src/Pure/drule.ML
author wenzelm
Thu Nov 23 21:29:50 2000 +0100 (2000-11-23)
changeset 10515 8430c8fa8a9f
parent 10441 d727c39c4a4b
child 10667 75a1c9575edb
permissions -rw-r--r--
standard: close_derivation;
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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 skip_flexpairs    : 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 read_insts        :
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          Sign.sg -> (indexname -> typ option) * (indexname -> sort option)
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                  -> (indexname -> typ option) * (indexname -> sort option)
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                  -> string list -> (string*string)list
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                  -> (indexname*ctyp)list * (cterm*cterm)list
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  val 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 forall_elim_vars_safe  : thm -> thm
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  val freeze_thaw       : thm -> thm * (thm -> thm)
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  val implies_elim_list : thm -> thm list -> thm
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  val implies_intr_list : cterm list -> thm -> thm
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  val instantiate       :
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    (indexname * ctyp) list * (cterm * cterm) list -> thm -> thm
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  val zero_var_indexes  : 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 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: Sign.sg -> (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 weak_eq_thm       : thm * thm -> bool
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  val eq_thm_sg         : 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 refl_implies      : thm
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  val symmetric_fun     : thm -> thm
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  val imp_cong          : thm
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  val swap_prems_eq     : thm
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  val equal_abs_elim    : cterm  -> thm -> thm
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  val equal_abs_elim_list: cterm list -> thm -> thm
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  val flexpair_abs_elim_list: cterm list -> thm -> thm
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  val asm_rl            : thm
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  val cut_rl            : thm
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  val revcut_rl         : thm
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  val thin_rl           : thm
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  val triv_forall_equality: thm
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  val swap_prems_rl     : thm
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  val equal_intr_rule   : thm
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  val inst              : string -> string -> thm -> thm
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  val instantiate'      : ctyp option list -> cterm option list -> thm -> thm
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  val incr_indexes_wrt  : int list -> ctyp list -> cterm list -> thm list -> thm -> thm
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end;
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signature DRULE =
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sig
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  include BASIC_DRULE
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  val rule_attribute    : ('a -> thm -> thm) -> 'a attribute
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  val tag_rule          : tag -> thm -> thm
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  val untag_rule        : string -> thm -> thm
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  val tag               : tag -> 'a attribute
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  val untag             : string -> 'a attribute
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  val tag_lemma         : 'a attribute
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  val tag_assumption    : 'a attribute
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  val tag_internal      : 'a attribute
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  val has_internal	: tag list -> bool
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  val close_derivation  : thm -> thm
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  val compose_single    : thm * int * thm -> thm
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  val add_rules		: thm list -> thm list -> thm list
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  val del_rules		: thm list -> thm list -> thm list
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  val merge_rules	: thm list * thm list -> thm list
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  val norm_hhf_eq	: thm
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  val triv_goal         : thm
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  val rev_triv_goal     : thm
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  val freeze_all        : thm -> thm
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  val mk_triv_goal      : cterm -> thm
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  val mk_cgoal          : cterm -> cterm
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  val assume_goal       : cterm -> 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 unvarifyT         : thm -> thm
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  val unvarify          : thm -> thm
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  val tvars_intr_list	: 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: much faster than calling cterm_of! **)
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(** SAME NAMES as in structure Logic: use compound identifiers! **)
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(*dest_implies for cterms. Note T=prop below*)
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fun dest_implies ct =
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    case term_of ct of
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        (Const("==>", _) $ _ $ _) =>
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            let val (ct1,ct2) = dest_comb ct
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            in  (#2 (dest_comb ct1), ct2)  end
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      | _ => raise TERM ("dest_implies", [term_of ct]) ;
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fun dest_equals ct =
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    case term_of ct of
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        (Const("==", _) $ _ $ _) =>
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            let val (ct1,ct2) = dest_comb ct
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            in  (#2 (dest_comb ct1), ct2)  end
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      | _ => raise TERM ("dest_equals", [term_of ct]) ;
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(*Discard flexflex pairs; return a cterm*)
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fun skip_flexpairs ct =
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    case term_of ct of
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        (Const("==>", _) $ (Const("=?=",_)$_$_) $ _) =>
