzelm@18468
   672
      (case try Thm.dest_comb ct of
wenzelm@18468
   673
        NONE => cv ct
wenzelm@18468
   674
      | SOME (A, B) =>
wenzelm@18468
   675
          (case (term_of A, term_of B) of
wenzelm@18468
   676
            (Const ("all", _), Abs (x, _, _)) =>
wenzelm@18468
   677
              let val (v, B') = Thm.dest_abs (SOME (gensym "all_")) B in
wenzelm@18468
   678
                Thm.combination (Thm.reflexive A)
wenzelm@18468
   679
                  (Thm.abstract_rule x v (forall_conv (n - 1) cv B'))
wenzelm@18468
   680
              end
wenzelm@18468
   681
          | _ => cv ct));
wenzelm@18468
   682
wenzelm@18468
   683
(*rewrite B in A1 ==> ... ==> An ==> B*)
wenzelm@18468
   684
fun concl_conv 0 cv ct = cv ct
wenzelm@18468
   685
  | concl_conv n cv ct =
wenzelm@18468
   686
      (case try dest_implies ct of
wenzelm@18468
   687
        NONE => cv ct
wenzelm@18468
   688
      | SOME (A, B) => imp_cong_rule (reflexive A) (concl_conv (n - 1) cv B));
skalberg@15001
   689
wenzelm@18468
   690
(*rewrite the A's in A1 ==> ... ==> An ==> B*)
wenzelm@18468
   691
fun prems_conv 0 _ = reflexive
wenzelm@18468
   692
  | prems_conv n cv =
wenzelm@18468
   693
      let
wenzelm@18468
   694
        fun conv i ct =
wenzelm@18468
   695
          if i = n + 1 then reflexive ct
wenzelm@18468
   696
          else
wenzelm@18468
   697
            (case try dest_implies ct of
wenzelm@18468
   698
              NONE => reflexive ct
wenzelm@18468
   699
            | SOME (A, B) => imp_cong_rule (cv i A) (conv (i + 1) B));
wenzelm@18468
   700
  in conv 1 end;
wenzelm@18468
   701
wenzelm@18468
   702
fun goals_conv pred cv = prems_conv ~1 (fn i => if pred i then cv else reflexive);
skalberg@15001
   703
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
skalberg@15001
   704
wenzelm@18468
   705
wenzelm@15669
   706
(*** Some useful meta-theorems ***)
clasohm@0
   707
clasohm@0
   708
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@12135
   709
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   710
val _ = store_thm "_" asm_rl;
clasohm@0
   711
clasohm@0
   712
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   713
val cut_rl =
wenzelm@12135
   714
  store_standard_thm_open "cut_rl"
wenzelm@9455
   715
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   716
wenzelm@252
   717
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   718
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   719
val revcut_rl =
paulson@4610
   720
  let val V = read_prop "PROP V"
paulson@4610
   721
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   722
  in
wenzelm@12135
   723
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   724
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   725
  end;
clasohm@0
   726
lcp@668
   727
(*for deleting an unwanted assumption*)
lcp@668
   728
val thin_rl =
paulson@4610
   729
  let val V = read_prop "PROP V"
paulson@4610
   730
      and W = read_prop "PROP W";
wenzelm@12135
   731
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   732
clasohm@0
   733
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   734
val triv_forall_equality =
paulson@4610
   735
  let val V  = read_prop "PROP V"
paulson@4610
   736
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@19421
   737
      and x  = cert (Free ("x", Term.aT []));
wenzelm@4016
   738
  in
wenzelm@12135
   739
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   740
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   741
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   742
  end;
clasohm@0
   743
wenzelm@19051
   744
(* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
wenzelm@19051
   745
   (PROP ?Phi ==> PROP ?Psi)
wenzelm@19051
   746
*)
wenzelm@19051
   747
val distinct_prems_rl =
wenzelm@19051
   748
  let
wenzelm@19051
   749
    val AAB = read_prop "PROP Phi ==> PROP Phi ==> PROP Psi"
wenzelm@19051
   750
    val A = read_prop "PROP Phi";
wenzelm@19051
   751
  in
wenzelm@19051
   752
    store_standard_thm_open "distinct_prems_rl"
wenzelm@19051
   753
      (implies_intr_list [AAB, A] (implies_elim_list (assume AAB) [assume A, assume A]))
wenzelm@19051
   754
  end;
wenzelm@19051
   755
nipkow@1756
   756
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   757
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   758
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   759
*)
nipkow@1756
   760
val swap_prems_rl =
paulson@4610
   761
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   762
      val major = assume cmajor;
paulson@4610
   763
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   764
      val minor1 = assume cminor1;
paulson@4610
   765
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   766
      val minor2 = assume cminor2;
wenzelm@12135
   767
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   768
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   769
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   770
  end;
nipkow@1756
   771
nipkow@3653
   772
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   773
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   774
   Introduction rule for == as a meta-theorem.
