src/Pure/drule.ML
author wenzelm
Mon Jun 05 21:54:21 2006 +0200 (2006-06-05)
changeset 19775 06cb6743adf6
parent 19753 b345d4e70ca9
child 19842 04120bdac80e
permissions -rw-r--r--
support embedded terms;
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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: 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 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: (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 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 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 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 inst: string -> string -> thm -> 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 dest_binop: cterm -> cterm * cterm
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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 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 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 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 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 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 sort_triv: theory -> typ * sort -> thm list
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  val unconstrainTs: thm -> thm
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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 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_binop ct =
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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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fun dest_implies ct =
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  (case Thm.term_of ct of
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    (Const ("==>", _) $ _ $ _) => dest_binop ct
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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 ("==", _) $ _ $ _) => dest_binop ct
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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 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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    #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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        val vars = map dest_Var (term_vars big);
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        val frees = map dest_Free (term_frees big);
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        val tvars = term_tvars big;
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        val tfrees = term_tfrees big;
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        fun typ(a,i) = if i<0 then AList.lookup (op =) frees a else AList.lookup (op =) vars (a,i);
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        fun sort(a,i) = if i<0 then AList.lookup (op =) tfrees a else AList.lookup (op =) tvars (a,i);
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    in (typ,sort) end;
clasohm@0
   303
wenzelm@15669
   304
fun add_used thm used =
wenzelm@15669
   305
  let val {prop, hyps, tpairs, ...} = Thm.rep_thm thm in
wenzelm@15669
   306
    add_term_tvarnames (prop, used)
wenzelm@15669
   307
    |> fold (curry add_term_tvarnames) hyps
wenzelm@15669
   308
    |> fold (curry add_term_tvarnames) (Thm.terms_of_tpairs tpairs)
wenzelm@15669
   309
  end;
wenzelm@15669
   310
wenzelm@7636
   311
wenzelm@9455
   312
clasohm@0
   313
(** Standardization of rules **)
clasohm@0
   314
wenzelm@18025
   315
(*vars in left-to-right order*)
wenzelm@18025
   316
fun tvars_of_terms ts = rev (fold Term.add_tvars ts []);
wenzelm@18025
   317
fun vars_of_terms ts = rev (fold Term.add_vars ts []);
wenzelm@18025
   318
fun tvars_of thm = tvars_of_terms [Thm.full_prop_of thm];
wenzelm@18025
   319
fun vars_of thm = vars_of_terms [Thm.full_prop_of thm];
wenzelm@18025
   320
wenzelm@18129
   321
fun fold_terms f th =
wenzelm@18129
   322
  let val {hyps, tpairs, prop, ...} = Thm.rep_thm th
wenzelm@18129
   323
  in f prop #> fold (fn (t, u) => f t #> f u) tpairs #> fold f hyps end;
wenzelm@18129
   324
wenzelm@18129
   325
fun tfrees_of th = rev (fold_terms Term.add_tfrees th []);
wenzelm@18129
   326
fun frees_of th = rev (fold_terms Term.add_frees th []);
wenzelm@18129
   327
wenzelm@19523
   328
wenzelm@19523
   329
(* type classes and sorts *)
wenzelm@19523
   330
wenzelm@19523
   331
fun sort_triv thy (T, S) =
wenzelm@19523
   332
  let
wenzelm@19523
   333
    val certT = Thm.ctyp_of thy;
wenzelm@19523
   334
    val cT = certT T;
wenzelm@19523
   335
    fun class_triv c =
wenzelm@19523
   336
      Thm.class_triv thy c
wenzelm@19523
   337
      |> Thm.instantiate ([(certT (TVar (("'a", 0), [c])), cT)], []);
wenzelm@19523
   338
  in map class_triv S end;
wenzelm@19523
   339
wenzelm@19504
   340
fun unconstrainTs th =
wenzelm@19504
   341
  fold_rev (Thm.unconstrainT o Thm.ctyp_of (Thm.theory_of_thm th) o TVar) (tvars_of th) th;
wenzelm@19504
   342
wenzelm@7636
   343
fun strip_shyps_warning thm =
wenzelm@7636
   344
  let
