src/Pure/drule.ML
author wenzelm
Tue Apr 15 16:12:05 2008 +0200 (2008-04-15 ago)
changeset 26653 60e0cf6bef89
parent 26627 dac6d56b7c8d
child 26939 1035c89b4c02
permissions -rw-r--r--
Thm.forall_elim_var(s);
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(*  Title:      Pure/drule.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1993  University of Cambridge
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Derived rules and other operations on theorems.
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*)
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infix 0 RS RSN RL RLN MRS MRL OF COMP INCR_COMP COMP_INCR;
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signature BASIC_DRULE =
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sig
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  val mk_implies: cterm * cterm -> cterm
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  val list_implies: cterm list * cterm -> cterm
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  val strip_imp_prems: cterm -> cterm list
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  val strip_imp_concl: cterm -> cterm
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  val cprems_of: thm -> cterm list
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  val cterm_fun: (term -> term) -> (cterm -> cterm)
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  val ctyp_fun: (typ -> typ) -> (ctyp -> ctyp)
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  val read_insts: theory -> (indexname -> typ option) * (indexname -> sort option) ->
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    (indexname -> typ option) * (indexname -> sort option) -> string list ->
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    (indexname * string) list -> (ctyp * ctyp) list * (cterm * cterm) list
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  val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
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  val forall_intr_list: cterm list -> thm -> thm
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  val forall_intr_frees: thm -> thm
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  val forall_intr_vars: thm -> thm
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  val forall_elim_list: cterm list -> thm -> thm
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  val gen_all: thm -> thm
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  val lift_all: cterm -> thm -> thm
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  val freeze_thaw: thm -> thm * (thm -> thm)
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  val freeze_thaw_robust: thm -> thm * (int -> thm -> thm)
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  val implies_elim_list: thm -> thm list -> thm
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  val implies_intr_list: cterm list -> thm -> thm
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  val instantiate: (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm
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  val zero_var_indexes_list: thm list -> thm list
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  val zero_var_indexes: thm -> thm
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  val implies_intr_hyps: thm -> thm
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  val standard: thm -> thm
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  val standard': thm -> thm
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  val rotate_prems: int -> thm -> thm
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  val rearrange_prems: int list -> thm -> thm
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  val RSN: thm * (int * thm) -> thm
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  val RS: thm * thm -> thm
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  val RLN: thm list * (int * thm list) -> thm list
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  val RL: thm list * thm list -> thm list
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  val MRS: thm list * thm -> thm
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  val MRL: thm list list * thm list -> thm list
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  val OF: thm * thm list -> thm
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  val compose: thm * int * thm -> thm list
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  val COMP: thm * thm -> thm
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  val INCR_COMP: thm * thm -> thm
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  val COMP_INCR: thm * thm -> thm
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  val read_instantiate_sg: theory -> (string*string)list -> thm -> thm
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  val read_instantiate: (string*string)list -> thm -> thm
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  val cterm_instantiate: (cterm*cterm)list -> thm -> thm
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  val size_of_thm: thm -> int
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  val reflexive_thm: thm
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  val symmetric_thm: thm
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  val transitive_thm: thm
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  val symmetric_fun: thm -> thm
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  val extensional: thm -> thm
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  val equals_cong: thm
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  val imp_cong: thm
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  val swap_prems_eq: thm
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  val asm_rl: thm
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  val cut_rl: thm
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  val revcut_rl: thm
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  val thin_rl: thm
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  val triv_forall_equality: thm
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  val distinct_prems_rl: thm
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  val swap_prems_rl: thm
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  val equal_intr_rule: thm
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  val equal_elim_rule1: thm
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  val equal_elim_rule2: thm
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  val instantiate': ctyp option list -> cterm option list -> thm -> thm
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end;
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signature DRULE =
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sig
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  include BASIC_DRULE
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  val generalize: string list * string list -> thm -> thm
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  val list_comb: cterm * cterm list -> cterm
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  val strip_comb: cterm -> cterm * cterm list
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  val strip_type: ctyp -> ctyp list * ctyp
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  val beta_conv: cterm -> cterm -> cterm
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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 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 imp_cong_rule: thm -> thm -> thm
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  val arg_cong_rule: cterm -> thm -> thm
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  val binop_cong_rule: cterm -> thm -> thm -> thm
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  val fun_cong_rule: thm -> cterm -> thm
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  val beta_eta_conversion: cterm -> thm
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  val eta_long_conversion: cterm -> thm
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  val eta_contraction_rule: thm -> thm
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  val norm_hhf_eq: thm
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  val is_norm_hhf: term -> bool
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  val norm_hhf: theory -> term -> term
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  val norm_hhf_cterm: cterm -> cterm
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  val protect: cterm -> cterm
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  val protectI: thm
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  val protectD: thm
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  val protect_cong: thm
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  val implies_intr_protected: cterm list -> thm -> thm
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  val termI: thm
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  val mk_term: cterm -> thm
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  val dest_term: thm -> cterm
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  val cterm_rule: (thm -> thm) -> cterm -> cterm
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  val term_rule: theory -> (thm -> thm) -> term -> term
