src/Pure/drule.ML
author wenzelm
Wed Nov 16 17:45:25 2005 +0100 (2005-11-16)
changeset 18179 cf4b265007bf
parent 18129 62adfb6a7060
child 18206 faaaa458198d
permissions -rw-r--r--
added protect_cong, cong_mono_thm;
outer_params: Syntax.deskolem;
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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;
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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 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:
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          theory -> (indexname -> typ option) * (indexname -> sort option)
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                  -> (indexname -> typ option) * (indexname -> sort option)
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                  -> string list -> (indexname * string) list
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                  -> (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 strip_shyps_warning: 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_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:
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    (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm
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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 assume_ax: theory -> string -> 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 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 eq_thm_thy: thm * thm -> bool
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  val eq_thm_prop: thm * thm -> bool
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  val weak_eq_thm: thm * thm -> bool
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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 imp_cong: thm
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  val swap_prems_eq: 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 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 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 inst: string -> string -> thm -> thm
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  val instantiate': ctyp option list -> cterm option list -> thm -> thm
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  val incr_indexes: thm -> thm -> thm
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  val incr_indexes_wrt: int list -> ctyp list -> cterm list -> thm 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 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 beta_conv: cterm -> cterm -> cterm
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  val plain_prop_of: thm -> term
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  val add_used: thm -> string list -> string list
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  val rule_attribute: ('a -> thm -> thm) -> 'a attribute
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  val tag_rule: tag -> thm -> thm
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  val untag_rule: string -> thm -> thm
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  val tag: tag -> 'a attribute
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  val untag: string -> 'a attribute
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  val get_kind: thm -> string
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  val kind: string -> 'a attribute
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  val theoremK: string
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  val lemmaK: string
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  val corollaryK: string
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  val internalK: string
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  val kind_internal: 'a attribute
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  val has_internal: tag list -> bool
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  val flexflex_unique: thm -> thm
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  val close_derivation: thm -> thm
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  val local_standard: 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 add_rules: thm list -> thm list -> thm list
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  val del_rules: thm list -> thm list -> thm list
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  val merge_rules: thm list * thm list -> thm list
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  val imp_cong': 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 goals_conv: (int -> bool) -> (cterm -> thm) -> cterm -> thm
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  val forall_conv: (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 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 freeze_all: thm -> thm
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  val tvars_of_terms: term list -> (indexname * sort) list
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  val vars_of_terms: term list -> (indexname * typ) list
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  val tvars_of: thm -> (indexname * sort) list
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  val vars_of: thm -> (indexname * typ) list
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  val tfrees_of: thm -> (string * sort) list
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  val frees_of: thm -> (string * typ) list
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  val fold_terms: (term -> 'a -> 'a) -> thm -> 'a -> 'a
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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 unvarifyT: thm -> thm
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  val unvarify: thm -> thm
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  val tvars_intr_list: string list -> thm -> (string * (indexname * sort)) list * thm
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  val remdups_rl: thm
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  val conj_intr: thm -> thm -> thm
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  val conj_intr_list: thm list -> thm
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  val conj_elim: thm -> thm * thm
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  val conj_elim_list: thm -> thm list
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  val conj_elim_precise: int -> thm -> thm list
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  val conj_intr_thm: thm
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  val conj_mono_thm: thm
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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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(* FIXME exception CTERM (!?) *)
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fun dest_implies ct =
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  (case Thm.term_of ct of
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    (Const ("==>", _) $ _ $ _) =>
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      let val (ct1, ct2) = Thm.dest_comb ct
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      in (#2 (Thm.dest_comb ct1), ct2) end
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  | _ => raise TERM ("dest_implies", [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 ("==", _) $ _ $ _) =>