wenzelm@16425
   345
    val str_of_sort = Pretty.str_of o Sign.pretty_sort (Thm.theory_of_thm thm);
wenzelm@7636
   346
    val thm' = Thm.strip_shyps thm;
wenzelm@7636
   347
    val xshyps = Thm.extra_shyps thm';
wenzelm@7636
   348
  in
wenzelm@7636
   349
    if null xshyps then ()
wenzelm@7636
   350
    else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
wenzelm@7636
   351
    thm'
wenzelm@7636
   352
  end;
wenzelm@7636
   353
wenzelm@19730
   354
(*Generalization over a list of variables*)
wenzelm@19730
   355
val forall_intr_list = fold_rev forall_intr;
clasohm@0
   356
clasohm@0
   357
(*Generalization over all suitable Free variables*)
clasohm@0
   358
fun forall_intr_frees th =
wenzelm@19730
   359
    let
wenzelm@19730
   360
      val {prop, hyps, tpairs, thy,...} = rep_thm th;
wenzelm@19730
   361
      val fixed = fold Term.add_frees (Thm.terms_of_tpairs tpairs @ hyps) [];
wenzelm@19730
   362
      val frees = Term.fold_aterms (fn Free v =>
wenzelm@19730
   363
        if member (op =) fixed v then I else insert (op =) v | _ => I) prop [];
wenzelm@19730
   364
    in fold (forall_intr o cterm_of thy o Free) frees th end;
clasohm@0
   365
wenzelm@18535
   366
(*Generalization over Vars -- canonical order*)
wenzelm@18535
   367
fun forall_intr_vars th =
wenzelm@18535
   368
  let val cert = Thm.cterm_of (Thm.theory_of_thm th)
wenzelm@18535
   369
  in forall_intr_list (map (cert o Var) (vars_of th)) th end;
wenzelm@18535
   370
wenzelm@7898
   371
val forall_elim_var = PureThy.forall_elim_var;
wenzelm@7898
   372
val forall_elim_vars = PureThy.forall_elim_vars;
clasohm@0
   373
wenzelm@18025
   374
fun outer_params t =
wenzelm@18025
   375
  let
wenzelm@18025
   376
    val vs = Term.strip_all_vars t;
wenzelm@18375
   377
    val xs = Term.variantlist (map (perhaps (try Syntax.dest_skolem) o #1) vs, []);
wenzelm@18025
   378
  in xs ~~ map #2 vs end;
wenzelm@18025
   379
wenzelm@18025
   380
(*generalize outermost parameters*)
wenzelm@18025
   381
fun gen_all th =
wenzelm@12719
   382
  let
wenzelm@18025
   383
    val {thy, prop, maxidx, ...} = Thm.rep_thm th;
wenzelm@18025
   384
    val cert = Thm.cterm_of thy;
wenzelm@18025
   385
    fun elim (x, T) = Thm.forall_elim (cert (Var ((x, maxidx + 1), T)));
wenzelm@18025
   386
  in fold elim (outer_params prop) th end;
wenzelm@18025
   387
wenzelm@18025
   388
(*lift vars wrt. outermost goal parameters
wenzelm@18118
   389
  -- reverses the effect of gen_all modulo higher-order unification*)
wenzelm@18025
   390
fun lift_all goal th =
wenzelm@18025
   391
  let
wenzelm@18025
   392
    val thy = Theory.merge (Thm.theory_of_cterm goal, Thm.theory_of_thm th);
wenzelm@18025
   393
    val cert = Thm.cterm_of thy;
wenzelm@19421
   394
    val maxidx = Thm.maxidx_of th;
wenzelm@18025
   395
    val ps = outer_params (Thm.term_of goal)
wenzelm@18025
   396
      |> map (fn (x, T) => Var ((x, maxidx + 1), Logic.incr_tvar (maxidx + 1) T));
wenzelm@18025
   397
    val Ts = map Term.fastype_of ps;
wenzelm@18025
   398
    val inst = vars_of th |> map (fn (xi, T) =>
wenzelm@18025
   399
      (cert (Var (xi, T)), cert (Term.list_comb (Var (xi, Ts ---> T), ps))));
wenzelm@18025
   400
  in
wenzelm@18025
   401
    th |> Thm.instantiate ([], inst)
wenzelm@18025
   402
    |> fold_rev (Thm.forall_intr o cert) ps
wenzelm@18025
   403
  end;
wenzelm@18025
   404
wenzelm@9554
   405
wenzelm@16949
   406
(*specialization over a list of cterms*)
wenzelm@16949
   407
val forall_elim_list = fold forall_elim;
clasohm@0
   408
wenzelm@16949
   409
(*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
wenzelm@16949
   410
val implies_intr_list = fold_rev implies_intr;
clasohm@0
   411
wenzelm@16949
   412
(*maps [| A1;...;An |] ==> B and [A1,...,An]  to  B*)
skalberg@15570
   413
fun implies_elim_list impth ths = Library.foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   414
clasohm@0
   415
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@252
   416
fun zero_var_indexes th =
wenzelm@16949
   417
  let
wenzelm@16949
   418
    val thy = Thm.theory_of_thm th;
wenzelm@16949
   419
    val certT = Thm.ctyp_of thy and cert = Thm.cterm_of thy;
wenzelm@16949
   420
    val (instT, inst) = Term.zero_var_indexes_inst (Thm.full_prop_of th);
wenzelm@16949
   421
    val cinstT = map (fn (v, T) => (certT (TVar v), certT T)) instT;
wenzelm@16949
   422
    val cinst = map (fn (v, t) => (cert (Var v), cert t)) inst;
wenzelm@16949
   423
  in Thm.adjust_maxidx_thm (Thm.instantiate (cinstT, cinst) th) end;
clasohm@0
   424
clasohm@0
   425
paulson@14394
   426
(** Standard form of object-rule: no hypotheses, flexflex constraints,
paulson@14394
   427
    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
wenzelm@10515
   428
wenzelm@16595
   429
(*Discharge all hypotheses.*)
wenzelm@16595
   430
fun implies_intr_hyps th =
wenzelm@16595
   431
  fold Thm.implies_intr (#hyps (Thm.crep_thm th)) th;
wenzelm@16595
   432
paulson@14394
   433
(*Squash a theorem's flexflex constraints provided it can be done uniquely.