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            skip_flexpairs (#2 (dest_implies ct))
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      | _ => ct;
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(* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
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fun 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 (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 skip_flexpairs o cprop_of;
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val proto_sign = Theory.sign_of ProtoPure.thy;
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val implies = cterm_of proto_sign Term.implies;
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(*cterm version of mk_implies*)
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fun mk_implies(A,B) = capply (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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(** 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 sign (rtypes,rsorts) (types,sorts) used insts =
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let
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    fun split([],tvs,vs) = (tvs,vs)
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      | split((sv,st)::l,tvs,vs) = (case Symbol.explode sv of
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                  "'"::cs => split(l,(Syntax.indexname cs,st)::tvs,vs)
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                | cs => split(l,tvs,(Syntax.indexname cs,st)::vs));
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    val (tvs,vs) = split(insts,[],[]);
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    fun readT((a,i),st) =
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        let val ixn = ("'" ^ a,i);
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            val S = case rsorts ixn of Some S => S | None => absent ixn;
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            val T = Sign.read_typ (sign,sorts) st;
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        in if Sign.typ_instance sign (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(sign,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 sign (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) => (ixn,ctyp_of sign 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,...} = rep_thm thm;
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        val big = list_comb(prop,hyps); (* bogus term! *)
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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 assoc(frees,a) else assoc(vars,(a,i));
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        fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i));
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    in (typ,sort) end;
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(** basic attributes **)
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(* dependent rules *)
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fun rule_attribute f (x, thm) = (x, (f x thm));
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(* add / delete tags *)
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fun map_tags f thm =
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  Thm.put_name_tags (Thm.name_of_thm thm, f (#2 (Thm.get_name_tags thm))) thm;
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fun tag_rule tg = map_tags (fn tgs => if tg mem tgs then tgs else tgs @ [tg]);
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fun untag_rule s = map_tags (filter_out (equal s o #1));
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fun tag tg x = rule_attribute (K (tag_rule tg)) x;
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fun untag s x = rule_attribute (K (untag_rule s)) x;
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fun simple_tag name x = tag (name, []) x;
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fun tag_lemma x = simple_tag "lemma" x;
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fun tag_assumption x = simple_tag "assumption" x;
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val internal_tag = ("internal", []);
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fun tag_internal x = tag internal_tag x;
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fun has_internal tags = exists (equal internal_tag) tags;
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(** Standardization of rules **)
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(*Strip extraneous shyps as far as possible*)
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fun strip_shyps_warning thm =
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  let
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    val str_of_sort = Sign.str_of_sort (Thm.sign_of_thm thm);
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    val thm' = Thm.strip_shyps thm;
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    val xshyps = Thm.extra_shyps thm';
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  in
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    if null xshyps then ()
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    else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
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    thm'
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  end;
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(*Generalization over a list of variables, IGNORING bad ones*)
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fun forall_intr_list [] th = th
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  | forall_intr_list (y::ys) th =
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        let val gth = forall_intr_list ys th
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        in  forall_intr y gth   handle THM _ =>  gth  end;
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(*Generalization over all suitable Free variables*)
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fun forall_intr_frees th =
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    let val {prop,sign,...} = rep_thm th
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    in  forall_intr_list
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         (map (cterm_of sign) (sort (make_ord atless) (term_frees prop)))
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         th
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    end;
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val forall_elim_var = PureThy.forall_elim_var;
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val forall_elim_vars = PureThy.forall_elim_vars;
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fun forall_elim_vars_safe th =
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  forall_elim_vars_safe (forall_elim_var (#maxidx (Thm.rep_thm th) + 1) th)
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    handle THM _ => th;
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(*Specialization over a list of cterms*)
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fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
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(* maps [A1,...,An], B   to   [| A1;...;An |] ==> B  *)
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fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
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(* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
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fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
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(*Reset Var indexes to zero, renaming to preserve distinctness*)
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fun zero_var_indexes th =