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      let val (ct1, ct2) = Thm.dest_comb ct
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      in (#2 (Thm.dest_comb ct1), ct2) end
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    | _ => raise TERM ("dest_equals", [term_of ct]));
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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 term_of ct of (Const("==>", _) $ _ $ _) =>
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        strip_imp_concl (#2 (Thm.dest_comb 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 implies = cterm_of ProtoPure.thy Term.implies;
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(*cterm version of mk_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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    #2 (Thm.dest_comb (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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(** 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 val {prop, hyps, tpairs, ...} = Thm.rep_thm thm;
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        (* bogus term! *)
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        val big = Term.list_comb
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                    (Term.list_comb (prop, hyps), Thm.terms_of_tpairs tpairs);
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   307
        val vars = map dest_Var (term_vars big);
wenzelm@252
   308
        val frees = map dest_Free (term_frees big);
wenzelm@252
   309
        val tvars = term_tvars big;
wenzelm@252
   310
        val tfrees = term_tfrees big;
haftmann@17325
   311
        fun typ(a,i) = if i<0 then AList.lookup (op =) frees a else AList.lookup (op =) vars (a,i);
haftmann@17325
   312
        fun sort(a,i) = if i<0 then AList.lookup (op =) tfrees a else AList.lookup (op =) tvars (a,i);
clasohm@0
   313
    in (typ,sort) end;
clasohm@0
   314
wenzelm@15669
   315
fun add_used thm used =
wenzelm@15669
   316
  let val {prop, hyps, tpairs, ...} = Thm.rep_thm thm in
wenzelm@15669
   317
    add_term_tvarnames (prop, used)
wenzelm@15669
   318
    |> fold (curry add_term_tvarnames) hyps
wenzelm@15669
   319
    |> fold (curry add_term_tvarnames) (Thm.terms_of_tpairs tpairs)
wenzelm@15669
   320
  end;
wenzelm@15669
   321
wenzelm@7636
   322
wenzelm@9455
   323
wenzelm@9455
   324
(** basic attributes **)
wenzelm@9455
   325
wenzelm@9455
   326
(* dependent rules *)
wenzelm@9455
   327
wenzelm@9455
   328
fun rule_attribute f (x, thm) = (x, (f x thm));
wenzelm@9455
   329
wenzelm@9455
   330
wenzelm@9455
   331
(* add / delete tags *)
wenzelm@9455
   332
wenzelm@9455
   333
fun map_tags f thm =
wenzelm@9455
   334
  Thm.put_name_tags (Thm.name_of_thm thm, f (#2 (Thm.get_name_tags thm))) thm;
wenzelm@9455
   335
wenzelm@9455
   336
fun tag_rule tg = map_tags (fn tgs => if tg mem tgs then tgs else tgs @ [tg]);
wenzelm@9455
   337
fun untag_rule s = map_tags (filter_out (equal s o #1));
wenzelm@9455
   338
wenzelm@9455
   339
fun tag tg x = rule_attribute (K (tag_rule tg)) x;
wenzelm@9455
   340
fun untag s x = rule_attribute (K (untag_rule s)) x;
wenzelm@9455
   341
wenzelm@9455
   342
fun simple_tag name x = tag (name, []) x;
wenzelm@9455
   343
wenzelm@11741
   344
wenzelm@11741
   345
(* theorem kinds *)
wenzelm@11741
   346
wenzelm@11741
   347
val theoremK = "theorem";
wenzelm@11741
   348
val lemmaK = "lemma";
wenzelm@11741
   349
val corollaryK = "corollary";
wenzelm@11741
   350
val internalK = "internal";
wenzelm@9455
   351
wenzelm@11741
   352
fun get_kind thm =
haftmann@17325
   353
  (case AList.lookup (op =) ((#2 o Thm.get_name_tags) thm) "kind" of
skalberg@15531
   354
    SOME (k :: _) => k
wenzelm@11741
   355
  | _ => "unknown");
wenzelm@11741
   356
wenzelm@11741
   357
fun kind_rule k = tag_rule ("kind", [k]) o untag_rule "kind";
wenzelm@12710
   358
fun kind k x = if k = "" then x else rule_attribute (K (kind_rule k)) x;
wenzelm@11741
   359
fun kind_internal x = kind internalK x;
wenzelm@11741
   360
fun has_internal tags = exists (equal internalK o fst) tags;
wenzelm@9455
   361
wenzelm@9455
   362
wenzelm@9455
   363
clasohm@0
   364
(** Standardization of rules **)
clasohm@0
   365
wenzelm@18025
   366
(*vars in left-to-right order*)
wenzelm@18025
   367
fun tvars_of_terms ts = rev (fold Term.add_tvars ts []);
wenzelm@18025
   368
fun vars_of_terms ts = rev (fold Term.add_vars ts []);
wenzelm@18025
   369
fun tvars_of thm = tvars_of_terms [Thm.full_prop_of thm];
wenzelm@18025
   370
fun vars_of thm = vars_of_terms [Thm.full_prop_of thm];
wenzelm@18025
   371
wenzelm@18129
   372
fun fold_terms f th =
wenzelm@18129
   373
  let val {hyps, tpairs, prop, ...} = Thm.rep_thm th
wenzelm@18129
   374
  in f prop #> fold (fn (t, u) => f t #> f u) tpairs #> fold f hyps end;
wenzelm@18129
   375
wenzelm@18129
   376
fun tfrees_of th = rev (fold_terms Term.add_tfrees th []);
wenzelm@18129
   377
fun frees_of th = rev (fold_terms Term.add_frees th []);
wenzelm@18129
   378
wenzelm@7636
   379
(*Strip extraneous shyps as far as possible*)
wenzelm@7636
   380
fun strip_shyps_warning thm =
wenzelm@7636
   381
  let
wenzelm@16425
   382
    val str_of_sort = Pretty.str_of o Sign.pretty_sort (Thm.theory_of_thm thm);
wenzelm@7636
   383
    val thm' = Thm.strip_shyps thm;
wenzelm@7636
   384
    val xshyps = Thm.extra_shyps thm';
wenzelm@7636
   385
  in
wenzelm@7636
   386
    if null xshyps then ()
wenzelm@7636
   387
    else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
wenzelm@7636
   388
    thm'
wenzelm@7636
   389
  end;
wenzelm@7636
   390
clasohm@0
   391
(*Generalization over a list of variables, IGNORING bad ones*)
clasohm@0
   392
fun forall_intr_list [] th = th
clasohm@0
   393
  | forall_intr_list (y::ys) th =
wenzelm@252
   394
        let val gth = forall_intr_list ys th
wenzelm@252
   395
        in  forall_intr y gth   handle THM _ =>  gth  end;
clasohm@0
   396
clasohm@0
   397
(*Generalization over all suitable Free variables*)
clasohm@0
   398
fun forall_intr_frees th =
wenzelm@16425
   399
    let val {prop,thy,...} = rep_thm th
clasohm@0
   400
    in  forall_intr_list
wenzelm@16983
   401
         (map (cterm_of thy) (sort Term.term_ord (term_frees prop)))
clasohm@0
   402
         th
clasohm@0
   403
    end;
clasohm@0
   404
wenzelm@7898
   405
val forall_elim_var = PureThy.forall_elim_var;
wenzelm@7898
   406
val forall_elim_vars = PureThy.forall_elim_vars;
clasohm@0
   407
wenzelm@18025
   408
fun outer_params t =
wenzelm@18025
   409
  let
wenzelm@18025
   410
    val vs = Term.strip_all_vars t;
wenzelm@18179
   411
    val xs = Term.variantlist (map (Syntax.deskolem o #1) vs, []);
wenzelm@18025
   412
  in xs ~~ map #2 vs end;
wenzelm@18025
   413
wenzelm@18025
   414
(*generalize outermost parameters*)
wenzelm@18025
   415
fun gen_all th =
wenzelm@12719
   416
  let
wenzelm@18025
   417
    val {thy, prop, maxidx, ...} = Thm.rep_thm th;
wenzelm@18025
   418
    val cert = Thm.cterm_of thy;
wenzelm@18025
   419
    fun elim (x, T) = Thm.forall_elim (cert (Var ((x, maxidx + 1), T)));
wenzelm@18025
   420
  in fold elim (outer_params prop) th end;
wenzelm@18025
   421
wenzelm@18025
   422
(*lift vars wrt. outermost goal parameters
wenzelm@18118
   423
  -- reverses the effect of gen_all modulo higher-order unification*)