paulson@14394
   434
  This step can lose information.*)
paulson@14387
   435
fun flexflex_unique th =
berghofe@17713
   436
  if null (tpairs_of th) then th else
paulson@14387
   437
    case Seq.chop (2, flexflex_rule th) of
paulson@14387
   438
      ([th],_) => th
paulson@14387
   439
    | ([],_)   => raise THM("flexflex_unique: impossible constraints", 0, [th])
paulson@14387
   440
    |      _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   441
wenzelm@10515
   442
fun close_derivation thm =
wenzelm@10515
   443
  if Thm.get_name_tags thm = ("", []) then Thm.name_thm ("", thm)
wenzelm@10515
   444
  else thm;
wenzelm@10515
   445
wenzelm@16949
   446
val standard' =
wenzelm@16949
   447
  implies_intr_hyps
wenzelm@16949
   448
  #> forall_intr_frees
wenzelm@19421
   449
  #> `Thm.maxidx_of
wenzelm@16949
   450
  #-> (fn maxidx =>
wenzelm@16949
   451
    forall_elim_vars (maxidx + 1)
wenzelm@16949
   452
    #> strip_shyps_warning
wenzelm@16949
   453
    #> zero_var_indexes
wenzelm@16949
   454
    #> Thm.varifyT
wenzelm@16949
   455
    #> Thm.compress);
wenzelm@1218
   456
wenzelm@16949
   457
val standard =
wenzelm@16949
   458
  flexflex_unique
wenzelm@16949
   459
  #> standard'
wenzelm@16949
   460
  #> close_derivation;
berghofe@11512
   461
wenzelm@16949
   462
val local_standard =
wenzelm@16949
   463
  strip_shyps
wenzelm@16949
   464
  #> zero_var_indexes
wenzelm@16949
   465
  #> Thm.compress
wenzelm@16949
   466
  #> close_derivation;
wenzelm@12005
   467
clasohm@0
   468
wenzelm@8328
   469
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   470
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   471
  Similar code in type/freeze_thaw*)
paulson@15495
   472
paulson@15495
   473
fun freeze_thaw_robust th =
paulson@15495
   474
 let val fth = freezeT th
wenzelm@16425
   475
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@15495
   476
 in
skalberg@15574
   477
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@15495
   478
       [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
paulson@15495
   479
     | vars =>
paulson@19753
   480
         let fun newName (Var(ix,_)) = (ix, gensym (string_of_indexname ix))
paulson@19753
   481
             val alist = map newName vars
paulson@15495
   482
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   483
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   484
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
paulson@15495
   485
             val insts = map mk_inst vars
paulson@15495
   486
             fun thaw i th' = (*i is non-negative increment for Var indexes*)
paulson@15495
   487
                 th' |> forall_intr_list (map #2 insts)
paulson@15495
   488
                     |> forall_elim_list (map (Thm.cterm_incr_indexes i o #1) insts)
paulson@15495
   489
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@15495
   490
 end;
paulson@15495
   491
paulson@15495
   492
(*Basic version of the function above. No option to rename Vars apart in thaw.
paulson@19753
   493
  The Frees created from Vars have nice names. FIXME: does not check for 
paulson@19753
   494
  clashes with variables in the assumptions, so delete and use freeze_thaw_robust instead?*)
paulson@4610
   495
fun freeze_thaw th =
paulson@7248
   496
 let val fth = freezeT th
wenzelm@16425
   497
     val {prop, tpairs, thy, ...} = rep_thm fth
paulson@7248
   498
 in
skalberg@15574
   499
   case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@7248
   500
       [] => (fth, fn x => x)
paulson@7248
   501
     | vars =>
wenzelm@8328
   502
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@8328
   503
                   let val v = variant used (string_of_indexname ix)
wenzelm@8328
   504
                   in  ((ix,v)::pairs, v::used)  end;
skalberg@15574
   505
             val (alist, _) = foldr newName ([], Library.foldr add_term_names
skalberg@15574
   506
               (prop :: Thm.terms_of_tpairs tpairs, [])) vars
wenzelm@8328
   507
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   508
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   509
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
wenzelm@8328
   510
             val insts = map mk_inst vars
wenzelm@8328
   511
             fun thaw th' =
wenzelm@8328
   512
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   513
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   514
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   515
 end;
paulson@4610
   516
paulson@7248
   517
(*Rotates a rule's premises to the left by k*)
paulson@7248
   518
val rotate_prems = permute_prems 0;
paulson@4610
   519
oheimb@11163
   520
(* permute prems, where the i-th position in the argument list (counting from 0)
oheimb@11163
   521
   gives the position within the original thm to be transferred to position i.
oheimb@11163
   522
   Any remaining trailing positions are left unchanged. *)
oheimb@11163
   523
val rearrange_prems = let
oheimb@11163
   524
  fun rearr new []      thm = thm
wenzelm@11815
   525
  |   rearr new (p::ps) thm = rearr (new+1)
oheimb@11163
   526
     (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
oheimb@11163
   527
     (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
oheimb@11163
   528
  in rearr 0 end;
paulson@4610
   529
wenzelm@252
   530
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   531
  Generalizes over Free variables,
clasohm@0
   532
  creates the assumption, and then strips quantifiers.
clasohm@0
   533
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   534
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   535
fun assume_ax thy sP =
wenzelm@16425
   536
  let val prop = Logic.close_form (term_of (read_cterm thy (sP, propT)))
wenzelm@16425
   537
  in forall_elim_vars 0 (Thm.assume (cterm_of thy prop)) end;
clasohm@0
   538
wenzelm@252
   539
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   540
fun tha RSN (i,thb) =
wenzelm@4270
   541
  case Seq.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   542
      ([th],_) => th
clasohm@0
   543
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   544
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   545
clasohm@0
   546
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   547
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   548
clasohm@0
   549
(*For joining lists of rules*)
wenzelm@252
   550
fun thas RLN (i,thbs) =