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    let val {prop,sign,...} = rep_thm th;
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        val vars = term_vars prop
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        val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
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        val inrs = add_term_tvars(prop,[]);
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        val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
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        val tye = ListPair.map (fn ((v,rs),a) => (v, TVar((a,0),rs)))
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                     (inrs, nms')
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        val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye;
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        fun varpairs([],[]) = []
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   315
          | varpairs((var as Var(v,T)) :: vars, b::bs) =
wenzelm@252
   316
                let val T' = typ_subst_TVars tye T
wenzelm@252
   317
                in (cterm_of sign (Var(v,T')),
wenzelm@252
   318
                    cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
wenzelm@252
   319
                end
wenzelm@252
   320
          | varpairs _ = raise TERM("varpairs", []);
paulson@8129
   321
    in Thm.instantiate (ctye, varpairs(vars,rev bs)) th end;
clasohm@0
   322
clasohm@0
   323
clasohm@0
   324
(*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers;
clasohm@0
   325
    all generality expressed by Vars having index 0.*)
wenzelm@10515
   326
wenzelm@10515
   327
fun close_derivation thm =
wenzelm@10515
   328
  if Thm.get_name_tags thm = ("", []) then Thm.name_thm ("", thm)
wenzelm@10515
   329
  else thm;
wenzelm@10515
   330
clasohm@0
   331
fun standard th =
wenzelm@10515
   332
  let val {maxidx,...} = rep_thm th in
wenzelm@10515
   333
    th
wenzelm@10515
   334
    |> implies_intr_hyps
wenzelm@10515
   335
    |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
wenzelm@10515
   336
    |> strip_shyps_warning
wenzelm@10515
   337
    |> zero_var_indexes |> Thm.varifyT |> Thm.compress |> close_derivation
wenzelm@1218
   338
  end;
wenzelm@1218
   339
clasohm@0
   340
wenzelm@8328
   341
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   342
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   343
  Similar code in type/freeze_thaw*)
paulson@4610
   344
fun freeze_thaw th =
paulson@7248
   345
 let val fth = freezeT th
paulson@7248
   346
     val {prop,sign,...} = rep_thm fth
paulson@7248
   347
 in
paulson@7248
   348
   case term_vars prop of
paulson@7248
   349
       [] => (fth, fn x => x)
paulson@7248
   350
     | vars =>
wenzelm@8328
   351
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@8328
   352
                   let val v = variant used (string_of_indexname ix)
wenzelm@8328
   353
                   in  ((ix,v)::pairs, v::used)  end;
wenzelm@8328
   354
             val (alist, _) = foldr newName
wenzelm@8328
   355
                                (vars, ([], add_term_names (prop, [])))
wenzelm@8328
   356
             fun mk_inst (Var(v,T)) =
wenzelm@8328
   357
                 (cterm_of sign (Var(v,T)),
wenzelm@8328
   358
                  cterm_of sign (Free(the (assoc(alist,v)), T)))
wenzelm@8328
   359
             val insts = map mk_inst vars
wenzelm@8328
   360
             fun thaw th' =
wenzelm@8328
   361
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   362
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   363
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   364
 end;
paulson@4610
   365
paulson@4610
   366
paulson@7248
   367
(*Rotates a rule's premises to the left by k*)
paulson@7248
   368
val rotate_prems = permute_prems 0;
paulson@4610
   369
paulson@4610
   370
wenzelm@252
   371
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   372
  Generalizes over Free variables,
clasohm@0
   373
  creates the assumption, and then strips quantifiers.
clasohm@0
   374
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   375
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   376
fun assume_ax thy sP =
wenzelm@6390
   377
    let val sign = Theory.sign_of thy
paulson@4610
   378
        val prop = Logic.close_form (term_of (read_cterm sign (sP, propT)))
lcp@229
   379
    in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
clasohm@0
   380
wenzelm@252
   381
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   382
fun tha RSN (i,thb) =
wenzelm@4270
   383
  case Seq.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   384
      ([th],_) => th
clasohm@0
   385
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   386
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   387
clasohm@0
   388
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   389
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   390
clasohm@0
   391
(*For joining lists of rules*)
wenzelm@252
   392
fun thas RLN (i,thbs) =
clasohm@0
   393
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   394
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
paulson@2672
   395
  in  List.concat (map resb thbs)  end;
clasohm@0
   396
clasohm@0
   397
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   398
lcp@11
   399
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   400
  makes proof trees*)
wenzelm@252
   401
fun rls MRS bottom_rl =
lcp@11
   402
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   403
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   404
  in  rs_aux 1 rls  end;
lcp@11
   405
lcp@11
   406
(*As above, but for rule lists*)
wenzelm@252
   407
fun rlss MRL bottom_rls =
lcp@11
   408
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   409
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   410
  in  rs_aux 1 rlss  end;
lcp@11
   411
wenzelm@9288
   412
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   413
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   414
wenzelm@252
   415
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   416
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   417
  ALWAYS deletes premise i *)
wenzelm@252
   418
fun compose(tha,i,thb) =
wenzelm@4270
   419
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   420
wenzelm@6946
   421
fun compose_single (tha,i,thb) =
wenzelm@6946
   422
  (case compose (tha,i,thb) of
wenzelm@6946
   423
    [th] => th
wenzelm@6946
   424
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   425
clasohm@0
   426
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   427
fun tha COMP thb =
clasohm@0
   428
    case compose(tha,1,thb) of
wenzelm@252
   429
        [th] => th
clasohm@0
   430
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   431
wenzelm@4016
   432
(** theorem equality **)
clasohm@0
   433
clasohm@0
   434
(*Do the two theorems have the same signature?*)
wenzelm@252
   435
fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2));
clasohm@0
   436
clasohm@0
   437
(*Useful "distance" function for BEST_FIRST*)
clasohm@0
   438
val size_of_thm = size_of_term o #prop o rep_thm;
clasohm@0
   439
wenzelm@9829
   440
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@9829
   441
fun del_rules rs rules = Library.gen_rems Thm.eq_thm (rules, rs);
wenzelm@9862
   442
fun add_rules rs rules = rs @ del_rules rs rules;
wenzelm@9829
   443
fun merge_rules (rules1, rules2) = Library.generic_merge Thm.eq_thm I I rules1 rules2;
wenzelm@9829
   444
clasohm@0
   445
lcp@1194
   446
(** Mark Staples's weaker version of eq_thm: ignores variable renaming and
lcp@1194
   447
    (some) type variable renaming **)
lcp@1194
   448
lcp@1194
   449
 (* Can't use term_vars, because it sorts the resulting list of variable names.