wenzelm@18025
   424
fun lift_all goal th =
wenzelm@18025
   425
  let
wenzelm@18025
   426
    val thy = Theory.merge (Thm.theory_of_cterm goal, Thm.theory_of_thm th);
wenzelm@18025
   427
    val cert = Thm.cterm_of thy;
wenzelm@18025
   428
    val {maxidx, ...} = Thm.rep_thm th;
wenzelm@18025
   429
    val ps = outer_params (Thm.term_of goal)
wenzelm@18025
   430
      |> map (fn (x, T) => Var ((x, maxidx + 1), Logic.incr_tvar (maxidx + 1) T));
wenzelm@18025
   431
    val Ts = map Term.fastype_of ps;
wenzelm@18025
   432
    val inst = vars_of th |> map (fn (xi, T) =>
wenzelm@18025
   433
      (cert (Var (xi, T)), cert (Term.list_comb (Var (xi, Ts ---> T), ps))));
wenzelm@18025
   434
  in
wenzelm@18025
   435
    th |> Thm.instantiate ([], inst)
wenzelm@18025
   436
    |> fold_rev (Thm.forall_intr o cert) ps
wenzelm@18025
   437
  end;
wenzelm@18025
   438
wenzelm@9554
   439
wenzelm@16949
   440
(*specialization over a list of cterms*)
wenzelm@16949
   441
val forall_elim_list = fold forall_elim;
clasohm@0
   442
wenzelm@16949
   443
(*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
wenzelm@16949
   444
val implies_intr_list = fold_rev implies_intr;
clasohm@0
   445
wenzelm@16949
   446
(*maps [| A1;...;An |] ==> B and [A1,...,An]  to  B*)
skalberg@15570
   447
fun implies_elim_list impth ths = Library.foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   448
clasohm@0
   449
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@252
   450
fun zero_var_indexes th =
wenzelm@16949
   451
  let
wenzelm@16949
   452
    val thy = Thm.theory_of_thm th;
wenzelm@16949
   453
    val certT = Thm.ctyp_of thy and cert = Thm.cterm_of thy;
wenzelm@16949
   454
    val (instT, inst) = Term.zero_var_indexes_inst (Thm.full_prop_of th);
wenzelm@16949
   455
    val cinstT = map (fn (v, T) => (certT (TVar v), certT T)) instT;
wenzelm@16949
   456
    val cinst = map (fn (v, t) => (cert (Var v), cert t)) inst;
wenzelm@16949
   457
  in Thm.adjust_maxidx_thm (Thm.instantiate (cinstT, cinst) th) end;
clasohm@0
   458
clasohm@0
   459
paulson@14394
   460
(** Standard form of object-rule: no hypotheses, flexflex constraints,
paulson@14394
   461
    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
wenzelm@10515
   462
wenzelm@16595
   463
(*Discharge all hypotheses.*)
wenzelm@16595
   464
fun implies_intr_hyps th =
wenzelm@16595
   465
  fold Thm.implies_intr (#hyps (Thm.crep_thm th)) th;
wenzelm@16595
   466
paulson@14394
   467
(*Squash a theorem's flexflex constraints provided it can be done uniquely.
paulson@14394
   468
  This step can lose information.*)
paulson@14387
   469
fun flexflex_unique th =
berghofe@17713
   470
  if null (tpairs_of th) then th else
paulson@14387
   471
    case Seq.chop (2, flexflex_rule th) of
paulson@14387
   472
      ([th],_) => th
paulson@14387
   473
    | ([],_)   => raise THM("flexflex_unique: impossible constraints", 0, [th])
paulson@14387
   474
    |      _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   475
wenzelm@10515
   476
fun close_derivation thm =
wenzelm@10515
   477
  if Thm.get_name_tags thm = ("", []) then Thm.name_thm ("", thm)
wenzelm@10515
   478
  else thm;
wenzelm@10515
   479
wenzelm@16949
   480
val standard' =
wenzelm@16949
   481
  implies_intr_hyps
wenzelm@16949
   482
  #> forall_intr_frees
wenzelm@16949
   483
  #> `(#maxidx o Thm.rep_thm)
wenzelm@16949
   484
  #-> (fn maxidx =>
wenzelm@16949
   485
    forall_elim_vars (maxidx + 1)
wenzelm@16949
   486
    #> strip_shyps_warning
wenzelm@16949
   487
    #> zero_var_indexes
wenzelm@16949
   488
    #> Thm.varifyT
wenzelm@16949
   489
    #> Thm.compress);
wenzelm@1218
   490
wenzelm@16949
   491
val standard =
wenzelm@16949
   492
  flexflex_unique
wenzelm@16949
   493
  #> standard'
wenzelm@16949
   494
  #> close_derivation;
berghofe@11512
   495
wenzelm@16949
   496
val local_standard =
wenzelm@16949
   497
  strip_shyps
wenzelm@16949
   498
  #> zero_var_indexes
wenzelm@16949
   499
  #> Thm.compress
wenzelm@16949
   500
  #> close_derivation;
wenzelm@12005
   501
clasohm@0
   502
wenzelm@8328
   503
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   504
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   505
  Similar code in type/freeze_thaw*)
paulson@15495
   506
paulson@15495
   507
fun freeze_thaw_robust th =
paulson@15495
   508
 let val fth = freezeT th
wenzelm@16425
   509
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@15495
   510
 in
skalberg@15574
   511
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@15495
   512
       [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
paulson@15495
   513
     | vars =>
paulson@15495
   514
         let fun newName (Var(ix,_), pairs) =
paulson@15495
   515
                   let val v = gensym (string_of_indexname ix)
paulson@15495
   516
                   in  ((ix,v)::pairs)  end;
skalberg@15574
   517
             val alist = foldr newName [] vars
paulson@15495
   518
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   519
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   520
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
paulson@15495
   521
             val insts = map mk_inst vars
paulson@15495
   522
             fun thaw i th' = (*i is non-negative increment for Var indexes*)
paulson@15495
   523
                 th' |> forall_intr_list (map #2 insts)
paulson@15495
   524
                     |> forall_elim_list (map (Thm.cterm_incr_indexes i o #1) insts)
paulson@15495
   525
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@15495
   526
 end;
paulson@15495
   527
paulson@15495
   528
(*Basic version of the function above. No option to rename Vars apart in thaw.
paulson@15495
   529
  The Frees created from Vars have nice names.*)
paulson@4610
   530
fun freeze_thaw th =
paulson@7248
   531
 let val fth = freezeT th
wenzelm@16425
   532
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@7248
   533
 in
skalberg@15574
   534
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@7248
   535
       [] => (fth, fn x => x)
paulson@7248
   536
     | vars =>
wenzelm@8328
   537
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@8328
   538
                   let val v = variant used (string_of_indexname ix)
wenzelm@8328
   539
                   in  ((ix,v)::pairs, v::used)  end;
skalberg@15574
   540
             val (alist, _) = foldr newName ([], Library.foldr add_term_names
skalberg@15574
   541
               (prop :: Thm.terms_of_tpairs tpairs, [])) vars
wenzelm@8328
   542
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   543
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   544
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
wenzelm@8328
   545
             val insts = map mk_inst vars
wenzelm@8328
   546
             fun thaw th' =
wenzelm@8328
   547
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   548
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   549
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   550
 end;
paulson@4610
   551
paulson@7248
   552
(*Rotates a rule's premises to the left by k*)
paulson@7248
   553
val rotate_prems = permute_prems 0;
paulson@4610
   554
oheimb@11163
   555
(* permute prems, where the i-th position in the argument list (counting from 0)
oheimb@11163
   556
   gives the position within the original thm to be transferred to position i.