clasohm@0
   551
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   552
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
wenzelm@19482
   553
  in maps resb thbs end;
clasohm@0
   554
clasohm@0
   555
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   556
lcp@11
   557
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   558
  makes proof trees*)
wenzelm@252
   559
fun rls MRS bottom_rl =
lcp@11
   560
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   561
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   562
  in  rs_aux 1 rls  end;
lcp@11
   563
lcp@11
   564
(*As above, but for rule lists*)
wenzelm@252
   565
fun rlss MRL bottom_rls =
lcp@11
   566
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   567
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   568
  in  rs_aux 1 rlss  end;
lcp@11
   569
wenzelm@9288
   570
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   571
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   572
wenzelm@252
   573
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   574
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   575
  ALWAYS deletes premise i *)
wenzelm@252
   576
fun compose(tha,i,thb) =
wenzelm@4270
   577
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   578
wenzelm@6946
   579
fun compose_single (tha,i,thb) =
wenzelm@6946
   580
  (case compose (tha,i,thb) of
wenzelm@6946
   581
    [th] => th
wenzelm@6946
   582
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   583
clasohm@0
   584
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   585
fun tha COMP thb =
clasohm@0
   586
    case compose(tha,1,thb) of
wenzelm@252
   587
        [th] => th
clasohm@0
   588
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   589
wenzelm@13105
   590
wenzelm@4016
   591
(** theorem equality **)
clasohm@0
   592
wenzelm@16425
   593
(*True if the two theorems have the same theory.*)
wenzelm@16425
   594
val eq_thm_thy = eq_thy o pairself Thm.theory_of_thm;
paulson@13650
   595
paulson@13650
   596
(*True if the two theorems have the same prop field, ignoring hyps, der, etc.*)
wenzelm@16720
   597
val eq_thm_prop = op aconv o pairself Thm.full_prop_of;
clasohm@0
   598
clasohm@0
   599
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   600
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   601
wenzelm@9829
   602
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@18922
   603
val del_rule = remove eq_thm_prop;
wenzelm@18922
   604
fun add_rule th = cons th o del_rule th;
wenzelm@18922
   605
val merge_rules = Library.merge eq_thm_prop;
wenzelm@9829
   606
wenzelm@18535
   607
(*weak_eq_thm: ignores variable renaming and (some) type variable renaming*)
wenzelm@13105
   608
val weak_eq_thm = Thm.eq_thm o pairself (forall_intr_vars o freezeT);
lcp@1194
   609
lcp@1194
   610
clasohm@0
   611
(*** Meta-Rewriting Rules ***)
clasohm@0
   612
wenzelm@16425
   613
fun read_prop s = read_cterm ProtoPure.thy (s, propT);
paulson@4610
   614
wenzelm@9455
   615
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   616
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@12135
   617
fun store_thm_open name thm = hd (PureThy.smart_store_thms_open (name, [thm]));
wenzelm@12135
   618
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   619
clasohm@0
   620
val reflexive_thm =
wenzelm@19421
   621
  let val cx = cert (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   622
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   623
clasohm@0
   624
val symmetric_thm =
wenzelm@14854
   625
  let val xy = read_prop "x == y"
wenzelm@16595
   626
  in store_standard_thm_open "symmetric" (Thm.implies_intr xy (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   627
clasohm@0
   628
val transitive_thm =
wenzelm@14854
   629
  let val xy = read_prop "x == y"
wenzelm@14854
   630
      val yz = read_prop "y == z"
clasohm@0
   631
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   632
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   633
nipkow@4679
   634
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   635
berghofe@11512
   636
fun extensional eq =
berghofe@11512
   637
  let val eq' =
berghofe@11512
   638
    abstract_rule "x" (snd (Thm.dest_comb (fst (dest_equals (cprop_of eq))))) eq
berghofe@11512
   639
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   640
wenzelm@18820
   641
val equals_cong =
wenzelm@18820
   642
  store_standard_thm_open "equals_cong" (Thm.reflexive (read_prop "x == y"));
wenzelm@18820
   643
berghofe@10414
   644
val imp_cong =
berghofe@10414
   645
  let
berghofe@10414
   646
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   647
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   648
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   649
    val A = read_prop "PROP A"
berghofe@10414
   650
  in
wenzelm@12135
   651
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   652
      (implies_intr AB (implies_intr A
berghofe@10414
   653
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   654
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   655
      (implies_intr AC (implies_intr A
berghofe@10414
   656
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   657
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   658
  end;
berghofe@10414
   659
berghofe@10414
   660
val swap_prems_eq =
berghofe@10414
   661
  let
berghofe@10414
   662
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   663
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   664
    val A = read_prop "PROP A"
berghofe@10414
   665
    val B = read_prop "PROP B"
berghofe@10414
   666
  in
wenzelm@12135
   667
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   668
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   669
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   670
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   671
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   672
  end;
lcp@229
   673
wenzelm@18468
   674
val imp_cong_rule = combination o combination (reflexive implies);
clasohm@0
   675
skalberg@15001
   676
local
skalberg@15001
   677
  val dest_eq = dest_equals o cprop_of
skalberg@15001
   678
  val rhs_of = snd o dest_eq
skalberg@15001
   679
in
skalberg@15001
   680
fun beta_eta_conversion t =
skalberg@15001
   681
  let val thm = beta_conversion true t
skalberg@15001
   682