nipkow@3653
   775
*)
nipkow@3653
   776
val equal_intr_rule =
paulson@4610
   777
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   778
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   779
  in
wenzelm@12135
   780
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   781
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   782
  end;
nipkow@3653
   783
wenzelm@19421
   784
(* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@13368
   785
val equal_elim_rule1 =
wenzelm@13368
   786
  let val eq = read_prop "PROP phi == PROP psi"
wenzelm@13368
   787
      and P = read_prop "PROP phi"
wenzelm@13368
   788
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   789
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   790
  end;
wenzelm@4285
   791
wenzelm@19421
   792
(* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@19421
   793
val equal_elim_rule2 =
wenzelm@19421
   794
  store_standard_thm_open "equal_elim_rule2" (symmetric_thm RS equal_elim_rule1);
wenzelm@19421
   795
wenzelm@12297
   796
(* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
wenzelm@12297
   797
val remdups_rl =
wenzelm@12297
   798
  let val P = read_prop "PROP phi" and Q = read_prop "PROP psi";
wenzelm@12297
   799
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   800
wenzelm@12297
   801
wenzelm@9554
   802
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@12297
   803
  Rewrite rule for HHF normalization.*)
wenzelm@9554
   804
wenzelm@9554
   805
val norm_hhf_eq =
wenzelm@9554
   806
  let
wenzelm@14854
   807
    val aT = TFree ("'a", []);
wenzelm@9554
   808
    val all = Term.all aT;
wenzelm@9554
   809
    val x = Free ("x", aT);
wenzelm@9554
   810
    val phi = Free ("phi", propT);
wenzelm@9554
   811
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   812
wenzelm@9554
   813
    val cx = cert x;
wenzelm@9554
   814
    val cphi = cert phi;
wenzelm@9554
   815
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   816
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   817
  in
wenzelm@9554
   818
    Thm.equal_intr
wenzelm@9554
   819
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   820
        |> Thm.forall_elim cx
wenzelm@9554
   821
        |> Thm.implies_intr cphi
wenzelm@9554
   822
        |> Thm.forall_intr cx
wenzelm@9554
   823
        |> Thm.implies_intr lhs)
wenzelm@9554
   824
      (Thm.implies_elim
wenzelm@9554
   825
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   826
        |> Thm.forall_intr cx
wenzelm@9554
   827
        |> Thm.implies_intr cphi
wenzelm@9554
   828
        |> Thm.implies_intr rhs)
wenzelm@12135
   829
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   830
  end;
wenzelm@9554
   831
wenzelm@18179
   832
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@18179
   833
wenzelm@12800
   834
fun is_norm_hhf tm =
wenzelm@12800
   835
  let
wenzelm@12800
   836
    fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@12800
   837
      | is_norm (t $ u) = is_norm t andalso is_norm u
wenzelm@12800
   838
      | is_norm (Abs (_, _, t)) = is_norm t
wenzelm@12800
   839
      | is_norm _ = true;
wenzelm@18929
   840
  in is_norm (Envir.beta_eta_contract tm) end;
wenzelm@12800
   841
wenzelm@16425
   842
fun norm_hhf thy t =
wenzelm@12800
   843
  if is_norm_hhf t then t
wenzelm@18179
   844
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   845
wenzelm@20298
   846
fun norm_hhf_cterm ct =
wenzelm@20298
   847
  if is_norm_hhf (Thm.term_of ct) then ct
wenzelm@20298
   848
  else cterm_fun (Pattern.rewrite_term (Thm.theory_of_cterm ct) [norm_hhf_prop] []) ct;
wenzelm@20298
   849
wenzelm@12800
   850
wenzelm@21603
   851
(* var indexes *)
wenzelm@21603
   852
wenzelm@21603
   853
fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
