src/Provers/eqsubst.ML
author dixon
Fri, 22 Apr 2005 15:10:42 +0200
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(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- *) 
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(*  Title:      Provers/eqsubst.ML
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    Author:     Lucas Dixon, University of Edinburgh
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                lucas.dixon@ed.ac.uk
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    Modified:   18 Feb 2005 - Lucas - 
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    Created:    29 Jan 2005
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*)
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(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- *) 
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(*  DESCRIPTION:
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    A Tactic to perform a substiution using an equation.
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*)
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(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- *)
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(* Logic specific data stub *)
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signature EQRULE_DATA =
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sig
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  (* to make a meta equality theorem in the current logic *)
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  val prep_meta_eq : thm -> thm list
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end;
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(* the signature of an instance of the SQSUBST tactic *)
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signature EQSUBST_TAC = 
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sig
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  type match = 
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       ((Term.indexname * Term.typ) list (* type instantiations *)
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        * (Term.indexname * Term.term) list) (* term instantiations *)
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       * (string * Term.typ) list (* fake named type abs env *)
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       * (string * Term.typ) list (* type abs env *)
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       * Term.term (* outer term *)
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  val prep_subst_in_asm :
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      (Sign.sg (* sign for matching *)
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       -> int (* maxidx *)
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       -> 'a (* input object kind *)
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       -> BasicIsaFTerm.FcTerm (* focusterm to search under *)
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       -> 'b) (* result type *)
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      -> int (* subgoal to subst in *)
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      -> Thm.thm (* target theorem with subgoals *)
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      -> int (* premise to subst in *)
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      -> (Thm.cterm list (* certified free var placeholders for vars *) 
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          * int (* premice no. to subst *)
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          * int (* number of assumptions of premice *)
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          * Thm.thm) (* premice as a new theorem for forward reasoning *)
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         * ('a -> 'b) (* matchf *)
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  val prep_subst_in_asms :
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      (Sign.sg -> int -> 'a -> BasicIsaFTerm.FcTerm -> 'b) 
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      -> int (* subgoal to subst in *)
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      -> Thm.thm (* target theorem with subgoals *)
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      -> ((Thm.cterm list (* certified free var placeholders for vars *) 
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          * int (* premice no. to subst *)
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          * int (* number of assumptions of premice *)
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          * Thm.thm) (* premice as a new theorem for forward reasoning *)
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         * ('a -> 'b)) (* matchf *)
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                       Seq.seq
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  val apply_subst_in_asm :
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      int (* subgoal *)
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      -> Thm.thm (* overall theorem *)
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      -> (Thm.cterm list (* certified free var placeholders for vars *) 
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          * int (* assump no being subst *)
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          * int (* num of premises of asm *) 
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          * Thm.thm) (* premthm *)
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      -> Thm.thm (* rule *)
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      -> match
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      -> Thm.thm Seq.seq
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  val prep_concl_subst :
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      (Sign.sg -> int -> 'a -> BasicIsaFTerm.FcTerm -> 'b) (* searchf *) 
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      -> int (* subgoal *)
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      -> Thm.thm (* overall goal theorem *)
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      -> (Thm.cterm list * Thm.thm) * ('a -> 'b) (* (cvfs, conclthm), matchf *)
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  val apply_subst_in_concl :
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        int (* subgoal *)
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        -> Thm.thm (* thm with all goals *)
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        -> Thm.cterm list (* certified free var placeholders for vars *)
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           * Thm.thm  (* trivial thm of goal concl *)
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            (* possible matches/unifiers *)
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        -> Thm.thm (* rule *)
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        -> match
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        -> Thm.thm Seq.seq (* substituted goal *)
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  val searchf_tlr_unify_all : 
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      (Sign.sg -> int ->
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       Term.term ->
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       BasicIsaFTerm.FcTerm ->
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       match Seq.seq)
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  val searchf_tlr_unify_valid : 