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   683
end;
skalberg@15001
   684
berghofe@15925
   685
fun eta_long_conversion ct = transitive (beta_eta_conversion ct)
berghofe@15925
   686
  (symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
berghofe@15925
   687
wenzelm@18337
   688
val abs_def =
wenzelm@18337
   689
  let
wenzelm@18337
   690
    fun contract_lhs th =
wenzelm@18337
   691
      Thm.transitive (Thm.symmetric (beta_eta_conversion (fst (dest_equals (cprop_of th))))) th;
wenzelm@18777
   692
    fun abstract cx th = Thm.abstract_rule
wenzelm@18777
   693
        (case Thm.term_of cx of Var ((x, _), _) => x | Free (x, _) => x | _ => "x") cx th
wenzelm@18777
   694
      handle THM _ => raise THM ("Malformed definitional equation", 0, [th]);
wenzelm@18337
   695
  in
wenzelm@18337
   696
    contract_lhs
wenzelm@18337
   697
    #> `(snd o strip_comb o fst o dest_equals o cprop_of)
wenzelm@18337
   698
    #-> fold_rev abstract
wenzelm@18337
   699
    #> contract_lhs
wenzelm@18337
   700
  end;
wenzelm@18337
   701
wenzelm@18468
   702
(*rewrite B in !!x1 ... xn. B*)
wenzelm@18251
   703
fun forall_conv 0 cv ct = cv ct
wenzelm@18251
   704
  | forall_conv n cv ct =
wenzelm@18468
   705
      (case try Thm.dest_comb ct of
wenzelm@18468
   706
        NONE => cv ct
wenzelm@18468
   707
      | SOME (A, B) =>
wenzelm@18468
   708
          (case (term_of A, term_of B) of
wenzelm@18468
   709
            (Const ("all", _), Abs (x, _, _)) =>
wenzelm@18468
   710
              let val (v, B') = Thm.dest_abs (SOME (gensym "all_")) B in
wenzelm@18468
   711
                Thm.combination (Thm.reflexive A)
wenzelm@18468
   712
                  (Thm.abstract_rule x v (forall_conv (n - 1) cv B'))
wenzelm@18468
   713
              end
wenzelm@18468
   714
          | _ => cv ct));
wenzelm@18468
   715
wenzelm@18468
   716
(*rewrite B in A1 ==> ... ==> An ==> B*)
wenzelm@18468
   717
fun concl_conv 0 cv ct = cv ct
wenzelm@18468
   718
  | concl_conv n cv ct =
wenzelm@18468
   719
      (case try dest_implies ct of
wenzelm@18468
   720
        NONE => cv ct
wenzelm@18468
   721
      | SOME (A, B) => imp_cong_rule (reflexive A) (concl_conv (n - 1) cv B));
skalberg@15001
   722
wenzelm@18468
   723
(*rewrite the A's in A1 ==> ... ==> An ==> B*)
wenzelm@18468
   724
fun prems_conv 0 _ = reflexive
wenzelm@18468
   725
  | prems_conv n cv =
wenzelm@18468
   726
      let
wenzelm@18468
   727
        fun conv i ct =
wenzelm@18468
   728
          if i = n + 1 then reflexive ct
wenzelm@18468
   729
          else
wenzelm@18468
   730
            (case try dest_implies ct of
wenzelm@18468
   731
              NONE => reflexive ct
wenzelm@18468
   732
            | SOME (A, B) => imp_cong_rule (cv i A) (conv (i + 1) B));
wenzelm@18468
   733
  in conv 1 end;
wenzelm@18468
   734
wenzelm@18468
   735
fun goals_conv pred cv = prems_conv ~1 (fn i => if pred i then cv else reflexive);
skalberg@15001
   736
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
skalberg@15001
   737
wenzelm@18468
   738
wenzelm@15669
   739
(*** Some useful meta-theorems ***)
clasohm@0
   740
clasohm@0
   741
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@12135
   742
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   743
val _ = store_thm "_" asm_rl;
clasohm@0
   744
clasohm@0
   745
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   746
val cut_rl =
wenzelm@12135
   747
  store_standard_thm_open "cut_rl"
wenzelm@9455
   748
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   749
wenzelm@252
   750
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   751
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   752
val revcut_rl =
paulson@4610
   753
  let val V = read_prop "PROP V"
paulson@4610
   754
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   755
  in
wenzelm@12135
   756
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   757
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   758
  end;
clasohm@0
   759
lcp@668
   760
(*for deleting an unwanted assumption*)
lcp@668
   761
val thin_rl =
paulson@4610
   762
  let val V = read_prop "PROP V"
paulson@4610
   763
      and W = read_prop "PROP W";
wenzelm@12135
   764
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   765
clasohm@0
   766
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   767
val triv_forall_equality =
paulson@4610
   768
  let val V  = read_prop "PROP V"
paulson@4610
   769
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@19421
   770
      and x  = cert (Free ("x", Term.aT []));
wenzelm@4016
   771
  in
wenzelm@12135
   772
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   773
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   774
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   775
  end;
clasohm@0
   776
wenzelm@19051
   777
(* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
wenzelm@19051
   778
   (PROP ?Phi ==> PROP ?Psi)
wenzelm@19051
   779
*)
wenzelm@19051
   780
val distinct_prems_rl =
wenzelm@19051
   781
  let
wenzelm@19051
   782
    val AAB = read_prop "PROP Phi ==> PROP Phi ==> PROP Psi"
wenzelm@19051
   783
    val A = read_prop "PROP Phi";
wenzelm@19051
   784
  in
wenzelm@19051
   785
    store_standard_thm_open "distinct_prems_rl"
wenzelm@19051
   786
      (implies_intr_list [AAB, A] (implies_elim_list (assume AAB) [assume A, assume A]))
wenzelm@19051
   787
  end;
wenzelm@19051
   788
nipkow@1756
   789
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   790
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   791
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   792
*)
nipkow@1756
   793
val swap_prems_rl =
paulson@4610
   794
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   795
      val major = assume cmajor;
paulson@4610
   796
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   797
      val minor1 = assume cminor1;
paulson@4610
   798
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   799
      val minor2 = assume cminor2;
wenzelm@12135
   800
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   801
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   802
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   803
  end;
nipkow@1756
   804
nipkow@3653
   805
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   806
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   807
   Introduction rule for == as a meta-theorem.