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  val dummy_thm: thm
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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 with_subgoal: int -> (thm -> thm) -> thm -> thm
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  val rename_bvars: (string * string) list -> thm -> thm
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  val rename_bvars': string option list -> thm -> thm
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  val incr_type_indexes: int -> thm -> thm
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  val incr_indexes: thm -> thm -> thm
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  val incr_indexes2: thm -> thm -> thm -> thm
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  val remdups_rl: thm
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  val multi_resolve: thm list -> thm -> thm Seq.seq
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  val multi_resolves: thm list -> thm list -> thm Seq.seq
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  val abs_def: thm -> thm
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  val read_instantiate_sg': theory -> (indexname * string) list -> thm -> thm
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  val read_instantiate': (indexname * string) list -> thm -> thm
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end;
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structure Drule: DRULE =
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struct
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(** some cterm->cterm operations: faster than calling cterm_of! **)
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(* 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) = Thm.dest_implies ct
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  in cA :: strip_imp_prems cB end
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  handle TERM _ => [];
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(* A1==>...An==>B  goes to B, where B is not an implication *)
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fun strip_imp_concl ct =
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  (case Thm.term_of ct of
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    Const ("==>", _) $ _ $ _ => strip_imp_concl (Thm.dest_arg ct)
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  | _ => ct);
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(*The premises of a theorem, as a cterm list*)
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val cprems_of = strip_imp_prems o cprop_of;
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fun cterm_fun f ct = Thm.cterm_of (Thm.theory_of_cterm ct) (f (Thm.term_of ct));
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fun ctyp_fun f cT = Thm.ctyp_of (Thm.theory_of_ctyp cT) (f (Thm.typ_of cT));
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fun certify t = Thm.cterm_of (Context.the_theory (Context.the_thread_data ())) t;
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val implies = certify Term.implies;
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fun mk_implies (A, B) = Thm.capply (Thm.capply implies A) B;
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(*cterm version of list_implies: [A1,...,An], B  goes to [|A1;==>;An|]==>B *)
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fun list_implies([], B) = B
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  | list_implies(A::AS, B) = mk_implies (A, list_implies(AS,B));
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(*cterm version of list_comb: maps  (f, [t1,...,tn])  to  f(t1,...,tn) *)
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fun list_comb (f, []) = f
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  | list_comb (f, t::ts) = list_comb (Thm.capply f t, ts);
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(*cterm version of strip_comb: maps  f(t1,...,tn)  to  (f, [t1,...,tn]) *)
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fun strip_comb ct =
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  let
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    fun stripc (p as (ct, cts)) =
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      let val (ct1, ct2) = Thm.dest_comb ct
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      in stripc (ct1, ct2 :: cts) end handle CTERM _ => p
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  in stripc (ct, []) end;
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(* cterm version of strip_type: maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T) *)
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fun strip_type cT = (case Thm.typ_of cT of
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    Type ("fun", _) =>
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      let
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        val [cT1, cT2] = Thm.dest_ctyp cT;
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        val (cTs, cT') = strip_type cT2
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      in (cT1 :: cTs, cT') end
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  | _ => ([], cT));
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(*Beta-conversion for cterms, where x is an abstraction. Simply returns the rhs
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  of the meta-equality returned by the beta_conversion rule.*)
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fun beta_conv x y =
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  Thm.dest_arg (cprop_of (Thm.beta_conversion false (Thm.capply x y)));
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(** reading of instantiations **)
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fun absent ixn =
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  error("No such variable in term: " ^ Term.string_of_vname ixn);
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fun inst_failure ixn =
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  error("Instantiation of " ^ Term.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_def_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) = Thm.read_def_cterms(thy,types,sorts) used false sTs;
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    fun mkcVar(ixn,T) =
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        let val U = typ_subst_TVars tye2 T
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        in cterm_of thy (Var(ixn,U)) end
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    val ixnTs = ListPair.zip(ixns, map snd sTs)
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in (map (fn (ixn, T) => (ctyp_of thy (TVar (ixn, sort_of ixn)),
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      ctyp_of thy T)) (tye2 @ tye),
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    ListPair.zip(map mkcVar ixnTs,cts))
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end;
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(*** Find the type (sort) associated with a (T)Var or (T)Free in a term
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     Used for establishing default types (of variables) and sorts (of
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     type variables) when reading another term.
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     Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
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***)
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fun types_sorts thm =
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  let
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    val vars = Thm.fold_terms Term.add_vars thm [];
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    val frees = Thm.fold_terms Term.add_frees thm [];
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    val tvars = Thm.fold_terms Term.add_tvars thm [];
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    val tfrees = Thm.fold_terms Term.add_tfrees thm [];
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    fun types (a, i) =
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      if i < 0 then AList.lookup (op =) frees a else AList.lookup (op =) vars (a, i);
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    fun sorts (a, i) =
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      if i < 0 then AList.lookup (op =) tfrees a else AList.lookup (op =) tvars (a, i);
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  in (types, sorts) end;
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val add_used =
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  (Thm.fold_terms o fold_types o fold_atyps)
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    (fn TFree (a, _) => insert (op =) a
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      | TVar ((a, _), _) => insert (op =) a
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      | _ => I);
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(** Standardization of rules **)
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(* type classes and sorts *)
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fun sort_triv thy (T, S) =