lcp@1194
   450
    We instead need the unique list noramlised by the order of appearance
lcp@1194
   451
    in the term. *)
lcp@1194
   452
fun term_vars' (t as Var(v,T)) = [t]
lcp@1194
   453
  | term_vars' (Abs(_,_,b)) = term_vars' b
lcp@1194
   454
  | term_vars' (f$a) = (term_vars' f) @ (term_vars' a)
lcp@1194
   455
  | term_vars' _ = [];
lcp@1194
   456
lcp@1194
   457
fun forall_intr_vars th =
lcp@1194
   458
  let val {prop,sign,...} = rep_thm th;
lcp@1194
   459
      val vars = distinct (term_vars' prop);
lcp@1194
   460
  in forall_intr_list (map (cterm_of sign) vars) th end;
lcp@1194
   461
wenzelm@1237
   462
fun weak_eq_thm (tha,thb) =
lcp@1194
   463
    eq_thm(forall_intr_vars (freezeT tha), forall_intr_vars (freezeT thb));
lcp@1194
   464
lcp@1194
   465
lcp@1194
   466
clasohm@0
   467
(*** Meta-Rewriting Rules ***)
clasohm@0
   468
paulson@4610
   469
fun read_prop s = read_cterm proto_sign (s, propT);
paulson@4610
   470
wenzelm@9455
   471
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   472
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@4016
   473
clasohm@0
   474
val reflexive_thm =
paulson@4610
   475
  let val cx = cterm_of proto_sign (Var(("x",0),TVar(("'a",0),logicS)))
wenzelm@9455
   476
  in store_standard_thm "reflexive" (Thm.reflexive cx) end;
clasohm@0
   477
clasohm@0
   478
val symmetric_thm =
paulson@4610
   479
  let val xy = read_prop "x::'a::logic == y"
wenzelm@9455
   480
  in store_standard_thm "symmetric" (Thm.implies_intr_hyps (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   481
clasohm@0
   482
val transitive_thm =
paulson@4610
   483
  let val xy = read_prop "x::'a::logic == y"
paulson@4610
   484
      val yz = read_prop "y::'a::logic == z"
clasohm@0
   485
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@9455
   486
  in store_standard_thm "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   487
nipkow@4679
   488
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   489
berghofe@10414
   490
val imp_cong =
berghofe@10414
   491
  let
berghofe@10414
   492
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   493
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   494
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   495
    val A = read_prop "PROP A"
berghofe@10414
   496
  in
berghofe@10414
   497
    store_standard_thm "imp_cong2" (implies_intr ABC (equal_intr
berghofe@10414
   498
      (implies_intr AB (implies_intr A
berghofe@10414
   499
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   500
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   501
      (implies_intr AC (implies_intr A
berghofe@10414
   502
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   503
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   504
  end;
berghofe@10414
   505
berghofe@10414
   506
val swap_prems_eq =
berghofe@10414
   507
  let
berghofe@10414
   508
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   509
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   510
    val A = read_prop "PROP A"
berghofe@10414
   511
    val B = read_prop "PROP B"
berghofe@10414
   512
  in
berghofe@10414
   513
    store_standard_thm "swap_prems_eq" (equal_intr
berghofe@10414
   514
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   515
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   516
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   517
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   518
  end;
lcp@229
   519
paulson@9547
   520
val refl_implies = reflexive implies;
clasohm@0
   521
clasohm@0
   522
clasohm@0
   523
(*** Some useful meta-theorems ***)
clasohm@0
   524
clasohm@0
   525
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@9455
   526
val asm_rl = store_standard_thm "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   527
val _ = store_thm "_" asm_rl;
clasohm@0
   528
clasohm@0
   529
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   530