wenzelm@21603
   854
wenzelm@21603
   855
fun incr_indexes2 th1 th2 =
wenzelm@21603
   856
  Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
wenzelm@21603
   857
wenzelm@21603
   858
fun th1 INCR_COMP th2 = incr_indexes th2 th1 COMP th2;
wenzelm@21603
   859
fun th1 COMP_INCR th2 = th1 COMP incr_indexes th1 th2;
wenzelm@21603
   860
wenzelm@9554
   861
wenzelm@16425
   862
(*** Instantiate theorem th, reading instantiations in theory thy ****)
paulson@8129
   863
paulson@8129
   864
(*Version that normalizes the result: Thm.instantiate no longer does that*)
wenzelm@21603
   865
fun instantiate instpair th =
wenzelm@21603
   866
  Thm.adjust_maxidx_thm ~1 (Thm.instantiate instpair th COMP_INCR asm_rl);
paulson@8129
   867
wenzelm@16425
   868
fun read_instantiate_sg' thy sinsts th =
paulson@8129
   869
    let val ts = types_sorts th;
wenzelm@15669
   870
        val used = add_used th [];
wenzelm@16425
   871
    in  instantiate (read_insts thy ts ts used sinsts) th  end;
berghofe@15797
   872
wenzelm@16425
   873
fun read_instantiate_sg thy sinsts th =
wenzelm@20298
   874
  read_instantiate_sg' thy (map (apfst Syntax.read_indexname) sinsts) th;
paulson@8129
   875
paulson@8129
   876
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   877
fun read_instantiate sinsts th =
wenzelm@16425
   878
    read_instantiate_sg (Thm.theory_of_thm th) sinsts th;
paulson@8129
   879
berghofe@15797
   880
fun read_instantiate' sinsts th =
wenzelm@16425
   881
    read_instantiate_sg' (Thm.theory_of_thm th) sinsts th;
berghofe@15797
   882
paulson@8129
   883
paulson@8129
   884
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   885
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   886
local
wenzelm@16425
   887
  fun add_types ((ct,cu), (thy,tye,maxidx)) =
wenzelm@16425
   888
    let val {thy=thyt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
wenzelm@16425
   889
        and {thy=thyu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   890
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
wenzelm@16425
   891
        val thy' = Theory.merge(thy, Theory.merge(thyt, thyu))
wenzelm@16949
   892
        val (tye',maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
wenzelm@10403
   893
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
wenzelm@16425
   894
    in  (thy', tye', maxi')  end;
paulson@8129
   895
in
paulson@22561
   896
fun cterm_instantiate [] th = th
paulson@22561
   897
  | cterm_instantiate ctpairs0 th =
wenzelm@16425
   898
  let val (thy,tye,_) = foldr add_types (Thm.theory_of_thm th, Vartab.empty, 0) ctpairs0
wenzelm@18179
   899
      fun instT(ct,cu) =
paulson@22287
   900
        let val inst = cterm_of thy o Term.map_types (Envir.norm_type tye) o term_of
paulson@14340
   901
        in (inst ct, inst cu) end
paulson@22307
   902
      fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy (Envir.norm_type tye T))
berghofe@8406
   903
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   904
  handle TERM _ =>
wenzelm@16425
   905
           raise THM("cterm_instantiate: incompatible theories",0,[th])
paulson@8129
   906
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   907
end;
paulson@8129
   908
paulson@8129
   909
wenzelm@19878
   910
(* global schematic variables *)
wenzelm@19878
   911
wenzelm@19878
   912
fun unvarify th =
wenzelm@19878
   913
  let
wenzelm@19878
   914
    val thy = Thm.theory_of_thm th;
wenzelm@19878
   915
    val cert = Thm.cterm_of thy;
wenzelm@19878
   916
    val certT = Thm.ctyp_of thy;
wenzelm@19878
   917
wenzelm@19878
   918
    val prop = Thm.full_prop_of th;
wenzelm@19878
   919
    val _ = map Logic.unvarify (prop :: Thm.hyps_of th)
wenzelm@19878
   920
      handle TERM (msg, _) => raise THM (msg, 0, [th]);