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  let
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    val certT = Thm.ctyp_of thy;
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    val cT = certT T;
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    fun class_triv c =
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      Thm.class_triv thy c
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      |> Thm.instantiate ([(certT (TVar ((Name.aT, 0), [c])), cT)], []);
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  in map class_triv S end;
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fun unconstrainTs th =
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  fold (Thm.unconstrainT o Thm.ctyp_of (Thm.theory_of_thm th) o TVar)
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    (Thm.fold_terms Term.add_tvars th []) th;
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(*Generalization over a list of variables*)
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val forall_intr_list = fold_rev forall_intr;
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(*Generalization over all suitable Free variables*)
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fun forall_intr_frees th =
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    let
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      val thy = Thm.theory_of_thm th;
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      val {prop, hyps, tpairs, ...} = rep_thm th;
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      val fixed = fold Term.add_frees (Thm.terms_of_tpairs tpairs @ hyps) [];
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      val frees = Term.fold_aterms (fn Free v =>
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        if member (op =) fixed v then I else insert (op =) v | _ => I) prop [];
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    in fold (forall_intr o cterm_of thy o Free) frees th end;
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(*Generalization over Vars -- canonical order*)
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fun forall_intr_vars th =
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  fold forall_intr
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    (map (Thm.cterm_of (Thm.theory_of_thm th) o Var) (Thm.fold_terms Term.add_vars th [])) th;
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fun outer_params t =
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  let val vs = Term.strip_all_vars t
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  in Name.variant_list [] (map (Name.clean o #1) vs) ~~ map #2 vs end;
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(*generalize outermost parameters*)
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fun gen_all th =
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  let
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    val thy = Thm.theory_of_thm th;
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    val {prop, maxidx, ...} = Thm.rep_thm th;
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    val cert = Thm.cterm_of thy;
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    fun elim (x, T) = Thm.forall_elim (cert (Var ((x, maxidx + 1), T)));
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  in fold elim (outer_params prop) th end;
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(*lift vars wrt. outermost goal parameters
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   305
  -- reverses the effect of gen_all modulo higher-order unification*)
wenzelm@18025
   306
fun lift_all goal th =
wenzelm@18025
   307
  let
wenzelm@18025
   308
    val thy = Theory.merge (Thm.theory_of_cterm goal, Thm.theory_of_thm th);
wenzelm@18025
   309
    val cert = Thm.cterm_of thy;
wenzelm@19421
   310
    val maxidx = Thm.maxidx_of th;
wenzelm@18025
   311
    val ps = outer_params (Thm.term_of goal)
wenzelm@18025
   312
      |> map (fn (x, T) => Var ((x, maxidx + 1), Logic.incr_tvar (maxidx + 1) T));
wenzelm@18025
   313
    val Ts = map Term.fastype_of ps;
wenzelm@22695
   314
    val inst = Thm.fold_terms Term.add_vars th [] |> map (fn (xi, T) =>
wenzelm@18025
   315
      (cert (Var (xi, T)), cert (Term.list_comb (Var (xi, Ts ---> T), ps))));
wenzelm@18025
   316
  in
wenzelm@18025
   317
    th |> Thm.instantiate ([], inst)
wenzelm@18025
   318
    |> fold_rev (Thm.forall_intr o cert) ps
wenzelm@18025
   319
  end;
wenzelm@18025
   320
wenzelm@19999
   321
(*direct generalization*)
wenzelm@19999
   322
fun generalize names th = Thm.generalize names (Thm.maxidx_of th + 1) th;
wenzelm@9554
   323
wenzelm@16949
   324
(*specialization over a list of cterms*)
wenzelm@16949
   325
val forall_elim_list = fold forall_elim;
clasohm@0
   326
wenzelm@16949
   327
(*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
wenzelm@16949
   328
val implies_intr_list = fold_rev implies_intr;
clasohm@0
   329
wenzelm@16949
   330
(*maps [| A1;...;An |] ==> B and [A1,...,An]  to  B*)
wenzelm@24978
   331
fun implies_elim_list impth ths = fold Thm.elim_implies ths impth;
clasohm@0
   332
clasohm@0
   333
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@21603
   334
fun zero_var_indexes_list [] = []
wenzelm@21603
   335
  | zero_var_indexes_list ths =
wenzelm@21603
   336
      let
wenzelm@21603
   337
        val thy = Theory.merge_list (map Thm.theory_of_thm ths);
wenzelm@21603
   338
        val certT = Thm.ctyp_of thy and cert = Thm.cterm_of thy;
wenzelm@21603
   339
        val (instT, inst) = TermSubst.zero_var_indexes_inst (map Thm.full_prop_of ths);
wenzelm@21603
   340
        val cinstT = map (fn (v, T) => (certT (TVar v), certT T)) instT;
wenzelm@21603
   341
        val cinst = map (fn (v, t) => (cert (Var v), cert t)) inst;
wenzelm@21603
   342
      in map (Thm.adjust_maxidx_thm ~1 o Thm.instantiate (cinstT, cinst)) ths end;
wenzelm@21603
   343
wenzelm@21603
   344
val zero_var_indexes = singleton zero_var_indexes_list;
clasohm@0
   345
clasohm@0
   346
paulson@14394
   347
(** Standard form of object-rule: no hypotheses, flexflex constraints,
paulson@14394
   348
    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
wenzelm@10515
   349
wenzelm@16595
   350
(*Discharge all hypotheses.*)
wenzelm@16595
   351
fun implies_intr_hyps th =
wenzelm@16595
   352
  fold Thm.implies_intr (#hyps (Thm.crep_thm th)) th;
wenzelm@16595
   353
paulson@14394
   354
(*Squash a theorem's flexflex constraints provided it can be done uniquely.
paulson@14394
   355
  This step can lose information.*)
paulson@14387
   356
fun flexflex_unique th =
berghofe@17713
   357
  if null (tpairs_of th) then th else
paulson@23439
   358
    case distinct Thm.eq_thm (Seq.list_of (flexflex_rule th)) of
paulson@23439
   359
      [th] => th
paulson@23439
   360
    | []   => raise THM("flexflex_unique: impossible constraints", 0, [th])
paulson@23439
   361
    |  _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   362
wenzelm@21603
   363
wenzelm@21603
   364
(* legacy standard operations *)
wenzelm@21603
   365
wenzelm@16949
   366
val standard' =
wenzelm@16949
   367
  implies_intr_hyps
wenzelm@16949
   368
  #> forall_intr_frees
wenzelm@19421
   369
  #> `Thm.maxidx_of
wenzelm@16949
   370
  #-> (fn maxidx =>
wenzelm@26653
   371
    Thm.forall_elim_vars (maxidx + 1)
wenzelm@20904
   372
    #> Thm.strip_shyps
wenzelm@16949
   373
    #> zero_var_indexes
wenzelm@26627
   374
    #> Thm.varifyT);
wenzelm@1218
   375
wenzelm@16949
   376
val standard =
wenzelm@21600
   377
  flexflex_unique
wenzelm@16949
   378
  #> standard'
wenzelm@26627
   379
  #> Thm.close_derivation;
berghofe@11512
   380
clasohm@0
   381
wenzelm@8328
   382
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   383
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   384
  Similar code in type/freeze_thaw*)
paulson@15495
   385
paulson@15495
   386
fun freeze_thaw_robust th =
wenzelm@19878
   387
 let val fth = Thm.freezeT th
wenzelm@26627
   388
     val thy = Thm.theory_of_thm fth
wenzelm@26627
   389
     val {prop, tpairs, ...} = rep_thm fth
paulson@15495
   390
 in
wenzelm@23178
   391
   case List.foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@15495
   392
       [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
paulson@15495
   393
     | vars =>
paulson@19753
   394
         let fun newName (Var(ix,_)) = (ix, gensym (string_of_indexname ix))
paulson@19753
   395
             val alist = map newName vars
paulson@15495
   396
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   397
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   398
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
paulson@15495
   399
             val insts = map mk_inst vars
paulson@15495
   400
             fun thaw i th' = (*i is non-negative increment for Var indexes*)
paulson@15495
   401
                 th' |> forall_intr_list (map #2 insts)
wenzelm@22906
   402
                     |> forall_elim_list (map (Thm.incr_indexes_cterm i o #1) insts)
paulson@15495
   403
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@15495
   404
 end;
paulson@15495
   405
paulson@15495
   406
(*Basic version of the function above. No option to rename Vars apart in thaw.