val cut_rl =
wenzelm@9455
   531
  store_standard_thm "cut_rl"
wenzelm@9455
   532
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   533
wenzelm@252
   534
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   535
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   536
val revcut_rl =
paulson@4610
   537
  let val V = read_prop "PROP V"
paulson@4610
   538
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   539
  in
wenzelm@9455
   540
    store_standard_thm "revcut_rl"
wenzelm@4016
   541
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   542
  end;
clasohm@0
   543
lcp@668
   544
(*for deleting an unwanted assumption*)
lcp@668
   545
val thin_rl =
paulson@4610
   546
  let val V = read_prop "PROP V"
paulson@4610
   547
      and W = read_prop "PROP W";
wenzelm@9455
   548
  in  store_standard_thm "thin_rl" (implies_intr V (implies_intr W (assume W)))
lcp@668
   549
  end;
lcp@668
   550
clasohm@0
   551
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   552
val triv_forall_equality =
paulson@4610
   553
  let val V  = read_prop "PROP V"
paulson@4610
   554
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@8086
   555
      and x  = read_cterm proto_sign ("x", TypeInfer.logicT);
wenzelm@4016
   556
  in
wenzelm@9455
   557
    store_standard_thm "triv_forall_equality"
wenzelm@9455
   558
      (standard (equal_intr (implies_intr QV (forall_elim x (assume QV)))
wenzelm@9455
   559
        (implies_intr V  (forall_intr x (assume V)))))
clasohm@0
   560
  end;
clasohm@0
   561
nipkow@1756
   562
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   563
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   564
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   565
*)
nipkow@1756
   566
val swap_prems_rl =
paulson@4610
   567
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   568
      val major = assume cmajor;
paulson@4610
   569
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   570
      val minor1 = assume cminor1;
paulson@4610
   571
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   572
      val minor2 = assume cminor2;
wenzelm@9455
   573
  in store_standard_thm "swap_prems_rl"
nipkow@1756
   574
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   575
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   576
  end;
nipkow@1756
   577
nipkow@3653
   578
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   579
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   580
   Introduction rule for == as a meta-theorem.
nipkow@3653
   581
*)
nipkow@3653
   582
val equal_intr_rule =
paulson@4610
   583
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   584
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   585
  in
wenzelm@9455
   586
    store_standard_thm "equal_intr_rule"
wenzelm@4016
   587
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   588
  end;
nipkow@3653
   589
wenzelm@4285
   590
wenzelm@9554
   591
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@9554
   592
  Rewrite rule for HHF normalization.
wenzelm@9554
   593
wenzelm@9554
   594
  Note: the syntax of ProtoPure is insufficient to handle this
wenzelm@9554
   595
  statement; storing it would be asking for trouble, e.g. when someone
wenzelm@9554
   596
  tries to print the theory later.
wenzelm@9554
   597
*)
wenzelm@9554
   598
wenzelm@9554
   599
val norm_hhf_eq =
wenzelm@9554
   600
  let
wenzelm@9554
   601
    val cert = Thm.cterm_of proto_sign;
wenzelm@9554
   602
    val aT = TFree ("'a", Term.logicS);
wenzelm@9554
   603
    val all = Term.all aT;
wenzelm@9554
   604
    val x = Free ("x", aT);
wenzelm@9554
   605
    val phi = Free ("phi", propT);
wenzelm@9554
   606
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   607
wenzelm@9554
   608
    val cx = cert x;
wenzelm@9554
   609
    val cphi = cert phi;
wenzelm@9554
   610
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   611
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   612