wenzelm@19878
   921
wenzelm@19878
   922
    val instT0 = rev (Term.add_tvars prop []) |> map (fn v as ((a, _), S) => (v, TFree (a, S)));
wenzelm@19878
   923
    val instT = map (fn (v, T) => (certT (TVar v), certT T)) instT0;
wenzelm@19878
   924
    val inst = rev (Term.add_vars prop []) |> map (fn ((a, i), T) =>
wenzelm@20509
   925
      let val T' = TermSubst.instantiateT instT0 T
wenzelm@19878
   926
      in (cert (Var ((a, i), T')), cert (Free ((a, T')))) end);
wenzelm@19878
   927
  in Thm.instantiate (instT, inst) th end;
wenzelm@19878
   928
wenzelm@19878
   929
wenzelm@19775
   930
(** protected propositions and embedded terms **)
wenzelm@4789
   931
wenzelm@4789
   932
local
wenzelm@18025
   933
  val A = cert (Free ("A", propT));
wenzelm@19878
   934
  val prop_def = unvarify ProtoPure.prop_def;
wenzelm@19878
   935
  val term_def = unvarify ProtoPure.term_def;
wenzelm@4789
   936
in
wenzelm@18025
   937
  val protect = Thm.capply (cert Logic.protectC);
wenzelm@21437
   938
  val protectI = store_thm "protectI" (PureThy.kind_rule Thm.internalK (standard
wenzelm@18025
   939
      (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A))));
wenzelm@21437
   940
  val protectD = store_thm "protectD" (PureThy.kind_rule Thm.internalK (standard
wenzelm@18025
   941
      (Thm.equal_elim prop_def (Thm.assume (protect A)))));
wenzelm@18179
   942
  val protect_cong = store_standard_thm_open "protect_cong" (Thm.reflexive (protect A));
wenzelm@19775
   943
wenzelm@21437
   944
  val termI = store_thm "termI" (PureThy.kind_rule Thm.internalK (standard
wenzelm@19775
   945
      (Thm.equal_elim (Thm.symmetric term_def) (Thm.forall_intr A (Thm.trivial A)))));
wenzelm@4789
   946
end;
wenzelm@4789
   947
wenzelm@18025
   948
fun implies_intr_protected asms th =
wenzelm@18118
   949
  let val asms' = map protect asms in
wenzelm@18118
   950
    implies_elim_list
wenzelm@18118
   951
      (implies_intr_list asms th)
wenzelm@18118
   952
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@18118
   953
    |> implies_intr_list asms'
wenzelm@18118
   954
  end;
wenzelm@11815
   955
wenzelm@19775
   956
fun mk_term ct =
wenzelm@19775
   957
  let
wenzelm@19775
   958
    val {thy, T, ...} = Thm.rep_cterm ct;
wenzelm@19775
   959
    val cert = Thm.cterm_of thy;
wenzelm@19775
   960
    val certT = Thm.ctyp_of thy;
wenzelm@19775
   961
    val a = certT (TVar (("'a", 0), []));
wenzelm@19775
   962
    val x = cert (Var (("x", 0), T));
wenzelm@19775
   963
  in Thm.instantiate ([(a, certT T)], [(x, ct)]) termI end;
wenzelm@19775
   964
wenzelm@19775
   965
fun dest_term th =
wenzelm@21566
   966
  let val cprop = strip_imp_concl (Thm.cprop_of th) in
wenzelm@19775
   967
    if can Logic.dest_term (Thm.term_of cprop) then
wenzelm@20579
   968
      Thm.dest_arg cprop
wenzelm@19775
   969
    else raise THM ("dest_term", 0, [th])
wenzelm@19775
   970
  end;
wenzelm@19775
   971
wenzelm@21519
   972
fun cterm_rule f = dest_term o f o mk_term;
wenzelm@21519
   973
fun term_rule thy f t = Thm.term_of (cterm_rule f (Thm.cterm_of thy t));
wenzelm@20881
   974
wenzelm@19775
   975
wenzelm@4789
   976
wenzelm@5688
   977
(** variations on instantiate **)
wenzelm@4285
   978
wenzelm@4285
   979
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   980
wenzelm@4285
   981
fun instantiate' cTs cts thm =
wenzelm@4285
   982
  let
wenzelm@4285
   983
    fun err msg =
wenzelm@4285
   984
      raise TYPE ("instantiate': " ^ msg,
wenzelm@19482
   985
        map_filter (Option.map Thm.typ_of) cTs,
wenzelm@19482
   986
        map_filter (Option.map Thm.term_of) cts);
wenzelm@4285
   987
wenzelm@4285
   988
    fun inst_of (v, ct) =
wenzelm@16425
   989
      (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
   990