wenzelm@19999
   407
  The Frees created from Vars have nice names. FIXME: does not check for
paulson@19753
   408
  clashes with variables in the assumptions, so delete and use freeze_thaw_robust instead?*)
paulson@4610
   409
fun freeze_thaw th =
wenzelm@19878
   410
 let val fth = Thm.freezeT th
wenzelm@26627
   411
     val thy = Thm.theory_of_thm fth
wenzelm@26627
   412
     val {prop, tpairs, ...} = rep_thm fth
paulson@7248
   413
 in
wenzelm@23178
   414
   case List.foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
paulson@7248
   415
       [] => (fth, fn x => x)
paulson@7248
   416
     | vars =>
wenzelm@8328
   417
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@20077
   418
                   let val v = Name.variant used (string_of_indexname ix)
wenzelm@8328
   419
                   in  ((ix,v)::pairs, v::used)  end;
wenzelm@23178
   420
             val (alist, _) = List.foldr newName ([], Library.foldr add_term_names
skalberg@15574
   421
               (prop :: Thm.terms_of_tpairs tpairs, [])) vars
wenzelm@8328
   422
             fun mk_inst (Var(v,T)) =
wenzelm@16425
   423
                 (cterm_of thy (Var(v,T)),
haftmann@17325
   424
                  cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
wenzelm@8328
   425
             val insts = map mk_inst vars
wenzelm@8328
   426
             fun thaw th' =
wenzelm@8328
   427
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   428
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   429
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   430
 end;
paulson@4610
   431
paulson@7248
   432
(*Rotates a rule's premises to the left by k*)
wenzelm@23537
   433
fun rotate_prems 0 = I
wenzelm@23537
   434
  | rotate_prems k = permute_prems 0 k;
wenzelm@23537
   435
wenzelm@23423
   436
fun with_subgoal i f = rotate_prems (i - 1) #> f #> rotate_prems (1 - i);
paulson@4610
   437
oheimb@11163
   438
(* permute prems, where the i-th position in the argument list (counting from 0)
oheimb@11163
   439
   gives the position within the original thm to be transferred to position i.
oheimb@11163
   440
   Any remaining trailing positions are left unchanged. *)
oheimb@11163
   441
val rearrange_prems = let
oheimb@11163
   442
  fun rearr new []      thm = thm
wenzelm@11815
   443
  |   rearr new (p::ps) thm = rearr (new+1)
oheimb@11163
   444
     (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
oheimb@11163
   445
     (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
oheimb@11163
   446
  in rearr 0 end;
paulson@4610
   447
wenzelm@252
   448
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   449
fun tha RSN (i,thb) =
wenzelm@19861
   450
  case Seq.chop 2 (biresolution false [(false,tha)] i thb) of
clasohm@0
   451
      ([th],_) => th
clasohm@0
   452
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   453
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   454
clasohm@0
   455
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   456
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   457
clasohm@0
   458
(*For joining lists of rules*)
wenzelm@252
   459
fun thas RLN (i,thbs) =
clasohm@0
   460
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   461
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
wenzelm@19482
   462
  in maps resb thbs end;
clasohm@0
   463
clasohm@0
   464
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   465
lcp@11
   466
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   467
  makes proof trees*)
wenzelm@252
   468
fun rls MRS bottom_rl =
lcp@11
   469
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   470
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   471
  in  rs_aux 1 rls  end;
lcp@11
   472
lcp@11
   473
(*As above, but for rule lists*)
wenzelm@252
   474
fun rlss MRL bottom_rls =
lcp@11
   475
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   476
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   477
  in  rs_aux 1 rlss  end;
lcp@11
   478
wenzelm@9288
   479
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   480
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   481
wenzelm@252
   482
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   483
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   484
  ALWAYS deletes premise i *)
wenzelm@252
   485
fun compose(tha,i,thb) =
paulson@24426
   486
    distinct Thm.eq_thm (Seq.list_of (bicompose false (false,tha,0) i thb));
clasohm@0
   487
wenzelm@6946
   488
fun compose_single (tha,i,thb) =
paulson@24426
   489
  case compose (tha,i,thb) of
wenzelm@6946
   490
    [th] => th
paulson@24426
   491
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]);
wenzelm@6946
   492
clasohm@0
   493
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   494
fun tha COMP thb =
paulson@24426
   495
    case compose(tha,1,thb) of
wenzelm@252
   496
        [th] => th
clasohm@0
   497
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   498
wenzelm@13105
   499
wenzelm@4016
   500
(** theorem equality **)
clasohm@0
   501
clasohm@0
   502
(*Useful "distance" function for BEST_FIRST*)
wenzelm@16720
   503
val size_of_thm = size_of_term o Thm.full_prop_of;
clasohm@0
   504
lcp@1194
   505
lcp@1194
   506
clasohm@0
   507
(*** Meta-Rewriting Rules ***)
clasohm@0
   508
wenzelm@26487
   509
val read_prop = certify o SimpleSyntax.read_prop;
wenzelm@26487
   510
wenzelm@26487
   511
fun store_thm name th =
wenzelm@26487
   512
  Context.>>> (Context.map_theory_result (PureThy.store_thm (name, th)));
paulson@4610
   513
wenzelm@26487
   514
fun store_thm_open name th =
wenzelm@26487
   515
  Context.>>> (Context.map_theory_result (PureThy.store_thm_open (name, th)));
wenzelm@26487
   516
wenzelm@26487
   517
fun store_standard_thm name th = store_thm name (standard th);
wenzelm@12135
   518
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   519
clasohm@0
   520
val reflexive_thm =
wenzelm@26487
   521
  let val cx = certify (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   522
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   523
clasohm@0
   524
val symmetric_thm =
wenzelm@24241
   525
  let val xy = read_prop "x::'a == y::'a"
wenzelm@16595
   526
  in store_standard_thm_open "symmetric" (Thm.implies_intr xy (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   527
clasohm@0
   528
val transitive_thm =
wenzelm@24241
   529
  let val xy = read_prop "x::'a == y::'a"
wenzelm@24241
   530
      val yz = read_prop "y::'a == z::'a"
clasohm@0
   531
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   532
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   533
nipkow@4679
   534
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   535
berghofe@11512
   536
fun extensional eq =
berghofe@11512
   537
  let val eq' =
wenzelm@22906
   538
    abstract_rule "x" (Thm.dest_arg (fst (Thm.dest_equals (cprop_of eq)))) eq
berghofe@11512
   539
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   540
wenzelm@18820
   541
val equals_cong =
wenzelm@24241
   542
  store_standard_thm_open "equals_cong" (Thm.reflexive (read_prop "x::'a == y::'a"));
wenzelm@18820
   543
berghofe@10414
   544
val imp_cong =
berghofe@10414
   545
  let
wenzelm@24241
   546
    val ABC = read_prop "A ==> B::prop == C::prop"
wenzelm@24241