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      (Sign.sg -> int ->
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       Term.term ->
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       BasicIsaFTerm.FcTerm ->
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       match Seq.seq)
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  val eqsubst_asm_meth : Thm.thm list -> Proof.method
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  val eqsubst_asm_tac : Thm.thm list -> int -> Thm.thm -> Thm.thm Seq.seq
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  val eqsubst_asm_tac' : 
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      (Sign.sg -> int ->
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       Term.term ->
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       BasicIsaFTerm.FcTerm ->
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       match Seq.seq) -> Thm.thm -> int -> Thm.thm -> Thm.thm Seq.seq
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  val eqsubst_meth : Thm.thm list -> Proof.method
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  val eqsubst_tac : Thm.thm list -> int -> Thm.thm -> Thm.thm Seq.seq
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  val eqsubst_tac' : 
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      (Sign.sg -> int ->
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       Term.term ->
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       BasicIsaFTerm.FcTerm ->
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       match Seq.seq) -> Thm.thm -> int -> Thm.thm -> Thm.thm Seq.seq
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  val meth : bool * Thm.thm list -> Proof.context -> Proof.method
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  val setup : (Theory.theory -> Theory.theory) list
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end;
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functor EQSubstTacFUN (structure EqRuleData : EQRULE_DATA) 
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  : EQSUBST_TAC
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= struct
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  (* a type abriviation for match infomration *)
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  type match = 
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       ((Term.indexname * Term.typ) list (* type instantiations *)
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         * (Term.indexname * Term.term) list) (* term instantiations *)
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        * (string * Term.typ) list (* fake named type abs env *)
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        * (string * Term.typ) list (* type abs env *)
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        * Term.term (* outer term *)
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(* FOR DEBUGGING...
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type trace_subst_errT = int (* subgoal *)
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        * Thm.thm (* thm with all goals *)
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        * (Thm.cterm list (* certified free var placeholders for vars *)
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           * Thm.thm)  (* trivial thm of goal concl *)
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            (* possible matches/unifiers *)
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        * Thm.thm (* rule *)
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        * (((Term.indexname * Term.typ) list (* type instantiations *)
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              * (Term.indexname * Term.term) list ) (* term instantiations *)
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             * (string * Term.typ) list (* Type abs env *)
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             * Term.term) (* outer term *);
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val trace_subst_err = (ref NONE : trace_subst_errT option ref);
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val trace_subst_search = ref false;
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exception trace_subst_exp of trace_subst_errT;
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 *)
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(* also defined in /HOL/Tools/inductive_codegen.ML, 
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   maybe move this to seq.ML ? *)
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infix 5 :->;
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fun s :-> f = Seq.flat (Seq.map f s);
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(* search from top, left to right, then down *)
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fun search_tlr_all_f f ft = 
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    let
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      fun maux ft = 
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          let val t' = (IsaFTerm.focus_of_fcterm ft) 
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            (* val _ = 
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                if !trace_subst_search then 
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                  (writeln ("Examining: " ^ (TermLib.string_of_term t'));
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                   TermLib.writeterm t'; ())
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                else (); *)
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          in 
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          (case t' of 
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            (_ $ _) => Seq.append(maux (IsaFTerm.focus_left ft), 
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                       Seq.append(f ft, 
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                                  maux (IsaFTerm.focus_right ft)))
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          | (Abs _) => Seq.append(f ft, maux (IsaFTerm.focus_abs ft))
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          | leaf => f ft) end
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    in maux ft end;
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(* search from top, left to right, then down *)
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fun search_tlr_valid_f f ft = 
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    let
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      fun maux ft = 
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          let 
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            val hereseq = if IsaFTerm.valid_match_start ft then f ft else Seq.empty
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          in 
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          (case (IsaFTerm.focus_of_fcterm ft) of 
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            (_ $ _) => Seq.append(maux (IsaFTerm.focus_left ft), 
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                       Seq.append(hereseq, 
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                                  maux (IsaFTerm.focus_right ft)))
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          | (Abs _) => Seq.append(hereseq, maux (IsaFTerm.focus_abs ft))
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          | leaf => hereseq)
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          end