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   991
berghofe@15797
   992
    fun tyinst_of (v, cT) =
wenzelm@16425
   993
      (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
   994
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
   995
wenzelm@20298
   996
    fun zip_vars xs ys =
wenzelm@20298
   997
      zip_options xs ys handle Library.UnequalLengths =>
wenzelm@20298
   998
        err "more instantiations than variables in thm";
wenzelm@4285
   999
wenzelm@4285
  1000
    (*instantiate types first!*)
wenzelm@4285
  1001
    val thm' =
wenzelm@4285
  1002
      if forall is_none cTs then thm
wenzelm@20298
  1003
      else Thm.instantiate
wenzelm@20298
  1004
        (map tyinst_of (zip_vars (rev (fold_terms Term.add_tvars thm [])) cTs), []) thm;
wenzelm@20579
  1005
    val thm'' =
wenzelm@4285
  1006
      if forall is_none cts then thm'
wenzelm@20298
  1007
      else Thm.instantiate
wenzelm@20298
  1008
        ([], map inst_of (zip_vars (rev (fold_terms Term.add_vars thm' [])) cts)) thm';
wenzelm@20298
  1009
    in thm'' end;
wenzelm@4285
  1010
wenzelm@4285
  1011
berghofe@14081
  1012
berghofe@14081
  1013
(** renaming of bound variables **)
berghofe@14081
  1014
berghofe@14081
  1015
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
  1016
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
  1017
berghofe@14081
  1018
fun rename_bvars [] thm = thm
berghofe@14081
  1019
  | rename_bvars vs thm =
berghofe@14081
  1020
    let
wenzelm@16425
  1021
      val {thy, prop, ...} = rep_thm thm;
haftmann@17325
  1022
      fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
berghofe@14081
  1023
        | ren (t $ u) = ren t $ ren u
berghofe@14081
  1024
        | ren t = t;
wenzelm@16425
  1025
    in equal_elim (reflexive (cterm_of thy (ren prop))) thm end;
berghofe@14081
  1026
berghofe@14081
  1027
berghofe@14081
  1028
(* renaming in left-to-right order *)
berghofe@14081
  1029
berghofe@14081
  1030
fun rename_bvars' xs thm =
berghofe@14081
  1031
  let
wenzelm@16425
  1032
    val {thy, prop, ...} = rep_thm thm;
berghofe@14081
  1033
    fun rename [] t = ([], t)
berghofe@14081
  1034
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
  1035
          let val (xs', t') = rename xs t
wenzelm@18929
  1036
          in (xs', Abs (the_default x x', T, t')) end
berghofe@14081
  1037
      | rename xs (t $ u) =
berghofe@14081
  1038
          let
berghofe@14081
  1039
            val (xs', t') = rename xs t;
berghofe@14081
  1040
            val (xs'', u') = rename xs' u
berghofe@14081
  1041
          in (xs'', t' $ u') end
berghofe@14081
  1042
      | rename xs t = (xs, t);
berghofe@14081
  1043
  in case rename xs prop of
wenzelm@16425
  1044
      ([], prop') => equal_elim (reflexive (cterm_of thy prop')) thm
berghofe@14081
  1045
    | _ => error "More names than abstractions in theorem"
berghofe@14081
  1046
  end;
berghofe@14081
  1047
berghofe@14081
  1048
wenzelm@11975
  1049
wenzelm@18225
  1050
(** multi_resolve **)
wenzelm@18225
  1051
wenzelm@18225
  1052
local
wenzelm@18225
  1053
wenzelm@18225
  1054
fun res th i rule =
wenzelm@18225
  1055
  Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
wenzelm@18225
  1056
wenzelm@18225
  1057
fun multi_res _ [] rule = Seq.single rule
wenzelm@18225
  1058
  | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
wenzelm@18225
  1059
wenzelm@18225
  1060
in
wenzelm@18225
  1061
wenzelm@18225
  1062
val multi_resolve = multi_res 1;
wenzelm@18225
  1063
fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
wenzelm@18225
  1064
wenzelm@18225
  1065
end;
wenzelm@18225
  1066
wenzelm@11975
  1067
end;
wenzelm@5903
  1068
wenzelm@5903
  1069
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
  1070
open BasicDrule;