nipkow@3653
   808
*)
nipkow@3653
   809
val equal_intr_rule =
paulson@4610
   810
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   811
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   812
  in
wenzelm@12135
   813
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   814
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   815
  end;
nipkow@3653
   816
wenzelm@19421
   817
(* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@13368
   818
val equal_elim_rule1 =
wenzelm@13368
   819
  let val eq = read_prop "PROP phi == PROP psi"
wenzelm@13368
   820
      and P = read_prop "PROP phi"
wenzelm@13368
   821
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   822
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   823
  end;
wenzelm@4285
   824
wenzelm@19421
   825
(* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@19421
   826
val equal_elim_rule2 =
wenzelm@19421
   827
  store_standard_thm_open "equal_elim_rule2" (symmetric_thm RS equal_elim_rule1);
wenzelm@19421
   828
wenzelm@12297
   829
(* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
wenzelm@12297
   830
val remdups_rl =
wenzelm@12297
   831
  let val P = read_prop "PROP phi" and Q = read_prop "PROP psi";
wenzelm@12297
   832
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   833
wenzelm@12297
   834
wenzelm@9554
   835
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@12297
   836
  Rewrite rule for HHF normalization.*)
wenzelm@9554
   837
wenzelm@9554
   838
val norm_hhf_eq =
wenzelm@9554
   839
  let
wenzelm@14854
   840
    val aT = TFree ("'a", []);
wenzelm@9554
   841
    val all = Term.all aT;
wenzelm@9554
   842
    val x = Free ("x", aT);
wenzelm@9554
   843
    val phi = Free ("phi", propT);
wenzelm@9554
   844
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   845
wenzelm@9554
   846
    val cx = cert x;
wenzelm@9554
   847
    val cphi = cert phi;
wenzelm@9554
   848
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   849
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   850
  in
wenzelm@9554
   851
    Thm.equal_intr
wenzelm@9554
   852
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   853
        |> Thm.forall_elim cx
wenzelm@9554
   854
        |> Thm.implies_intr cphi
wenzelm@9554
   855
        |> Thm.forall_intr cx
wenzelm@9554
   856
        |> Thm.implies_intr lhs)
wenzelm@9554
   857
      (Thm.implies_elim
wenzelm@9554
   858
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   859
        |> Thm.forall_intr cx
wenzelm@9554
   860
        |> Thm.implies_intr cphi
wenzelm@9554
   861
        |> Thm.implies_intr rhs)
wenzelm@12135
   862
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   863
  end;
wenzelm@9554
   864
wenzelm@18179
   865
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@18179
   866
wenzelm@12800
   867
fun is_norm_hhf tm =
wenzelm@12800
   868
  let
wenzelm@12800
   869
    fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@12800
   870
      | is_norm (t $ u) = is_norm t andalso is_norm u
wenzelm@12800
   871
      | is_norm (Abs (_, _, t)) = is_norm t
wenzelm@12800
   872
      | is_norm _ = true;
wenzelm@18929
   873
  in is_norm (Envir.beta_eta_contract tm) end;
wenzelm@12800
   874
wenzelm@16425
   875
fun norm_hhf thy t =
wenzelm@12800
   876
  if is_norm_hhf t then t
wenzelm@18179
   877
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   878
wenzelm@12800
   879
wenzelm@9554
   880
wenzelm@16425
   881
(*** Instantiate theorem th, reading instantiations in theory thy ****)
paulson@8129
   882
paulson@8129
   883
(*Version that normalizes the result: Thm.instantiate no longer does that*)
paulson@8129
   884
fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
paulson@8129
   885
wenzelm@16425
   886
fun read_instantiate_sg' thy sinsts th =
paulson@8129
   887
    let val ts = types_sorts th;
wenzelm@15669
   888
        val used = add_used th [];
wenzelm@16425
   889
    in  instantiate (read_insts thy ts ts used sinsts) th  end;
berghofe@15797
   890
wenzelm@16425
   891
fun read_instantiate_sg thy sinsts th =
wenzelm@16425
   892
  read_instantiate_sg' thy (map (apfst Syntax.indexname) sinsts) th;
paulson@8129
   893
paulson@8129
   894
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   895
fun read_instantiate sinsts th =
wenzelm@16425
   896
    read_instantiate_sg (Thm.theory_of_thm th) sinsts th;
paulson@8129
   897
berghofe@15797
   898
fun read_instantiate' sinsts th =
wenzelm@16425
   899
    read_instantiate_sg' (Thm.theory_of_thm th) sinsts th;
berghofe@15797
   900
paulson@8129
   901
paulson@8129
   902
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   903
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   904
local
wenzelm@16425
   905
  fun add_types ((ct,cu), (thy,tye,maxidx)) =
wenzelm@16425
   906
    let val {thy=thyt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
wenzelm@16425
   907
        and {thy=thyu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   908
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
wenzelm@16425
   909
        val thy' = Theory.merge(thy, Theory.merge(thyt, thyu))
wenzelm@16949
   910
        val (tye',maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
wenzelm@10403
   911
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
wenzelm@16425
   912
    in  (thy', tye', maxi')  end;
paulson@8129
   913
in
paulson@8129
   914
fun cterm_instantiate ctpairs0 th =
wenzelm@16425
   915
  let val (thy,tye,_) = foldr add_types (Thm.theory_of_thm th, Vartab.empty, 0) ctpairs0
wenzelm@18179
   916
      fun instT(ct,cu) =