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    in maux ft end;
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(* search all unifications *)
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fun searchf_tlr_unify_all sgn maxidx lhs  = 
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    IsaFTerm.find_fcterm_matches 
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      search_tlr_all_f 
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      (IsaFTerm.clean_unify_ft sgn maxidx lhs);
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(* search only for 'valid' unifiers (non abs subterms and non vars) *)
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fun searchf_tlr_unify_valid sgn maxidx lhs  = 
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    IsaFTerm.find_fcterm_matches 
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      search_tlr_valid_f 
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      (IsaFTerm.clean_unify_ft sgn maxidx lhs);
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(* apply a substitution in the conclusion of the theorem th *)
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(* cfvs are certified free var placeholders for goal params *)
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(* conclthm is a theorem of for just the conclusion *)
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(* m is instantiation/match information *)
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(* rule is the equation for substitution *)
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fun apply_subst_in_concl i th (cfvs, conclthm) rule m = 
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    (RWInst.rw m rule conclthm)
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      |> IsaND.schemify_frees_to_vars cfvs
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      |> RWInst.beta_eta_contract_tac
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      |> (fn r => Tactic.rtac r i th);
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(*
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 |> (fn r => Thm.bicompose false (false, r, Thm.nprems_of r) i th)
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*)
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(* substitute within the conclusion of goal i of gth, using a meta
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equation rule. Note that we assume rule has var indicies zero'd *)
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fun prep_concl_subst searchf i gth = 
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    let 
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      val th = Thm.incr_indexes 1 gth;
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      val tgt_term = Thm.prop_of th;
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      val sgn = Thm.sign_of_thm th;
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      val ctermify = Thm.cterm_of sgn;
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      val trivify = Thm.trivial o ctermify;
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      val (fixedbody, fvs) = IsaND.fix_alls_term i tgt_term;
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      val cfvs = rev (map ctermify fvs);
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      val conclterm = Logic.strip_imp_concl fixedbody;
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      val conclthm = trivify conclterm;
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      val maxidx = Term.maxidx_of_term conclterm;
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    in
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      ((cfvs, conclthm), 
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       (fn lhs => searchf sgn maxidx lhs 
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                          ((IsaFTerm.focus_right  
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                            o IsaFTerm.focus_left
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                            o IsaFTerm.fcterm_of_term 
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                            o Thm.prop_of) conclthm)))
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    end;
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(* substitute using an object or meta level equality *)
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fun eqsubst_tac' searchf instepthm i th = 
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    let 
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      val (cvfsconclthm, findmatchf) = 
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          prep_concl_subst searchf i th;
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      val stepthms = 
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          Seq.map Drule.zero_var_indexes 
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                  (Seq.of_list (EqRuleData.prep_meta_eq instepthm));
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      fun rewrite_with_thm r =
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          let val (lhs,_) = Logic.dest_equals (Thm.concl_of r);
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          in (findmatchf lhs)
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             :-> (apply_subst_in_concl i th cvfsconclthm r) end;
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    in (stepthms :-> rewrite_with_thm) end;
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(* substitute using one of the given theorems *)
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fun eqsubst_tac instepthms i th = 
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    if Thm.nprems_of th < i then Seq.empty else
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    (Seq.of_list instepthms) 
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    :-> (fn r => eqsubst_tac' searchf_tlr_unify_valid r i th);
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(* inthms are the given arguments in Isar, and treated as eqstep with
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   the first one, then the second etc *)
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fun eqsubst_meth inthms =
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    Method.METHOD 
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      (fn facts =>
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          HEADGOAL ( Method.insert_tac facts THEN' eqsubst_tac inthms ));
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fun apply_subst_in_asm i th (cfvs, j, nprems, pth) rule m = 
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    (RWInst.rw m rule pth)
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      |> Thm.permute_prems 0 ~1
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      |> IsaND.schemify_frees_to_vars cfvs
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      |> RWInst.beta_eta_contract_tac
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      |> (fn r => Tactic.dtac r i th);
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(*
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? should I be using bicompose what if we match more than one
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assumption, even after instantiation ? (back will work, but it would
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be nice to avoid the redudent search)
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something like... 