oheimb@11163
   557
   Any remaining trailing positions are left unchanged. *)
oheimb@11163
   558
val rearrange_prems = let
oheimb@11163
   559
  fun rearr new []      thm = thm
wenzelm@11815
   560
  |   rearr new (p::ps) thm = rearr (new+1)
oheimb@11163
   561
     (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
oheimb@11163
   562
     (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
oheimb@11163
   563
  in rearr 0 end;
paulson@4610
   564
wenzelm@252
   565
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   566
  Generalizes over Free variables,
clasohm@0
   567
  creates the assumption, and then strips quantifiers.
clasohm@0
   568
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   569
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   570
fun assume_ax thy sP =
wenzelm@16425
   571
  let val prop = Logic.close_form (term_of (read_cterm thy (sP, propT)))
wenzelm@16425
   572
  in forall_elim_vars 0 (Thm.assume (cterm_of thy prop)) end;
clasohm@0
   573
wenzelm@252
   574
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   575
fun tha RSN (i,thb) =
wenzelm@4270
   576
  case Seq.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   577
      ([th],_) => th
clasohm@0
   578
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   579
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   580
clasohm@0
   581
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   582
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   583
clasohm@0
   584
(*For joining lists of rules*)
wenzelm@252
   585
fun thas RLN (i,thbs) =
clasohm@0
   586
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   587
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
paulson@2672
   588
  in  List.concat (map resb thbs)  end;
clasohm@0
   589
clasohm@0
   590
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   591
lcp@11
   592
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   593
  makes proof trees*)
wenzelm@252
   594
fun rls MRS bottom_rl =
lcp@11
   595
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   596
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   597
  in  rs_aux 1 rls  end;
lcp@11
   598
lcp@11
   599
(*As above, but for rule lists*)
wenzelm@252
   600
fun rlss MRL bottom_rls =
lcp@11
   601
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   602
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   603
  in  rs_aux 1 rlss  end;
lcp@11
   604
wenzelm@9288
   605
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   606
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   607
wenzelm@252
   608
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   609
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   610
  ALWAYS deletes premise i *)
wenzelm@252
   611
fun compose(tha,i,thb) =
wenzelm@4270
   612
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   613
wenzelm@6946
   614
fun compose_single (tha,i,thb) =
wenzelm@6946
   615
  (case compose (tha,i,thb) of
wenzelm@6946
   616
    [th] => th
wenzelm@6946
   617
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   618
clasohm@0
   619
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   620
fun tha COMP thb =
clasohm@0
   621
    case compose(tha,1,thb) of
wenzelm@252
   622
        [th] => th
clasohm@0
   623
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   624
wenzelm@13105
   625
wenzelm@4016
   626
(** theorem equality **)
clasohm@0
   627
wenzelm@16425
   628
(*True if the two theorems have the same theory.*)
wenzelm@16425
   629
val eq_thm_thy = eq_thy o pairself Thm.theory_of_thm;
paulson@13650
   630
paulson@13650
   631
(*True if the two theorems have the same prop field, ignoring hyps, der, etc.*)
wenzelm@16720
   632
val eq_thm_prop = op aconv o pairself Thm.full_prop_of;
clasohm@0
   633
clasohm@0
   634
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   635
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   636
wenzelm@9829
   637
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@13105
   638
fun del_rules rs rules = Library.gen_rems eq_thm_prop (rules, rs);
wenzelm@9862
   639
fun add_rules rs rules = rs @ del_rules rs rules;
wenzelm@12373
   640
val del_rule = del_rules o single;
wenzelm@12373
   641
val add_rule = add_rules o single;
wenzelm@13105
   642
fun merge_rules (rules1, rules2) = gen_merge_lists' eq_thm_prop rules1 rules2;
wenzelm@9829
   643
lcp@1194
   644
(** Mark Staples's weaker version of eq_thm: ignores variable renaming and
lcp@1194
   645
    (some) type variable renaming **)
lcp@1194
   646
lcp@1194
   647
 (* Can't use term_vars, because it sorts the resulting list of variable names.
lcp@1194
   648
    We instead need the unique list noramlised by the order of appearance
lcp@1194
   649
    in the term. *)
lcp@1194
   650
fun term_vars' (t as Var(v,T)) = [t]
lcp@1194
   651
  | term_vars' (Abs(_,_,b)) = term_vars' b
lcp@1194
   652
  | term_vars' (f$a) = (term_vars' f) @ (term_vars' a)
lcp@1194
   653
  | term_vars' _ = [];
lcp@1194
   654
lcp@1194
   655
fun forall_intr_vars th =
wenzelm@16425
   656
  let val {prop,thy,...} = rep_thm th;
lcp@1194
   657
      val vars = distinct (term_vars' prop);
wenzelm@16425
   658
  in forall_intr_list (map (cterm_of thy) vars) th end;
lcp@1194
   659
wenzelm@13105
   660
val weak_eq_thm = Thm.eq_thm o pairself (forall_intr_vars o freezeT);
lcp@1194
   661
lcp@1194
   662
clasohm@0
   663
(*** Meta-Rewriting Rules ***)
clasohm@0
   664
wenzelm@16425
   665
fun read_prop s = read_cterm ProtoPure.thy (s, propT);
paulson@4610
   666
wenzelm@9455
   667
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   668
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@12135
   669
fun store_thm_open name thm = hd (PureThy.smart_store_thms_open (name, [thm]));
wenzelm@12135
   670
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   671
clasohm@0
   672
val reflexive_thm =
wenzelm@16425
   673
  let val cx = cterm_of ProtoPure.thy (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   674
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   675
clasohm@0
   676
val symmetric_thm =
wenzelm@14854
   677
  let val xy = read_prop "x == y"
wenzelm@16595
   678
  in store_standard_thm_open "symmetric" (Thm.implies_intr xy (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   679
clasohm@0
   680
val transitive_thm =
wenzelm@14854
   681
  let val xy = read_prop "x == y"
wenzelm@14854
   682
      val yz = read_prop "y == z"
clasohm@0
   683
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   684
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   685
nipkow@4679
   686
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   687
berghofe@11512
   688
fun extensional eq =
berghofe@11512
   689
  let val eq' =
berghofe@11512
   690
    abstract_rule "x" (snd (Thm.dest_comb (fst (dest_equals (cprop_of eq))))) eq