   547
    val AB = read_prop "A ==> B"
wenzelm@24241
   548
    val AC = read_prop "A ==> C"
wenzelm@24241
   549
    val A = read_prop "A"
berghofe@10414
   550
  in
wenzelm@12135
   551
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   552
      (implies_intr AB (implies_intr A
berghofe@10414
   553
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   554
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   555
      (implies_intr AC (implies_intr A
berghofe@10414
   556
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   557
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   558
  end;
berghofe@10414
   559
berghofe@10414
   560
val swap_prems_eq =
berghofe@10414
   561
  let
wenzelm@24241
   562
    val ABC = read_prop "A ==> B ==> C"
wenzelm@24241
   563
    val BAC = read_prop "B ==> A ==> C"
wenzelm@24241
   564
    val A = read_prop "A"
wenzelm@24241
   565
    val B = read_prop "B"
berghofe@10414
   566
  in
wenzelm@12135
   567
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   568
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   569
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   570
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   571
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   572
  end;
lcp@229
   573
wenzelm@22938
   574
val imp_cong_rule = Thm.combination o Thm.combination (Thm.reflexive implies);
wenzelm@22938
   575
wenzelm@23537
   576
fun arg_cong_rule ct th = Thm.combination (Thm.reflexive ct) th;    (*AP_TERM in LCF/HOL*)
wenzelm@23537
   577
fun fun_cong_rule th ct = Thm.combination th (Thm.reflexive ct);    (*AP_THM in LCF/HOL*)
wenzelm@23568
   578
fun binop_cong_rule ct th1 th2 = Thm.combination (arg_cong_rule ct th1) th2;
clasohm@0
   579
skalberg@15001
   580
local
wenzelm@22906
   581
  val dest_eq = Thm.dest_equals o cprop_of
skalberg@15001
   582
  val rhs_of = snd o dest_eq
skalberg@15001
   583
in
skalberg@15001
   584
fun beta_eta_conversion t =
skalberg@15001
   585
  let val thm = beta_conversion true t
skalberg@15001
   586
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   587
end;
skalberg@15001
   588
berghofe@15925
   589
fun eta_long_conversion ct = transitive (beta_eta_conversion ct)
berghofe@15925
   590
  (symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
berghofe@15925
   591
paulson@20861
   592
(*Contract all eta-redexes in the theorem, lest they give rise to needless abstractions*)
paulson@20861
   593
fun eta_contraction_rule th =
paulson@20861
   594
  equal_elim (eta_conversion (cprop_of th)) th;
paulson@20861
   595
wenzelm@24947
   596
wenzelm@24947
   597
(* abs_def *)
wenzelm@24947
   598
wenzelm@24947
   599
(*
wenzelm@24947
   600
   f ?x1 ... ?xn == u
wenzelm@24947
   601
  --------------------
wenzelm@24947
   602
   f == %x1 ... xn. u
wenzelm@24947
   603
*)
wenzelm@24947
   604
wenzelm@24947
   605
local
wenzelm@24947
   606
wenzelm@24947
   607
fun contract_lhs th =
wenzelm@24947
   608
  Thm.transitive (Thm.symmetric (beta_eta_conversion
wenzelm@24947
   609
    (fst (Thm.dest_equals (cprop_of th))))) th;
wenzelm@24947
   610
wenzelm@24947
   611
fun var_args ct =
wenzelm@24947
   612
  (case try Thm.dest_comb ct of
wenzelm@24947
   613
    SOME (f, arg) =>
wenzelm@24947
   614
      (case Thm.term_of arg of
wenzelm@24947
   615
        Var ((x, _), _) => update (eq_snd (op aconvc)) (x, arg) (var_args f)
wenzelm@24947
   616
      | _ => [])
wenzelm@24947
   617
  | NONE => []);
wenzelm@24947
   618
wenzelm@24947
   619
in
wenzelm@24947
   620
wenzelm@24947
   621
fun abs_def th =
wenzelm@18337
   622
  let
wenzelm@24947
   623
    val th' = contract_lhs th;
wenzelm@24947
   624
    val args = var_args (Thm.lhs_of th');
wenzelm@24947
   625
  in contract_lhs (fold (uncurry Thm.abstract_rule) args th') end;
wenzelm@24947
   626
wenzelm@24947
   627
end;
wenzelm@24947
   628
wenzelm@18337
   629
wenzelm@18468
   630
wenzelm@15669
   631
(*** Some useful meta-theorems ***)
clasohm@0
   632
clasohm@0
   633
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@24241
   634
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "?psi"));
wenzelm@7380
   635
val _ = store_thm "_" asm_rl;
clasohm@0
   636
clasohm@0
   637
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   638
val cut_rl =
wenzelm@12135
   639
  store_standard_thm_open "cut_rl"
wenzelm@24241
   640
    (Thm.trivial (read_prop "?psi ==> ?theta"));
clasohm@0
   641
wenzelm@252
   642
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   643
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   644
val revcut_rl =
wenzelm@24241
   645
  let val V = read_prop "V"
wenzelm@24241
   646
      and VW = read_prop "V ==> W";
wenzelm@4016
   647
  in
wenzelm@12135
   648
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   649
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   650
  end;
clasohm@0
   651
lcp@668
   652
(*for deleting an unwanted assumption*)
lcp@668
   653
val thin_rl =
wenzelm@24241
   654
  let val V = read_prop "V"
wenzelm@24241
   655
      and W = read_prop "W";
wenzelm@12135
   656
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   657
clasohm@0
   658
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   659
val triv_forall_equality =
wenzelm@24241
   660
  let val V  = read_prop "V"
wenzelm@24241
   661
      and QV = read_prop "!!x::'a. V"
wenzelm@26487
   662
      and x  = certify (Free ("x", Term.aT []));
wenzelm@4016
   663
  in
wenzelm@12135
   664
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   665
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   666
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   667
  end;
clasohm@0
   668
wenzelm@19051
   669
(* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
wenzelm@19051
   670
   (PROP ?Phi ==> PROP ?Psi)
wenzelm@19051
   671
*)
wenzelm@19051
   672
val distinct_prems_rl =
wenzelm@19051
   673
  let
wenzelm@24241
   674
    val AAB = read_prop "Phi ==> Phi ==> Psi"
wenzelm@24241
   675
    val A = read_prop "Phi";
wenzelm@19051
   676
  in
wenzelm@19051
   677
    store_standard_thm_open "distinct_prems_rl"
wenzelm@19051
   678
      (implies_intr_list [AAB, A] (implies_elim_list (assume AAB) [assume A, assume A]))
wenzelm@19051
   679
  end;
wenzelm@19051
   680
nipkow@1756
   681
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   682
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   683
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   684
*)
nipkow@1756
   685
val swap_prems_rl =
wenzelm@24241
   686
  let val cmajor = read_prop "PhiA ==> PhiB ==> Psi";
nipkow@1756
   687
      val major = assume cmajor;
wenzelm@24241
   688
      val cminor1 = read_prop "PhiA";
nipkow@1756
   689
      val minor1 = assume cminor1;
wenzelm@24241
   690
      val cminor2 = read_prop "PhiB";
nipkow@1756
   691
      val minor2 = assume cminor2;
wenzelm@12135
   692
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   693
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   694
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   695
  end;
nipkow@1756
   696
nipkow@3653
   697
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   698
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   699
   Introduction rule for == as a meta-theorem.