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 |> Thm.lift_rule (th, i)
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 |> (fn r => Thm.bicompose false (false, r, Thm.nprems_of r - nprems) i th)
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*)
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(* prepare to substitute within the j'th premise of subgoal i of gth,
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using a meta-level equation. Note that we assume rule has var indicies
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zero'd. Note that we also assume that premt is the j'th premice of
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subgoal i of gth. Note the repetition of work done for each
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assumption, i.e. this can be made more efficient for search over
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multiple assumptions.  *)
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fun prep_subst_in_asm searchf i gth j = 
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    let 
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      val th = Thm.incr_indexes 1 gth;
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      val tgt_term = Thm.prop_of th;
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      val sgn = Thm.sign_of_thm th;
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      val ctermify = Thm.cterm_of sgn;
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      val trivify = Thm.trivial o ctermify;
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      val (fixedbody, fvs) = IsaND.fix_alls_term i tgt_term;
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      val cfvs = rev (map ctermify fvs);
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      val asmt = Library.nth_elem(j - 1,(Logic.strip_imp_prems fixedbody));
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      val asm_nprems = length (Logic.strip_imp_prems asmt);
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      val pth = trivify asmt;
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      val maxidx = Term.maxidx_of_term asmt;
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    in
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      ((cfvs, j, asm_nprems, pth), 
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       (fn lhs => (searchf sgn maxidx lhs
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                           ((IsaFTerm.focus_right 
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                             o IsaFTerm.fcterm_of_term 
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                             o Thm.prop_of) pth))))
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    end;
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(* prepare subst in every possible assumption *)
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fun prep_subst_in_asms searchf i gth = 
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    Seq.map 
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      (prep_subst_in_asm searchf i gth)
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      (Seq.of_list (IsaPLib.mk_num_list
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                      (length (Logic.prems_of_goal (Thm.prop_of gth) i))));
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(* substitute in an assumption using an object or meta level equality *)
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fun eqsubst_asm_tac' searchf instepthm i th = 
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    let 
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      val asmpreps = prep_subst_in_asms searchf i th;
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      val stepthms = 
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          Seq.map Drule.zero_var_indexes 
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                  (Seq.of_list (EqRuleData.prep_meta_eq instepthm))
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      fun rewrite_with_thm (asminfo, findmatchf) r =
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          let val (lhs,_) = Logic.dest_equals (Thm.concl_of r);
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          in (findmatchf lhs)
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             :-> (apply_subst_in_asm i th asminfo r) end;
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    in
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      (asmpreps :-> (fn a => stepthms :-> rewrite_with_thm a))
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    end;
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(* substitute using one of the given theorems *)
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fun eqsubst_asm_tac instepthms i th = 
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    if Thm.nprems_of th < i then Seq.empty else
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    (Seq.of_list instepthms) 
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    :-> (fn r => eqsubst_asm_tac' searchf_tlr_unify_valid r i th);
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(* inthms are the given arguments in Isar, and treated as eqstep with
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   the first one, then the second etc *)
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fun eqsubst_asm_meth inthms =
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    Method.METHOD 
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      (fn facts =>
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          HEADGOAL (Method.insert_tac facts THEN' eqsubst_asm_tac inthms ));
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(* combination method that takes a flag (true indicates that subst
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should be done to an assumption, false = apply to the conclusion of
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the goal) as well as the theorems to use *)
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fun meth (asmflag, inthms) ctxt = 
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    if asmflag then eqsubst_asm_meth inthms else eqsubst_meth inthms;
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(* syntax for options, given "(asm)" will give back true, without
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   gives back false *)
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val options_syntax =
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    (Args.parens (Args.$$$ "asm") >> (K true)) ||
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     (Scan.succeed false);
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(* method syntax, first take options, then theorems *)
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fun meth_syntax meth src ctxt =
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    meth (snd (Method.syntax ((Scan.lift options_syntax) 
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                                -- Attrib.local_thms) src ctxt)) 
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         ctxt;
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(* setup function for adding method to theory. *)
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val setup = 
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    [Method.add_method ("subst", meth_syntax meth, "Substiution with an equation. Use \"(asm)\" option to substitute in an assumption.")];
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end;