berghofe@11512
   691
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   692
berghofe@10414
   693
val imp_cong =
berghofe@10414
   694
  let
berghofe@10414
   695
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   696
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   697
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   698
    val A = read_prop "PROP A"
berghofe@10414
   699
  in
wenzelm@12135
   700
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   701
      (implies_intr AB (implies_intr A
berghofe@10414
   702
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   703
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   704
      (implies_intr AC (implies_intr A
berghofe@10414
   705
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   706
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   707
  end;
berghofe@10414
   708
berghofe@10414
   709
val swap_prems_eq =
berghofe@10414
   710
  let
berghofe@10414
   711
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   712
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   713
    val A = read_prop "PROP A"
berghofe@10414
   714
    val B = read_prop "PROP B"
berghofe@10414
   715
  in
wenzelm@12135
   716
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   717
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   718
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   719
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   720
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   721
  end;
lcp@229
   722
skalberg@15001
   723
val imp_cong' = combination o combination (reflexive implies)
clasohm@0
   724
berghofe@13325
   725
fun abs_def thm =
berghofe@13325
   726
  let
berghofe@13325
   727
    val (_, cvs) = strip_comb (fst (dest_equals (cprop_of thm)));
skalberg@15574
   728
    val thm' = foldr (fn (ct, thm) => Thm.abstract_rule
berghofe@13325
   729
      (case term_of ct of Var ((a, _), _) => a | Free (a, _) => a | _ => "x")
skalberg@15574
   730
        ct thm) thm cvs
berghofe@13325
   731
  in transitive
berghofe@13325
   732
    (symmetric (eta_conversion (fst (dest_equals (cprop_of thm'))))) thm'
berghofe@13325
   733
  end;
berghofe@13325
   734
clasohm@0
   735
skalberg@15001
   736
local
skalberg@15001
   737
  val dest_eq = dest_equals o cprop_of
skalberg@15001
   738
  val rhs_of = snd o dest_eq
skalberg@15001
   739
in
skalberg@15001
   740
fun beta_eta_conversion t =
skalberg@15001
   741
  let val thm = beta_conversion true t
skalberg@15001
   742
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   743
end;
skalberg@15001
   744
berghofe@15925
   745
fun eta_long_conversion ct = transitive (beta_eta_conversion ct)
berghofe@15925
   746
  (symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
berghofe@15925
   747
skalberg@15001
   748
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
skalberg@15001
   749
fun goals_conv pred cv =
skalberg@15001
   750
  let fun gconv i ct =
skalberg@15001
   751
        let val (A,B) = dest_implies ct
skalberg@15001
   752
        in imp_cong' (if pred i then cv A else reflexive A) (gconv (i+1) B) end
skalberg@15001
   753
        handle TERM _ => reflexive ct
skalberg@15001
   754
  in gconv 1 end
skalberg@15001
   755
skalberg@15001
   756
(* Rewrite A in !!x1,...,xn. A *)
skalberg@15001
   757
fun forall_conv cv ct =
skalberg@15001
   758
  let val p as (ct1, ct2) = Thm.dest_comb ct
skalberg@15001
   759
  in (case pairself term_of p of
skalberg@15001
   760
      (Const ("all", _), Abs (s, _, _)) =>
wenzelm@16682
   761
         let val (v, ct') = Thm.dest_abs (SOME (gensym "all_")) ct2;
skalberg@15001
   762
         in Thm.combination (Thm.reflexive ct1)
skalberg@15001
   763
           (Thm.abstract_rule s v (forall_conv cv ct'))
skalberg@15001
   764
         end
skalberg@15001
   765
    | _ => cv ct)
skalberg@15001
   766
  end handle TERM _ => cv ct;
skalberg@15001
   767
skalberg@15001
   768
(*Use a conversion to transform a theorem*)
skalberg@15001
   769
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
skalberg@15001
   770
wenzelm@15669
   771
(*** Some useful meta-theorems ***)
clasohm@0
   772
clasohm@0
   773
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@12135
   774
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   775
val _ = store_thm "_" asm_rl;
clasohm@0
   776
clasohm@0
   777
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   778
val cut_rl =
wenzelm@12135
   779
  store_standard_thm_open "cut_rl"
wenzelm@9455
   780
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   781
wenzelm@252
   782
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   783
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   784
val revcut_rl =
paulson@4610
   785
  let val V = read_prop "PROP V"
paulson@4610
   786
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   787
  in
wenzelm@12135
   788
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   789
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   790
  end;
clasohm@0
   791
lcp@668
   792
(*for deleting an unwanted assumption*)
lcp@668
   793
val thin_rl =
paulson@4610
   794
  let val V = read_prop "PROP V"
paulson@4610
   795
      and W = read_prop "PROP W";
wenzelm@12135
   796
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   797
clasohm@0
   798
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   799
val triv_forall_equality =
paulson@4610
   800
  let val V  = read_prop "PROP V"
paulson@4610
   801
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@16425
   802
      and x  = read_cterm ProtoPure.thy ("x", TypeInfer.logicT);
wenzelm@4016
   803
  in
wenzelm@12135
   804
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   805
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   806
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   807
  end;
clasohm@0
   808
nipkow@1756
   809
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   810
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   811
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   812
*)
nipkow@1756
   813
val swap_prems_rl =
paulson@4610
   814
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   815
      val major = assume cmajor;
paulson@4610
   816
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   817
      val minor1 = assume cminor1;
paulson@4610
   818
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   819
      val minor2 = assume cminor2;
wenzelm@12135
   820
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   821
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   822
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   823
  end;
nipkow@1756
   824
nipkow@3653
   825
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   826
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   827
   Introduction rule for == as a meta-theorem.