nipkow@3653
   700
*)
nipkow@3653
   701
val equal_intr_rule =
wenzelm@24241
   702
  let val PQ = read_prop "phi ==> psi"
wenzelm@24241
   703
      and QP = read_prop "psi ==> phi"
wenzelm@4016
   704
  in
wenzelm@12135
   705
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   706
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   707
  end;
nipkow@3653
   708
wenzelm@19421
   709
(* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@13368
   710
val equal_elim_rule1 =
wenzelm@24241
   711
  let val eq = read_prop "phi::prop == psi::prop"
wenzelm@24241
   712
      and P = read_prop "phi"
wenzelm@13368
   713
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   714
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   715
  end;
wenzelm@4285
   716
wenzelm@19421
   717
(* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
wenzelm@19421
   718
val equal_elim_rule2 =
wenzelm@19421
   719
  store_standard_thm_open "equal_elim_rule2" (symmetric_thm RS equal_elim_rule1);
wenzelm@19421
   720
wenzelm@12297
   721
(* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
wenzelm@12297
   722
val remdups_rl =
wenzelm@24241
   723
  let val P = read_prop "phi" and Q = read_prop "psi";
wenzelm@12297
   724
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   725
wenzelm@12297
   726
wenzelm@9554
   727
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@12297
   728
  Rewrite rule for HHF normalization.*)
wenzelm@9554
   729
wenzelm@9554
   730
val norm_hhf_eq =
wenzelm@9554
   731
  let
wenzelm@14854
   732
    val aT = TFree ("'a", []);
wenzelm@9554
   733
    val all = Term.all aT;
wenzelm@9554
   734
    val x = Free ("x", aT);
wenzelm@9554
   735
    val phi = Free ("phi", propT);
wenzelm@9554
   736
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   737
wenzelm@26487
   738
    val cx = certify x;
wenzelm@26487
   739
    val cphi = certify phi;
wenzelm@26487
   740
    val lhs = certify (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@26487
   741
    val rhs = certify (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   742
  in
wenzelm@9554
   743
    Thm.equal_intr
wenzelm@9554
   744
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   745
        |> Thm.forall_elim cx
wenzelm@9554
   746
        |> Thm.implies_intr cphi
wenzelm@9554
   747
        |> Thm.forall_intr cx
wenzelm@9554
   748
        |> Thm.implies_intr lhs)
wenzelm@9554
   749
      (Thm.implies_elim
wenzelm@9554
   750
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   751
        |> Thm.forall_intr cx
wenzelm@9554
   752
        |> Thm.implies_intr cphi
wenzelm@9554
   753
        |> Thm.implies_intr rhs)
wenzelm@12135
   754
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   755
  end;
wenzelm@9554
   756
wenzelm@18179
   757
val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
wenzelm@18179
   758
wenzelm@12800
   759
fun is_norm_hhf tm =
wenzelm@12800
   760
  let
wenzelm@12800
   761
    fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@12800
   762
      | is_norm (t $ u) = is_norm t andalso is_norm u
wenzelm@12800
   763
      | is_norm (Abs (_, _, t)) = is_norm t
wenzelm@12800
   764
      | is_norm _ = true;
wenzelm@18929
   765
  in is_norm (Envir.beta_eta_contract tm) end;
wenzelm@12800
   766
wenzelm@16425
   767
fun norm_hhf thy t =
wenzelm@12800
   768
  if is_norm_hhf t then t
wenzelm@18179
   769
  else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
wenzelm@18179
   770
wenzelm@20298
   771
fun norm_hhf_cterm ct =
wenzelm@20298
   772
  if is_norm_hhf (Thm.term_of ct) then ct
wenzelm@20298
   773
  else cterm_fun (Pattern.rewrite_term (Thm.theory_of_cterm ct) [norm_hhf_prop] []) ct;
wenzelm@20298
   774
wenzelm@12800
   775
wenzelm@21603
   776
(* var indexes *)
wenzelm@21603
   777
paulson@24426
   778
(*Increment the indexes of only the type variables*)
paulson@24426
   779
fun incr_type_indexes inc th =
paulson@24426
   780
  let val tvs = term_tvars (prop_of th)
paulson@24426
   781
      and thy = theory_of_thm th
paulson@24426
   782
      fun inc_tvar ((a,i),s) = pairself (ctyp_of thy) (TVar ((a,i),s), TVar ((a,i+inc),s))
paulson@24426
   783
  in Thm.instantiate (map inc_tvar tvs, []) th end;
paulson@24426
   784
wenzelm@21603
   785
fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
wenzelm@21603
   786
wenzelm@21603
   787
fun incr_indexes2 th1 th2 =
wenzelm@21603
   788
  Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
wenzelm@21603
   789
wenzelm@21603
   790
fun th1 INCR_COMP th2 = incr_indexes th2 th1 COMP th2;
wenzelm@21603
   791
fun th1 COMP_INCR th2 = th1 COMP incr_indexes th1 th2;
wenzelm@21603
   792
wenzelm@9554
   793
wenzelm@16425
   794
(*** Instantiate theorem th, reading instantiations in theory thy ****)
paulson@8129
   795
paulson@8129
   796
(*Version that normalizes the result: Thm.instantiate no longer does that*)
wenzelm@21603
   797
fun instantiate instpair th =
wenzelm@21603
   798
  Thm.adjust_maxidx_thm ~1 (Thm.instantiate instpair th COMP_INCR asm_rl);
paulson@8129
   799
wenzelm@16425
   800
fun read_instantiate_sg' thy sinsts th =
paulson@8129
   801
    let val ts = types_sorts th;
wenzelm@15669
   802
        val used = add_used th [];