wenzelm@16425
   917
        let val inst = cterm_of thy o Envir.subst_TVars tye o term_of
paulson@14340
   918
        in (inst ct, inst cu) end
wenzelm@16425
   919
      fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy T)
berghofe@8406
   920
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   921
  handle TERM _ =>
wenzelm@16425
   922
           raise THM("cterm_instantiate: incompatible theories",0,[th])
paulson@8129
   923
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   924
end;
paulson@8129
   925
paulson@8129
   926
paulson@8129
   927
(** Derived rules mainly for METAHYPS **)
paulson@8129
   928
paulson@8129
   929
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
paulson@8129
   930
fun equal_abs_elim ca eqth =
wenzelm@16425
   931
  let val {thy=thya, t=a, ...} = rep_cterm ca
paulson@8129
   932
      and combth = combination eqth (reflexive ca)
wenzelm@16425
   933
      val {thy,prop,...} = rep_thm eqth
paulson@8129
   934
      val (abst,absu) = Logic.dest_equals prop
wenzelm@19421
   935
      val cert = cterm_of (Theory.merge (thy,thya))
wenzelm@19421
   936
  in  transitive (symmetric (beta_conversion false (cert (abst$a))))
wenzelm@19421
   937
           (transitive combth (beta_conversion false (cert (absu$a))))
paulson@8129
   938
  end
paulson@8129
   939
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
paulson@8129
   940
paulson@8129
   941
(*Calling equal_abs_elim with multiple terms*)
skalberg@15574
   942
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) th (rev cts);
paulson@8129
   943
paulson@8129
   944
wenzelm@19775
   945
(** protected propositions and embedded terms **)
wenzelm@4789
   946
wenzelm@4789
   947
local
wenzelm@18025
   948
  val A = cert (Free ("A", propT));
wenzelm@18025
   949
  val prop_def = #1 (freeze_thaw ProtoPure.prop_def);
wenzelm@19775
   950
  val term_def = #1 (freeze_thaw ProtoPure.term_def);
wenzelm@4789
   951
in
wenzelm@18025
   952
  val protect = Thm.capply (cert Logic.protectC);
wenzelm@18799
   953
  val protectI = store_thm "protectI" (PureThy.kind_rule PureThy.internalK (standard
wenzelm@18025
   954
      (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A))));
wenzelm@18799
   955
  val protectD = store_thm "protectD" (PureThy.kind_rule PureThy.internalK (standard
wenzelm@18025
   956
      (Thm.equal_elim prop_def (Thm.assume (protect A)))));
wenzelm@18179
   957
  val protect_cong = store_standard_thm_open "protect_cong" (Thm.reflexive (protect A));
wenzelm@19775
   958
wenzelm@19775
   959
  val termI = store_thm "termI" (PureThy.kind_rule PureThy.internalK (standard
wenzelm@19775
   960
      (Thm.equal_elim (Thm.symmetric term_def) (Thm.forall_intr A (Thm.trivial A)))));
wenzelm@4789
   961
end;
wenzelm@4789
   962
wenzelm@18025
   963
fun implies_intr_protected asms th =
wenzelm@18118
   964
  let val asms' = map protect asms in
wenzelm@18118
   965
    implies_elim_list
wenzelm@18118
   966
      (implies_intr_list asms th)
wenzelm@18118
   967
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@18118
   968
    |> implies_intr_list asms'
wenzelm@18118
   969
  end;
wenzelm@11815
   970
wenzelm@19775
   971
fun mk_term ct =
wenzelm@19775
   972
  let
wenzelm@19775
   973
    val {thy, T, ...} = Thm.rep_cterm ct;
wenzelm@19775
   974
    val cert = Thm.cterm_of thy;
wenzelm@19775
   975
    val certT = Thm.ctyp_of thy;
wenzelm@19775
   976
    val a = certT (TVar (("'a", 0), []));
wenzelm@19775
   977
    val x = cert (Var (("x", 0), T));
wenzelm@19775
   978
  in Thm.instantiate ([(a, certT T)], [(x, ct)]) termI end;
wenzelm@19775
   979
wenzelm@19775
   980
fun dest_term th =
wenzelm@19775
   981
  let val cprop = Thm.cprop_of th in
wenzelm@19775
   982
    if can Logic.dest_term (Thm.term_of cprop) then
wenzelm@19775
   983
      #2 (Thm.dest_comb cprop)
wenzelm@19775
   984
    else raise THM ("dest_term", 0, [th])
wenzelm@19775
   985
  end;
wenzelm@19775
   986
wenzelm@19775
   987
wenzelm@4789
   988
wenzelm@5688
   989
(** variations on instantiate **)
wenzelm@4285
   990
paulson@8550
   991
(*shorthand for instantiating just one variable in the current theory*)
wenzelm@16425
   992
fun inst x t = read_instantiate_sg (the_context()) [(x,t)];
paulson@8550
   993
paulson@8550
   994
wenzelm@4285
   995
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   996
wenzelm@4285
   997
fun instantiate' cTs cts thm =
wenzelm@4285
   998
  let
wenzelm@4285
   999
    fun err msg =
wenzelm@4285
  1000
      raise TYPE ("instantiate': " ^ msg,
wenzelm@19482
  1001
        map_filter (Option.map Thm.typ_of) cTs,
wenzelm@19482
  1002
        map_filter (Option.map Thm.term_of) cts);
wenzelm@4285
  1003
wenzelm@4285
  1004
    fun inst_of (v, ct) =
wenzelm@16425
  1005
      (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
  1006
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
  1007
berghofe@15797
  1008
    fun tyinst_of (v, cT) =
wenzelm@16425
  1009
      (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
  1010
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
  1011
wenzelm@4285
  1012
    fun zip_vars _ [] = []
skalberg@15531
  1013
      | zip_vars (_ :: vs) (NONE :: opt_ts) = zip_vars vs opt_ts
skalberg@15531
  1014
      | zip_vars (v :: vs) (SOME t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
wenzelm@4285
  1015
      | zip_vars [] _ = err "more instantiations than variables in thm";
wenzelm@4285
  1016
wenzelm@4285
  1017
    (*instantiate types first!*)
wenzelm@4285
  1018
    val thm' =
wenzelm@4285
  1019