  in
wenzelm@9554
   613
    Thm.equal_intr
wenzelm@9554
   614
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   615
        |> Thm.forall_elim cx
wenzelm@9554
   616
        |> Thm.implies_intr cphi
wenzelm@9554
   617
        |> Thm.forall_intr cx
wenzelm@9554
   618
        |> Thm.implies_intr lhs)
wenzelm@9554
   619
      (Thm.implies_elim
wenzelm@9554
   620
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   621
        |> Thm.forall_intr cx
wenzelm@9554
   622
        |> Thm.implies_intr cphi
wenzelm@9554
   623
        |> Thm.implies_intr rhs)
wenzelm@10441
   624
    |> store_standard_thm "norm_hhf_eq"
wenzelm@9554
   625
  end;
wenzelm@9554
   626
wenzelm@9554
   627
paulson@8129
   628
(*** Instantiate theorem th, reading instantiations under signature sg ****)
paulson@8129
   629
paulson@8129
   630
(*Version that normalizes the result: Thm.instantiate no longer does that*)
paulson@8129
   631
fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
paulson@8129
   632
paulson@8129
   633
fun read_instantiate_sg sg sinsts th =
paulson@8129
   634
    let val ts = types_sorts th;
paulson@8129
   635
        val used = add_term_tvarnames(#prop(rep_thm th),[]);
paulson@8129
   636
    in  instantiate (read_insts sg ts ts used sinsts) th  end;
paulson@8129
   637
paulson@8129
   638
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   639
fun read_instantiate sinsts th =
paulson@8129
   640
    read_instantiate_sg (#sign (rep_thm th)) sinsts th;
paulson@8129
   641
paulson@8129
   642
paulson@8129
   643
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   644
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   645
local
paulson@8129
   646
  fun add_types ((ct,cu), (sign,tye,maxidx)) =
paulson@8129
   647
    let val {sign=signt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
paulson@8129
   648
        and {sign=signu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   649
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
paulson@8129
   650
        val sign' = Sign.merge(sign, Sign.merge(signt, signu))
paulson@8129
   651
        val (tye',maxi') = Type.unify (#tsig(Sign.rep_sg sign')) maxi tye (T,U)
wenzelm@10403
   652
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
paulson@8129
   653
    in  (sign', tye', maxi')  end;
paulson@8129
   654
in
paulson@8129
   655
fun cterm_instantiate ctpairs0 th =
berghofe@8406
   656
  let val (sign,tye,_) = foldr add_types (ctpairs0, (#sign(rep_thm th), Vartab.empty, 0))
berghofe@8406
   657
      fun instT(ct,cu) = let val inst = subst_TVars_Vartab tye
paulson@8129
   658
                         in (cterm_fun inst ct, cterm_fun inst cu) end
paulson@8129
   659
      fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
berghofe@8406
   660
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   661
  handle TERM _ =>
paulson@8129
   662
           raise THM("cterm_instantiate: incompatible signatures",0,[th])
paulson@8129
   663
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   664
end;
paulson@8129
   665
paulson@8129
   666
paulson@8129
   667
(** Derived rules mainly for METAHYPS **)
paulson@8129
   668
paulson@8129
   669
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
paulson@8129
   670
fun equal_abs_elim ca eqth =
paulson@8129
   671
  let val {sign=signa, t=a, ...} = rep_cterm ca
paulson@8129
   672
      and combth = combination eqth (reflexive ca)
paulson@8129
   673
      val {sign,prop,...} = rep_thm eqth
paulson@8129
   674
      val (abst,absu) = Logic.dest_equals prop
paulson@8129
   675
      val cterm = cterm_of (Sign.merge (sign,signa))
berghofe@10414
   676
  in  transitive (symmetric (beta_conversion false (cterm (abst$a))))
berghofe@10414
   677
           (transitive combth (beta_conversion false (cterm (absu$a))))
paulson@8129
   678
  end
paulson@8129
   679
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
paulson@8129
   680
paulson@8129