wenzelm@16425
   803
    in  instantiate (read_insts thy ts ts used sinsts) th  end;
berghofe@15797
   804
wenzelm@16425
   805
fun read_instantiate_sg thy sinsts th =
wenzelm@20298
   806
  read_instantiate_sg' thy (map (apfst Syntax.read_indexname) sinsts) th;
paulson@8129
   807
paulson@8129
   808
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   809
fun read_instantiate sinsts th =
wenzelm@16425
   810
    read_instantiate_sg (Thm.theory_of_thm th) sinsts th;
paulson@8129
   811
berghofe@15797
   812
fun read_instantiate' sinsts th =
wenzelm@16425
   813
    read_instantiate_sg' (Thm.theory_of_thm th) sinsts th;
berghofe@15797
   814
paulson@8129
   815
paulson@8129
   816
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   817
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   818
local
wenzelm@16425
   819
  fun add_types ((ct,cu), (thy,tye,maxidx)) =
wenzelm@26627
   820
    let
wenzelm@26627
   821
        val thyt = Thm.theory_of_cterm ct;
wenzelm@26627
   822
        val thyu = Thm.theory_of_cterm cu;
wenzelm@26627
   823
        val {t, T, maxidx = maxt, ...} = Thm.rep_cterm ct;
wenzelm@26627
   824
        val {t = u, T = U, maxidx = maxu, ...} = Thm.rep_cterm cu;
paulson@8129
   825
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
wenzelm@16425
   826
        val thy' = Theory.merge(thy, Theory.merge(thyt, thyu))
wenzelm@16949
   827
        val (tye',maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
berghofe@25470
   828
          handle Type.TUNIFY => raise TYPE ("Ill-typed instantiation:\nType\n" ^
berghofe@25470
   829
            Sign.string_of_typ thy' (Envir.norm_type tye T) ^
berghofe@25470
   830
            "\nof variable " ^
berghofe@25470
   831
            Sign.string_of_term thy' (Term.map_types (Envir.norm_type tye) t) ^
berghofe@25470
   832
            "\ncannot be unified with type\n" ^
berghofe@25470
   833
            Sign.string_of_typ thy' (Envir.norm_type tye U) ^ "\nof term " ^
berghofe@25470
   834
            Sign.string_of_term thy' (Term.map_types (Envir.norm_type tye) u),
berghofe@25470
   835
            [T, U], [t, u])
wenzelm@16425
   836
    in  (thy', tye', maxi')  end;
paulson@8129
   837
in
paulson@22561
   838
fun cterm_instantiate [] th = th
paulson@22561
   839
  | cterm_instantiate ctpairs0 th =
wenzelm@23178
   840
  let val (thy,tye,_) = List.foldr add_types (Thm.theory_of_thm th, Vartab.empty, 0) ctpairs0
wenzelm@18179
   841
      fun instT(ct,cu) =
paulson@22287
   842
        let val inst = cterm_of thy o Term.map_types (Envir.norm_type tye) o term_of
paulson@14340
   843
        in (inst ct, inst cu) end
paulson@22307
   844
      fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy (Envir.norm_type tye T))
berghofe@8406
   845
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   846
  handle TERM _ =>
wenzelm@16425
   847
           raise THM("cterm_instantiate: incompatible theories",0,[th])
paulson@8129
   848
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   849
end;
paulson@8129
   850
paulson@8129
   851
wenzelm@19775
   852
(** protected propositions and embedded terms **)
wenzelm@4789
   853
wenzelm@4789
   854
local
wenzelm@26487
   855
  val A = certify (Free ("A", propT));
wenzelm@26424
   856
  val get_axiom = Thm.unvarify o Thm.get_axiom (Context.the_theory (Context.the_thread_data ()));
wenzelm@26424
   857
  val prop_def = get_axiom "prop_def";
wenzelm@26424
   858
  val term_def = get_axiom "term_def";
wenzelm@4789
   859
in
wenzelm@26487
   860
  val protect = Thm.capply (certify Logic.protectC);
wenzelm@21437
   861
  val protectI = store_thm "protectI" (PureThy.kind_rule Thm.internalK (standard
wenzelm@18025
   862
      (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A))));
wenzelm@21437
   863
  val protectD = store_thm "protectD" (PureThy.kind_rule Thm.internalK (standard
wenzelm@18025
   864
      (Thm.equal_elim prop_def (Thm.assume (protect A)))));
wenzelm@18179
   865
  val protect_cong = store_standard_thm_open "protect_cong" (Thm.reflexive (protect A));
wenzelm@19775
   866
wenzelm@21437
   867
  val termI = store_thm "termI" (PureThy.kind_rule Thm.internalK (standard
wenzelm@19775
   868
      (Thm.equal_elim (Thm.symmetric term_def) (Thm.forall_intr A (Thm.trivial A)))));
wenzelm@4789
   869
end;
wenzelm@4789
   870
wenzelm@18025
   871
fun implies_intr_protected asms th =
wenzelm@18118
   872
  let val asms' = map protect asms in
wenzelm@18118
   873
    implies_elim_list
wenzelm@18118
   874
      (implies_intr_list asms th)
wenzelm@18118
   875
      (map (fn asm' => Thm.assume asm' RS protectD) asms')
wenzelm@18118
   876
    |> implies_intr_list asms'
wenzelm@18118
   877
  end;
wenzelm@11815
   878
wenzelm@19775
   879
fun mk_term ct =
wenzelm@19775
   880
  let
wenzelm@26627
   881
    val thy = Thm.theory_of_cterm ct;
wenzelm@19775
   882
    val cert = Thm.cterm_of thy;
wenzelm@19775
   883
    val certT = Thm.ctyp_of thy;
wenzelm@26627
   884
    val T = Thm.typ_of (Thm.ctyp_of_term ct);
wenzelm@19775
   885
    val a = certT (TVar (("'a", 0), []));
wenzelm@19775
   886
    val x = cert (Var (("x", 0), T));
wenzelm@19775
   887
  in Thm.instantiate ([(a, certT T)], [(x, ct)]) termI end;