      if forall is_none cTs then thm
berghofe@15797
  1020
      else Thm.instantiate (map tyinst_of (zip_vars (tvars_of thm) cTs), []) thm;
wenzelm@4285
  1021
    in
wenzelm@4285
  1022
      if forall is_none cts then thm'
wenzelm@4285
  1023
      else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
wenzelm@4285
  1024
    end;
wenzelm@4285
  1025
wenzelm@4285
  1026
berghofe@14081
  1027
berghofe@14081
  1028
(** renaming of bound variables **)
berghofe@14081
  1029
berghofe@14081
  1030
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
  1031
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
  1032
berghofe@14081
  1033
fun rename_bvars [] thm = thm
berghofe@14081
  1034
  | rename_bvars vs thm =
berghofe@14081
  1035
    let
wenzelm@16425
  1036
      val {thy, prop, ...} = rep_thm thm;
haftmann@17325
  1037
      fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
berghofe@14081
  1038
        | ren (t $ u) = ren t $ ren u
berghofe@14081
  1039
        | ren t = t;
wenzelm@16425
  1040
    in equal_elim (reflexive (cterm_of thy (ren prop))) thm end;
berghofe@14081
  1041
berghofe@14081
  1042
berghofe@14081
  1043
(* renaming in left-to-right order *)
berghofe@14081
  1044
berghofe@14081
  1045
fun rename_bvars' xs thm =
berghofe@14081
  1046
  let
wenzelm@16425
  1047
    val {thy, prop, ...} = rep_thm thm;
berghofe@14081
  1048
    fun rename [] t = ([], t)
berghofe@14081
  1049
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
  1050
          let val (xs', t') = rename xs t
wenzelm@18929
  1051
          in (xs', Abs (the_default x x', T, t')) end
berghofe@14081
  1052
      | rename xs (t $ u) =
berghofe@14081
  1053
          let
berghofe@14081
  1054
            val (xs', t') = rename xs t;
berghofe@14081
  1055
            val (xs'', u') = rename xs' u
berghofe@14081
  1056
          in (xs'', t' $ u') end
berghofe@14081
  1057
      | rename xs t = (xs, t);
berghofe@14081
  1058
  in case rename xs prop of
wenzelm@16425
  1059
      ([], prop') => equal_elim (reflexive (cterm_of thy prop')) thm
berghofe@14081
  1060
    | _ => error "More names than abstractions in theorem"
berghofe@14081
  1061
  end;
berghofe@14081
  1062
berghofe@14081
  1063
berghofe@14081
  1064
wenzelm@5688
  1065
(* unvarify(T) *)
wenzelm@5688
  1066
wenzelm@5688
  1067
(*assume thm in standard form, i.e. no frees, 0 var indexes*)
wenzelm@5688
  1068
wenzelm@5688
  1069
fun unvarifyT thm =
wenzelm@5688
  1070
  let
wenzelm@16425
  1071
    val cT = Thm.ctyp_of (Thm.theory_of_thm thm);
skalberg@15531
  1072
    val tfrees = map (fn ((x, _), S) => SOME (cT (TFree (x, S)))) (tvars_of thm);
wenzelm@5688
  1073
  in instantiate' tfrees [] thm end;
wenzelm@5688
  1074
wenzelm@5688
  1075
fun unvarify raw_thm =
wenzelm@5688
  1076
  let
wenzelm@5688
  1077
    val thm = unvarifyT raw_thm;
wenzelm@16425
  1078
    val ct = Thm.cterm_of (Thm.theory_of_thm thm);
skalberg@15531
  1079
    val frees = map (fn ((x, _), T) => SOME (ct (Free (x, T)))) (vars_of thm);
wenzelm@5688
  1080
  in instantiate' [] frees thm end;
wenzelm@5688
  1081
wenzelm@5688
  1082
wenzelm@8605
  1083
(* tvars_intr_list *)
wenzelm@8605
  1084
wenzelm@8605
  1085
fun tvars_intr_list tfrees thm =
wenzelm@18129
  1086
  apfst (map (fn ((s, S), ixn) => (s, (ixn, S)))) (Thm.varifyT'
berghofe@15797
  1087
    (gen_rems (op = o apfst fst) (tfrees_of thm, tfrees)) thm);
wenzelm@8605
  1088
wenzelm@8605
  1089
wenzelm@6435
  1090
(* increment var indexes *)
wenzelm@6435
  1091
wenzelm@19421
  1092
fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
wenzelm@18025
  1093
wenzelm@19124
  1094
fun incr_indexes2 th1 th2 =
wenzelm@19421
  1095
  Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
wenzelm@6435
  1096
wenzelm@6435
  1097
wenzelm@8328
  1098
(* freeze_all *)
wenzelm@8328
  1099
wenzelm@8328
  1100
(*freeze all (T)Vars; assumes thm in standard form*)
wenzelm@8328
  1101
wenzelm@8328
  1102
fun freeze_all_TVars thm =
wenzelm@8328
  1103
  (case tvars_of thm of
wenzelm@8328
  1104
    [] => thm
wenzelm@8328
  1105
  | tvars =>
wenzelm@16425
  1106
      let val cert = Thm.ctyp_of (Thm.theory_of_thm thm)
skalberg@15531
  1107
      in instantiate' (map (fn ((x, _), S) => SOME (cert (TFree (x, S)))) tvars) [] thm end);
wenzelm@8328
  1108
wenzelm@8328
  1109
fun freeze_all_Vars thm =
wenzelm@8328
  1110
  (case vars_of thm of
wenzelm@8328
  1111
    [] => thm
wenzelm@8328
  1112
  | vars =>
wenzelm@16425
  1113
      let val cert = Thm.cterm_of (Thm.theory_of_thm thm)
skalberg@15531
  1114
      in instantiate' [] (map (fn ((x, _), T) => SOME (cert (Free (x, T)))) vars) thm end);
wenzelm@8328
  1115
wenzelm@8328
  1116
val freeze_all = freeze_all_Vars o freeze_all_TVars;
wenzelm@8328
  1117
wenzelm@8328
  1118
wenzelm@11975
  1119
wenzelm@18225
  1120
(** multi_resolve **)
wenzelm@18225
  1121
wenzelm@18225
  1122
local
wenzelm@18225
  1123
wenzelm@18225
  1124
fun res th i rule =
wenzelm@18225
  1125
  Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
wenzelm@18225
  1126
wenzelm@18225
  1127
fun multi_res _ [] rule = Seq.single rule
wenzelm@18225
  1128
  | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
wenzelm@18225
  1129
wenzelm@18225
  1130
in
wenzelm@18225
  1131
wenzelm@18225
  1132
val multi_resolve = multi_res 1;
wenzelm@18225
  1133
fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
wenzelm@18225
  1134
wenzelm@18225
  1135
end;
wenzelm@18225
  1136
wenzelm@11975
  1137
end;
wenzelm@5903
  1138
wenzelm@5903
  1139
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
  1140
open BasicDrule;