   681
(*Calling equal_abs_elim with multiple terms*)
paulson@8129
   682
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
paulson@8129
   683
paulson@8129
   684
local
paulson@8129
   685
  val alpha = TVar(("'a",0), [])     (*  type ?'a::{}  *)
paulson@8129
   686
  fun err th = raise THM("flexpair_inst: ", 0, [th])
paulson@8129
   687
  fun flexpair_inst def th =
paulson@8129
   688
    let val {prop = Const _ $ t $ u,  sign,...} = rep_thm th
paulson@8129
   689
        val cterm = cterm_of sign
paulson@8129
   690
        fun cvar a = cterm(Var((a,0),alpha))
paulson@8129
   691
        val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)]
paulson@8129
   692
                   def
paulson@8129
   693
    in  equal_elim def' th
paulson@8129
   694
    end
paulson@8129
   695
    handle THM _ => err th | Bind => err th
paulson@8129
   696
in
paulson@8129
   697
val flexpair_intr = flexpair_inst (symmetric ProtoPure.flexpair_def)
paulson@8129
   698
and flexpair_elim = flexpair_inst ProtoPure.flexpair_def
paulson@8129
   699
end;
paulson@8129
   700
paulson@8129
   701
(*Version for flexflex pairs -- this supports lifting.*)
paulson@8129
   702
fun flexpair_abs_elim_list cts =
paulson@8129
   703
    flexpair_intr o equal_abs_elim_list cts o flexpair_elim;
paulson@8129
   704
paulson@8129
   705
paulson@8129
   706
(*** GOAL (PROP A) <==> PROP A ***)
wenzelm@4789
   707
wenzelm@4789
   708
local
wenzelm@4789
   709
  val A = read_prop "PROP A";
wenzelm@4789
   710
  val G = read_prop "GOAL (PROP A)";
wenzelm@4789
   711
  val (G_def, _) = freeze_thaw ProtoPure.Goal_def;
wenzelm@4789
   712
in
wenzelm@9455
   713
  val triv_goal = store_thm "triv_goal"
wenzelm@9455
   714
    (tag_rule internal_tag (standard (Thm.equal_elim (Thm.symmetric G_def) (Thm.assume A))));
wenzelm@9455
   715
  val rev_triv_goal = store_thm "rev_triv_goal"
wenzelm@9455
   716
    (tag_rule internal_tag (standard (Thm.equal_elim G_def (Thm.assume G))));
wenzelm@4789
   717
end;
wenzelm@4789
   718
wenzelm@9460
   719
val mk_cgoal = Thm.capply (Thm.cterm_of proto_sign Logic.goal_const);
wenzelm@6995
   720
fun assume_goal ct = Thm.assume (mk_cgoal ct) RS rev_triv_goal;
wenzelm@6995
   721
wenzelm@4789
   722
wenzelm@4285
   723
wenzelm@5688
   724
(** variations on instantiate **)
wenzelm@4285
   725
paulson@8550
   726
(*shorthand for instantiating just one variable in the current theory*)
paulson@8550
   727
fun inst x t = read_instantiate_sg (sign_of (the_context())) [(x,t)];
paulson@8550
   728
paulson@8550
   729
wenzelm@4285
   730
(* collect vars *)
wenzelm@4285
   731
wenzelm@4285
   732
val add_tvarsT = foldl_atyps (fn (vs, TVar v) => v ins vs | (vs, _) => vs);
wenzelm@4285
   733
val add_tvars = foldl_types add_tvarsT;
wenzelm@4285
   734
val add_vars = foldl_aterms (fn (vs, Var v) => v ins vs | (vs, _) => vs);
wenzelm@4285
   735
wenzelm@5903
   736
fun tvars_of_terms ts = rev (foldl add_tvars ([], ts));
wenzelm@5903
   737
fun vars_of_terms ts = rev (foldl add_vars ([], ts));
wenzelm@5903
   738
wenzelm@5903
   739
fun tvars_of thm = tvars_of_terms [#prop (Thm.rep_thm thm)];
wenzelm@5903
   740
fun vars_of thm = vars_of_terms [#prop (Thm.rep_thm thm)];
wenzelm@4285
   741
wenzelm@4285
   742
wenzelm@4285
   743
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   744
wenzelm@4285
   745
fun instantiate' cTs cts thm =
wenzelm@4285
   746
  let
wenzelm@4285
   747
    fun err msg =
wenzelm@4285
   748
      raise TYPE ("instantiate': " ^ msg,
wenzelm@4285
   749
        mapfilter (apsome Thm.typ_of) cTs,
wenzelm@4285
   750
        mapfilter (apsome Thm.term_of) cts);
wenzelm@4285
   751
wenzelm@4285
   752
    fun inst_of (v, ct) =
wenzelm@4285
   753
      (Thm.cterm_of (#sign (Thm.rep_cterm ct)) (Var v), ct)
wenzelm@4285
   754
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   755
wenzelm@4285
   756
    fun zip_vars _ [] = []
wenzelm@4285
   757