nipkow@3653
   828
*)
nipkow@3653
   829
val equal_intr_rule =
paulson@4610
   830
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   831
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   832
  in
wenzelm@12135
   833
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   834
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   835
  end;
nipkow@3653
   836
wenzelm@13368
   837
(* [| PROP ?phi == PROP ?psi; PROP ?phi |] ==> PROP ?psi *)
wenzelm@13368
   838
val equal_elim_rule1 =
wenzelm@13368
   839
  let val eq = read_prop "PROP phi == PROP psi"
wenzelm@13368
   840
      and P = read_prop "PROP phi"
wenzelm@13368
   841
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   842
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   843
  end;
wenzelm@4285
   844
wenzelm@12297
   845
(* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
wenzelm@12297
   846
wenzelm@12297
   847
val remdups_rl =
wenzelm@12297
   848
  let val P = read_prop "PROP phi" and Q = read_prop "PROP psi";
wenzelm@12297
   849
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   850
wenzelm@12297
   851
wenzelm@9554
   852
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@12297
   853
  Rewrite rule for HHF normalization.*)
wenzelm@9554
   854
wenzelm@9554
   855
val norm_hhf_eq =
wenzelm@9554
   856
  let
wenzelm@16425
   857
    val cert = Thm.cterm_of ProtoPure.thy;
wenzelm@14854
   858
    val aT = TFree ("'a", []);
wenzelm@9554
   859
    val all = Term.all aT;
wenzelm@9554
   860
    val x = Free ("x", aT);
wenzelm@9554
   861
    val phi = Free ("phi", propT);
wenzelm@9554
   862
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   863
wenzelm@9554
   864
    val cx = cert x;
wenzelm@9554
   865
    val cphi = cert phi;
wenzelm@9554
   866
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   867
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   868
  in
wenzelm@9554
   869
    Thm.equal_intr
wenzelm@9554
   870
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   871
        |> Thm.forall_elim cx
wenzelm@9554
   872
        |> Thm.implies_intr cphi
wenzelm@9554
   873
        |> Thm.forall_intr cx
wenzelm@9554
   874
        |> Thm.implies_intr lhs)
wenzelm@9554
   875
      (Thm.implies_elim
wenzelm@9554
   876
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   877
        |> Thm.forall_intr cx
wenzelm@9554
   878
        |> Thm.implies_intr cphi
wenzelm@9554
   879
        |> Thm.implies_intr rhs)
wenzelm@12135
   880
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   881
  end;
wenzelm@9554
   882
wenzelm@18179
   883
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@18179
   884
wenzelm@12800
   885
fun is_norm_hhf tm =
wenzelm@12800
   886
  let
wenzelm@12800
   887
    fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@12800
   888
      | is_norm (t $ u) = is_norm t andalso is_norm u
wenzelm@12800
   889
      | is_norm (Abs (_, _, t)) = is_norm t
wenzelm@12800
   890
      | is_norm _ = true;
wenzelm@12800
   891
  in is_norm (Pattern.beta_eta_contract tm) end;
wenzelm@12800
   892
wenzelm@16425
   893
fun norm_hhf thy t =
wenzelm@12800
   894
  if is_norm_hhf t then t
wenzelm@18179
   895
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   896
wenzelm@12800
   897
wenzelm@9554
   898
wenzelm@16425
   899
(*** Instantiate theorem th, reading instantiations in theory thy ****)
paulson@8129
   900
paulson@8129
   901
(*Version that normalizes the result: Thm.instantiate no longer does that*)
paulson@8129
   902
fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
paulson@8129
   903
wenzelm@16425
   904
fun read_instantiate_sg' thy sinsts th =
paulson@8129
   905
    let val ts = types_sorts th;
wenzelm@15669
   906
        val used = add_used th [];
wenzelm@16425
   907
    in  instantiate (read_insts thy ts ts used sinsts) th  end;
berghofe@15797
   908
wenzelm@16425
   909
fun read_instantiate_sg thy sinsts th =
wenzelm@16425
   910
  read_instantiate_sg' thy (map (apfst Syntax.indexname) sinsts) th;
paulson@8129
   911
paulson@8129
   912
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   913
fun read_instantiate sinsts th =
wenzelm@16425
   914
    read_instantiate_sg (Thm.theory_of_thm th) sinsts th;
paulson@8129
   915
berghofe@15797
   916
fun read_instantiate' sinsts th =
wenzelm@16425
   917
    read_instantiate_sg' (Thm.theory_of_thm th) sinsts th;
berghofe@15797
   918
paulson@8129
   919
paulson@8129
   920
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   921
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   922
local
wenzelm@16425
   923
  fun add_types ((ct,cu), (thy,tye,maxidx)) =
wenzelm@16425
   924
    let val {thy=thyt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
wenzelm@16425
   925
        and {thy=thyu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   926
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
wenzelm@16425
   927
        val thy' = Theory.merge(thy, Theory.merge(thyt, thyu))
wenzelm@16949
   928
        val (tye',maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
wenzelm@10403
   929
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
wenzelm@16425
   930
    in  (thy', tye', maxi')  end;
paulson@8129
   931
in
paulson@8129
   932
fun cterm_instantiate ctpairs0 th =
wenzelm@16425
   933
  let val (thy,tye,_) = foldr add_types (Thm.theory_of_thm th, Vartab.empty, 0) ctpairs0
wenzelm@18179
   934
      fun instT(ct,cu) =
wenzelm@16425
   935
        let val inst = cterm_of thy o Envir.subst_TVars tye o term_of
paulson@14340
   936
        in (inst ct, inst cu) end
wenzelm@16425
   937
      fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy T)
berghofe@8406
   938
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   939
  handle TERM _ =>
wenzelm@16425
   940
           raise THM("cterm_instantiate: incompatible theories",0,[th])
paulson@8129
   941
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   942
end;
paulson@8129
   943
paulson@8129
   944
paulson@8129
   945
(** Derived rules mainly for METAHYPS **)
paulson@8129
   946
paulson@8129