wenzelm@19775
   888
wenzelm@19775
   889
fun dest_term th =
wenzelm@21566
   890
  let val cprop = strip_imp_concl (Thm.cprop_of th) in
wenzelm@19775
   891
    if can Logic.dest_term (Thm.term_of cprop) then
wenzelm@20579
   892
      Thm.dest_arg cprop
wenzelm@19775
   893
    else raise THM ("dest_term", 0, [th])
wenzelm@19775
   894
  end;
wenzelm@19775
   895
wenzelm@21519
   896
fun cterm_rule f = dest_term o f o mk_term;
wenzelm@21519
   897
fun term_rule thy f t = Thm.term_of (cterm_rule f (Thm.cterm_of thy t));
wenzelm@20881
   898
wenzelm@26487
   899
val dummy_thm = mk_term (certify (Term.dummy_pattern propT));
wenzelm@24005
   900
wenzelm@24005
   901
wenzelm@4789
   902
wenzelm@5688
   903
(** variations on instantiate **)
wenzelm@4285
   904
wenzelm@4285
   905
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   906
wenzelm@4285
   907
fun instantiate' cTs cts thm =
wenzelm@4285
   908
  let
wenzelm@4285
   909
    fun err msg =
wenzelm@4285
   910
      raise TYPE ("instantiate': " ^ msg,
wenzelm@19482
   911
        map_filter (Option.map Thm.typ_of) cTs,
wenzelm@19482
   912
        map_filter (Option.map Thm.term_of) cts);
wenzelm@4285
   913
wenzelm@4285
   914
    fun inst_of (v, ct) =
wenzelm@16425
   915
      (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
wenzelm@4285
   916
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   917
berghofe@15797
   918
    fun tyinst_of (v, cT) =
wenzelm@16425
   919
      (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
berghofe@15797
   920
        handle TYPE (msg, _, _) => err msg;
berghofe@15797
   921
wenzelm@20298
   922
    fun zip_vars xs ys =
wenzelm@20298
   923
      zip_options xs ys handle Library.UnequalLengths =>
wenzelm@20298
   924
        err "more instantiations than variables in thm";
wenzelm@4285
   925
wenzelm@4285
   926
    (*instantiate types first!*)
wenzelm@4285
   927
    val thm' =
wenzelm@4285
   928
      if forall is_none cTs then thm
wenzelm@20298
   929
      else Thm.instantiate
wenzelm@22695
   930
        (map tyinst_of (zip_vars (rev (Thm.fold_terms Term.add_tvars thm [])) cTs), []) thm;
wenzelm@20579
   931
    val thm'' =
wenzelm@4285
   932
      if forall is_none cts then thm'
wenzelm@20298
   933
      else Thm.instantiate
wenzelm@22695
   934
        ([], map inst_of (zip_vars (rev (Thm.fold_terms Term.add_vars thm' [])) cts)) thm';
wenzelm@20298
   935
    in thm'' end;
wenzelm@4285
   936
wenzelm@4285
   937
berghofe@14081
   938
berghofe@14081
   939
(** renaming of bound variables **)
berghofe@14081
   940
berghofe@14081
   941
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
   942
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
   943
berghofe@14081
   944
fun rename_bvars [] thm = thm
berghofe@14081
   945
  | rename_bvars vs thm =
wenzelm@26627
   946
      let
wenzelm@26627
   947
        val cert = Thm.cterm_of (Thm.theory_of_thm thm);
wenzelm@26627
   948
        fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
wenzelm@26627
   949
          | ren (t $ u) = ren t $ ren u
wenzelm@26627
   950
          | ren t = t;
wenzelm@26627
   951
      in equal_elim (reflexive (cert (ren (Thm.prop_of thm)))) thm end;
berghofe@14081
   952
berghofe@14081
   953
berghofe@14081
   954
(* renaming in left-to-right order *)
berghofe@14081
   955
berghofe@14081
   956
fun rename_bvars' xs thm =
berghofe@14081
   957
  let
wenzelm@26627
   958
    val cert = Thm.cterm_of (Thm.theory_of_thm thm);
wenzelm@26627
   959
    val prop = Thm.prop_of thm;
berghofe@14081
   960
    fun rename [] t = ([], t)
berghofe@14081
   961
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
   962
          let val (xs', t') = rename xs t
wenzelm@18929
   963
          in (xs', Abs (the_default x x', T, t')) end
berghofe@14081
   964
      | rename xs (t $ u) =
berghofe@14081
   965
          let
berghofe@14081
   966
            val (xs', t') = rename xs t;
berghofe@14081
   967
            val (xs'', u') = rename xs' u
berghofe@14081
   968
          in (xs'', t' $ u') end
berghofe@14081
   969
      | rename xs t = (xs, t);
berghofe@14081
   970
  in case rename xs prop of
wenzelm@26627
   971
      ([], prop') => equal_elim (reflexive (cert prop')) thm
berghofe@14081
   972
    | _ => error "More names than abstractions in theorem"
berghofe@14081
   973
  end;
berghofe@14081
   974
berghofe@14081
   975
wenzelm@11975
   976
wenzelm@18225
   977
(** multi_resolve **)
wenzelm@18225
   978
wenzelm@18225
   979
local
wenzelm@18225
   980
wenzelm@18225
   981
fun res th i rule =
wenzelm@18225
   982
  Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
wenzelm@18225
   983
wenzelm@18225
   984
fun multi_res _ [] rule = Seq.single rule
wenzelm@18225
   985
  | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
wenzelm@18225
   986
wenzelm@18225
   987
in
wenzelm@18225
   988
wenzelm@18225
   989
val multi_resolve = multi_res 1;
wenzelm@18225
   990
fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
wenzelm@18225
   991
wenzelm@18225
   992
end;
wenzelm@18225
   993
wenzelm@11975
   994
end;
wenzelm@5903
   995
wenzelm@5903
   996
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
   997
open BasicDrule;