      | zip_vars (_ :: vs) (None :: opt_ts) = zip_vars vs opt_ts
wenzelm@4285
   758
      | zip_vars (v :: vs) (Some t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
wenzelm@4285
   759
      | zip_vars [] _ = err "more instantiations than variables in thm";
wenzelm@4285
   760
wenzelm@4285
   761
    (*instantiate types first!*)
wenzelm@4285
   762
    val thm' =
wenzelm@4285
   763
      if forall is_none cTs then thm
wenzelm@4285
   764
      else Thm.instantiate (zip_vars (map fst (tvars_of thm)) cTs, []) thm;
wenzelm@4285
   765
    in
wenzelm@4285
   766
      if forall is_none cts then thm'
wenzelm@4285
   767
      else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
wenzelm@4285
   768
    end;
wenzelm@4285
   769
wenzelm@4285
   770
wenzelm@5688
   771
(* unvarify(T) *)
wenzelm@5688
   772
wenzelm@5688
   773
(*assume thm in standard form, i.e. no frees, 0 var indexes*)
wenzelm@5688
   774
wenzelm@5688
   775
fun unvarifyT thm =
wenzelm@5688
   776
  let
wenzelm@5688
   777
    val cT = Thm.ctyp_of (Thm.sign_of_thm thm);
wenzelm@5688
   778
    val tfrees = map (fn ((x, _), S) => Some (cT (TFree (x, S)))) (tvars_of thm);
wenzelm@5688
   779
  in instantiate' tfrees [] thm end;
wenzelm@5688
   780
wenzelm@5688
   781
fun unvarify raw_thm =
wenzelm@5688
   782
  let
wenzelm@5688
   783
    val thm = unvarifyT raw_thm;
wenzelm@5688
   784
    val ct = Thm.cterm_of (Thm.sign_of_thm thm);
wenzelm@5688
   785
    val frees = map (fn ((x, _), T) => Some (ct (Free (x, T)))) (vars_of thm);
wenzelm@5688
   786
  in instantiate' [] frees thm end;
wenzelm@5688
   787
wenzelm@5688
   788
wenzelm@8605
   789
(* tvars_intr_list *)
wenzelm@8605
   790
wenzelm@8605
   791
fun tfrees_of thm =
wenzelm@8605
   792
  let val {hyps, prop, ...} = Thm.rep_thm thm
wenzelm@8605
   793
  in foldr Term.add_term_tfree_names (prop :: hyps, []) end;
wenzelm@8605
   794
wenzelm@8605
   795
fun tvars_intr_list tfrees thm =
wenzelm@8605
   796
  Thm.varifyT' (tfrees_of thm \\ tfrees) thm;
wenzelm@8605
   797
wenzelm@8605
   798
wenzelm@6435
   799
(* increment var indexes *)
wenzelm@6435
   800
wenzelm@6435
   801
fun incr_indexes_wrt is cTs cts thms =
wenzelm@6435
   802
  let
wenzelm@6435
   803
    val maxidx =
wenzelm@6435
   804
      foldl Int.max (~1, is @
wenzelm@6435
   805
        map (maxidx_of_typ o #T o Thm.rep_ctyp) cTs @
wenzelm@6435
   806
        map (#maxidx o Thm.rep_cterm) cts @
wenzelm@6435
   807
        map (#maxidx o Thm.rep_thm) thms);
berghofe@10414
   808
  in Thm.incr_indexes (maxidx + 1) end;
wenzelm@6435
   809
wenzelm@6435
   810
wenzelm@8328
   811
(* freeze_all *)
wenzelm@8328
   812
wenzelm@8328
   813
(*freeze all (T)Vars; assumes thm in standard form*)
wenzelm@8328
   814
wenzelm@8328
   815
fun freeze_all_TVars thm =
wenzelm@8328
   816
  (case tvars_of thm of
wenzelm@8328
   817
    [] => thm
wenzelm@8328
   818
  | tvars =>
wenzelm@8328
   819
      let val cert = Thm.ctyp_of (Thm.sign_of_thm thm)
wenzelm@8328
   820
      in instantiate' (map (fn ((x, _), S) => Some (cert (TFree (x, S)))) tvars) [] thm end);
wenzelm@8328
   821
wenzelm@8328
   822
fun freeze_all_Vars thm =
wenzelm@8328
   823
  (case vars_of thm of
wenzelm@8328
   824
    [] => thm
wenzelm@8328
   825
  | vars =>
wenzelm@8328
   826
      let val cert = Thm.cterm_of (Thm.sign_of_thm thm)
wenzelm@8328
   827
      in instantiate' [] (map (fn ((x, _), T) => Some (cert (Free (x, T)))) vars) thm end);
wenzelm@8328
   828
wenzelm@8328
   829
val freeze_all = freeze_all_Vars o freeze_all_TVars;
wenzelm@8328
   830
wenzelm@8328
   831
wenzelm@5688
   832
(* mk_triv_goal *)
wenzelm@5688
   833
wenzelm@5688
   834
(*make an initial proof state, "PROP A ==> (PROP A)" *)
paulson@5311
   835
fun mk_triv_goal ct = instantiate' [] [Some ct] triv_goal;
paulson@5311
   836
clasohm@0
   837
end;
wenzelm@252
   838
wenzelm@5903
   839
wenzelm@5903
   840
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
   841
open BasicDrule;