   947
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
paulson@8129
   948
fun equal_abs_elim ca eqth =
wenzelm@16425
   949
  let val {thy=thya, t=a, ...} = rep_cterm ca
paulson@8129
   950
      and combth = combination eqth (reflexive ca)
wenzelm@16425
   951
      val {thy,prop,...} = rep_thm eqth
paulson@8129
   952
      val (abst,absu) = Logic.dest_equals prop
wenzelm@16425
   953
      val cterm = cterm_of (Theory.merge (thy,thya))
berghofe@10414
   954
  in  transitive (symmetric (beta_conversion false (cterm (abst$a))))
berghofe@10414
   955
           (transitive combth (beta_conversion false (cterm (absu$a))))
paulson@8129
   956
  end
paulson@8129
   957
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
paulson@8129
   958
paulson@8129
   959
(*Calling equal_abs_elim with multiple terms*)
skalberg@15574
   960
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) th (rev cts);
paulson@8129
   961
paulson@8129
   962
wenzelm@18025
   963
(** protected propositions **)
wenzelm@4789
   964
wenzelm@4789
   965
local
wenzelm@16425
   966
  val cert = Thm.cterm_of ProtoPure.thy;
wenzelm@18025
   967
  val A = cert (Free ("A", propT));
wenzelm@18025
   968
  val prop_def = #1 (freeze_thaw ProtoPure.prop_def);
wenzelm@4789
   969
in
wenzelm@18025
   970
  val protect = Thm.capply (cert Logic.protectC);
wenzelm@18025
   971
  val protectI = store_thm "protectI" (kind_rule internalK (standard
wenzelm@18025
   972
      (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A))));
wenzelm@18025
   973
  val protectD = store_thm "protectD" (kind_rule internalK (standard
wenzelm@18025
   974
      (Thm.equal_elim prop_def (Thm.assume (protect A)))));
wenzelm@18179
   975
  val protect_cong = store_standard_thm_open "protect_cong" (Thm.reflexive (protect A));
wenzelm@4789
   976
end;
wenzelm@4789
   977
wenzelm@18025
   978
fun implies_intr_protected asms th =
wenzelm@18118
   979
  let val asms' = map protect asms in
wenzelm@18118
   980
    implies_elim_list
wenzelm@18118
   981
      (implies_intr_list asms th)
wenzelm@18118
   982
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@18118
   983
    |> implies_intr_list asms'
wenzelm@18118
   984
  end;
wenzelm@11815
   985
wenzelm@4789
   986
wenzelm@5688
   987
(** variations on instantiate **)
wenzelm@4285
   988
paulson@8550
   989
(*shorthand for instantiating just one variable in the current theory*)
wenzelm@16425
   990
fun inst x t = read_instantiate_sg (the_context()) [(x,t)];
paulson@8550
   991
paulson@8550
   992
wenzelm@4285
   993
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   994
wenzelm@4285
   995
fun instantiate' cTs cts thm =
wenzelm@4285
   996
  let
wenzelm@4285
   997
    fun err msg =
wenzelm@4285
   998
      raise TYPE ("instantiate': " ^ msg,
skalberg@15570
   999
        List.mapPartial (Option.map Thm.typ_of) cTs,
skalberg@15570
  1000
        List.mapPartial (Option.map Thm.term_of) cts);
wenzelm@4285
  1001
wenzelm@4285
  1002
    fun inst_of (v, ct) =
wenzelm@16425
  1003
      (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
  1004
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
  1005
berghofe@15797
  1006
    fun tyinst_of (v, cT) =
wenzelm@16425
  1007
      (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
  1008
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
  1009
wenzelm@4285
  1010
    fun zip_vars _ [] = []
skalberg@15531
  1011
      | zip_vars (_ :: vs) (NONE :: opt_ts) = zip_vars vs opt_ts
skalberg@15531
  1012
      | zip_vars (v :: vs) (SOME t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
wenzelm@4285
  1013
      | zip_vars [] _ = err "more instantiations than variables in thm";
wenzelm@4285
  1014
wenzelm@4285
  1015
    (*instantiate types first!*)
wenzelm@4285
  1016
    val thm' =
wenzelm@4285
  1017
      if forall is_none cTs then thm
berghofe@15797
  1018
      else Thm.instantiate (map tyinst_of (zip_vars (tvars_of thm) cTs), []) thm;
wenzelm@4285
  1019
    in
wenzelm@4285
  1020
      if forall is_none cts then thm'
wenzelm@4285
  1021
      else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
wenzelm@4285
  1022
    end;
wenzelm@4285
  1023
wenzelm@4285
  1024
berghofe@14081
  1025
berghofe@14081
  1026
(** renaming of bound variables **)
berghofe@14081
  1027
berghofe@14081
  1028
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
  1029
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
  1030
berghofe@14081
  1031
fun rename_bvars [] thm = thm
berghofe@14081
  1032
  | rename_bvars vs thm =
berghofe@14081
  1033
    let
wenzelm@16425
  1034
      val {thy, prop, ...} = rep_thm thm;
haftmann@17325
  1035
      fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
berghofe@14081
  1036
        | ren (t $ u) = ren t $ ren u
berghofe@14081
  1037
        | ren t = t;
wenzelm@16425
  1038
    in equal_elim (reflexive (cterm_of thy (ren prop))) thm end;
berghofe@14081
  1039
berghofe@14081
  1040
berghofe@14081
  1041
(* renaming in left-to-right order *)
berghofe@14081
  1042
berghofe@14081
  1043
fun rename_bvars' xs thm =
berghofe@14081
  1044
  let
wenzelm@16425
  1045
    val {thy, prop, ...} = rep_thm thm;
berghofe@14081
  1046
    fun rename [] t = ([], t)
berghofe@14081
  1047
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
  1048
          let val (xs', t') = rename xs t
skalberg@15570
  1049
          in (xs', Abs (getOpt (x',x), T, t')) end
berghofe@14081
  1050
      | rename xs (t $ u) =
berghofe@14081
  1051
          let
berghofe@14081
  1052
            val (xs', t') = rename xs t;
berghofe@14081
  1053
            val (xs'', u') = rename xs' u
berghofe@14081
  1054
          in (xs'', t' $ u') end
berghofe@14081
  1055
      | rename xs t = (xs, t);
berghofe@14081
  1056
  in case rename xs prop of
wenzelm@16425
  1057
      ([], prop') => equal_elim (reflexive (cterm_of thy prop')) thm
berghofe@14081
  1058
    | _ => error "More names than abstractions in theorem"
berghofe@14081
  1059
  end;
berghofe@14081
  1060
berghofe@14081
  1061
berghofe@14081
  1062
wenzelm@5688
  1063
(* unvarify(T) *)
wenzelm@5688
  1064
wenzelm@5688
  1065
(*assume thm in standard form, i.e. no frees, 0 var indexes*)
wenzelm@5688
  1066
wenzelm@5688
  1067
fun unvarifyT thm =
wenzelm@5688
  1068
  let
wenzelm@16425
  1069
    val cT = Thm.ctyp_of (Thm.theory_of_thm thm);
skalberg@15531
  1070
    val tfrees = map (fn ((x, _), S) => SOME (cT (TFree (x, S)))) (tvars_of thm);
wenzelm@5688
  1071
  in instantiate' tfrees [] thm end;
wenzelm@5688
  1072
wenzelm@5688
  1073
fun unvarify raw_thm =
wenzelm@5688
  1074
  let
wenzelm@5688
  1075
    val thm = unvarifyT raw_thm;
wenzelm@16425
  1076
    val ct = Thm.cterm_of (Thm.theory_of_thm thm);
skalberg@15531
  1077
    val frees = map (fn ((x, _), T) => SOME (ct (Free (x, T)))) (vars_of thm);
wenzelm@5688
  1078
  in instantiate' [] frees thm end;
wenzelm@5688
  1079
wenzelm@5688
  1080
wenzelm@8605
  1081
(* tvars_intr_list *)
wenzelm@8605
  1082
wenzelm@8605
  1083
fun tvars_intr_list tfrees thm =
wenzelm@18129
  1084
  apfst (map (fn ((s, S), ixn) => (s, (ixn, S)))) (Thm.varifyT'
berghofe@15797
  1085
    (gen_rems (op = o apfst fst) (tfrees_of thm, tfrees)) thm);
wenzelm@8605
  1086
wenzelm@8605
  1087
wenzelm@6435
  1088
(* increment var indexes *)
wenzelm@6435
  1089
wenzelm@18025
  1090
fun incr_indexes th = Thm.incr_indexes (#maxidx (Thm.rep_thm th) + 1);
wenzelm@18025
  1091
wenzelm@6435
  1092
fun incr_indexes_wrt is cTs cts thms =
wenzelm@6435
  1093
  let
wenzelm@6435
  1094
    val maxidx =
skalberg@15570
  1095
      Library.foldl Int.max (~1, is @
wenzelm@6435
  1096
        map (maxidx_of_typ o #T o Thm.rep_ctyp) cTs @
wenzelm@6435
  1097
        map (#maxidx o Thm.rep_cterm) cts @
wenzelm@6435
  1098
        map (#maxidx o Thm.rep_thm) thms);
berghofe@10414
  1099
  in Thm.incr_indexes (maxidx + 1) end;
wenzelm@6435
  1100
wenzelm@6435
  1101
wenzelm@8328
  1102
(* freeze_all *)
wenzelm@8328
  1103
wenzelm@8328
  1104
(*freeze all (T)Vars; assumes thm in standard form*)
wenzelm@8328
  1105
wenzelm@8328
  1106
fun freeze_all_TVars thm =
wenzelm@8328
  1107
  (case tvars_of thm of
wenzelm@8328
  1108
    [] => thm
wenzelm@8328
  1109
  | tvars =>
wenzelm@16425
  1110
      let val cert = Thm.ctyp_of (Thm.theory_of_thm thm)
skalberg@15531
  1111
      in instantiate' (map (fn ((x, _), S) => SOME (cert (TFree (x, S)))) tvars) [] thm end);
wenzelm@8328
  1112
wenzelm@8328
  1113
fun freeze_all_Vars thm =
wenzelm@8328
  1114
  (case vars_of thm of
wenzelm@8328
  1115
    [] => thm
wenzelm@8328
  1116
  | vars =>
wenzelm@16425
  1117
      let val cert = Thm.cterm_of (Thm.theory_of_thm thm)
skalberg@15531
  1118
      in instantiate' [] (map (fn ((x, _), T) => SOME (cert (Free (x, T)))) vars) thm end);
wenzelm@8328
  1119
wenzelm@8328
  1120
val freeze_all = freeze_all_Vars o freeze_all_TVars;
wenzelm@8328
  1121
wenzelm@8328
  1122
wenzelm@11975
  1123
wenzelm@11975
  1124
(** meta-level conjunction **)
wenzelm@11975
  1125
wenzelm@11975
  1126
local
wenzelm@11975
  1127
  val A = read_prop "PROP A";
wenzelm@11975
  1128
  val B = read_prop "PROP B";
wenzelm@11975
  1129
  val C = read_prop "PROP C";
wenzelm@18179
  1130
  val D = read_prop "PROP D";
wenzelm@18179
  1131
  val AC = read_prop "PROP A ==> PROP C";
wenzelm@18179
  1132
  val BD = read_prop "PROP B ==> PROP D";
wenzelm@11975
  1133
  val ABC = read_prop "PROP A ==> PROP B ==> PROP C";
wenzelm@18179
  1134
  val A_B = read_prop "!!X. (PROP A ==> PROP B ==> PROP X) ==> PROP X";
wenzelm@11975
  1135
wenzelm@11975
  1136
  val proj1 =
wenzelm@11975
  1137
    forall_intr_list [A, B] (implies_intr_list [A, B] (Thm.assume A))
wenzelm@11975
  1138
    |> forall_elim_vars 0;
wenzelm@11975
  1139
wenzelm@11975
  1140
  val proj2 =
wenzelm@11975
  1141
    forall_intr_list [A, B] (implies_intr_list [A, B] (Thm.assume B))
wenzelm@11975
  1142
    |> forall_elim_vars 0;
wenzelm@11975
  1143
wenzelm@11975
  1144
  val conj_intr_rule =
wenzelm@11975
  1145
    forall_intr_list [A, B] (implies_intr_list [A, B]
wenzelm@11975
  1146
      (Thm.forall_intr C (Thm.implies_intr ABC
wenzelm@11975
  1147
        (implies_elim_list (Thm.assume ABC) [Thm.assume A, Thm.assume B]))))
wenzelm@11975
  1148
    |> forall_elim_vars 0;
wenzelm@11975
  1149
in
wenzelm@11975
  1150
wenzelm@18025
  1151
fun conj_intr tha thb = thb COMP (tha COMP incr_indexes_wrt [] [] [] [tha, thb] conj_intr_rule);
wenzelm@12756
  1152
wenzelm@12756
  1153
fun conj_intr_list [] = asm_rl
wenzelm@12756
  1154
  | conj_intr_list ths = foldr1 (uncurry conj_intr) ths;
wenzelm@11975
  1155
wenzelm@11975
  1156
fun conj_elim th =
wenzelm@11975
  1157
  let val th' = forall_elim_var (#maxidx (Thm.rep_thm th) + 1) th
wenzelm@18025
  1158
  in (incr_indexes th' proj1 COMP th', incr_indexes th' proj2 COMP th') end;
wenzelm@11975
  1159
wenzelm@11975
  1160
fun conj_elim_list th =
wenzelm@11975
  1161
  let val (th1, th2) = conj_elim th
wenzelm@11975
  1162
  in conj_elim_list th1 @ conj_elim_list th2 end handle THM _ => [th];
wenzelm@11975
  1163
wenzelm@12756
  1164
fun conj_elim_precise 0 _ = []
wenzelm@12756
  1165
  | conj_elim_precise 1 th = [th]
wenzelm@12135
  1166
  | conj_elim_precise n th =
wenzelm@12135
  1167
      let val (th1, th2) = conj_elim th
wenzelm@12135
  1168
      in th1 :: conj_elim_precise (n - 1) th2 end;
wenzelm@12135
  1169
wenzelm@12135
  1170
val conj_intr_thm = store_standard_thm_open "conjunctionI"
wenzelm@12135
  1171
  (implies_intr_list [A, B] (conj_intr (Thm.assume A) (Thm.assume B)));
wenzelm@12135
  1172
wenzelm@18179
  1173
val conj_mono_thm = store_standard_thm_open "conjunction_mono"
wenzelm@18179
  1174
  (Thm.assume A_B |> conj_elim |> (fn (a, b) =>
wenzelm@18179
  1175
    conj_intr
wenzelm@18179
  1176
      (Thm.implies_elim (Thm.assume AC) a)
wenzelm@18179
  1177
      (Thm.implies_elim (Thm.assume BD) b))
wenzelm@18179
  1178
  |> implies_intr_list [AC, BD, A_B]);
wenzelm@18179
  1179
clasohm@0
  1180
end;
wenzelm@252
  1181
wenzelm@11975
  1182
end;
wenzelm@5903
  1183
wenzelm@5903
  1184
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
  1185
open BasicDrule;