src/Pure/goals.ML
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(*  Title: 	Pure/goals.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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Goal stack package.  The goal stack initially holds a dummy proof, and can
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never become empty.  Each goal stack consists of a list of levels.  The
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undo list is a list of goal stacks.  Finally, there may be a stack of
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pending proofs.
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*)
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signature GOALS =
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  sig
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  type proof
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  val ba		: int -> unit
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  val back		: unit -> unit
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  val bd		: thm -> int -> unit
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  val bds		: thm list -> int -> unit
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  val be		: thm -> int -> unit
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  val bes		: thm list -> int -> unit
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  val br		: thm -> int -> unit
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  val brs		: thm list -> int -> unit
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  val bw		: thm -> unit
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  val bws		: thm list -> unit
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  val by		: tactic -> unit
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  val byev		: tactic list -> unit
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  val chop		: unit -> unit
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  val choplev		: int -> unit
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  val fa		: unit -> unit
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  val fd		: thm -> unit
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  val fds		: thm list -> unit
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  val fe		: thm -> unit
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  val fes		: thm list -> unit
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  val filter_goal	: (term*term->bool) -> thm list -> int -> thm list
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  val fr		: thm -> unit
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  val frs		: thm list -> unit
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  val getgoal		: int -> term
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  val gethyps		: int -> thm list
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  val goal		: theory -> string -> thm list
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  val goalw		: theory -> thm list -> string -> thm list
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  val goalw_cterm	: thm list -> cterm -> thm list
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  val pop_proof		: unit -> thm list
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  val pr		: unit -> unit
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  val pr_latex		: unit -> unit
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  val printgoal_latex	: int -> unit
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  val premises		: unit -> thm list
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  val prin		: term -> unit
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  val printyp		: typ -> unit
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  val pprint_term	: term -> pprint_args -> unit
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  val pprint_typ	: typ -> pprint_args -> unit
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  val print_exn		: exn -> 'a
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  val print_sign_exn	: Sign.sg -> exn -> 'a
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  val prlev		: int -> unit
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  val proof_timing	: bool ref
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  val prove_goal	: theory -> string -> (thm list -> tactic list) -> thm
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  val prove_goalw      : theory->thm list->string->(thm list->tactic list)->thm
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  val prove_goalw_cterm	: thm list->cterm->(thm list->tactic list)->thm
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  val push_proof	: unit -> unit
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  val read		: string -> term
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  val ren		: string -> int -> unit
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  val restore_proof	: proof -> thm list
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  val result		: unit -> thm  
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  val result_error_ref  : (thm -> string -> thm) ref
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  val rotate_proof	: unit -> thm list
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  val uresult		: unit -> thm  
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  val save_proof	: unit -> proof
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  val topthm		: unit -> thm
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  val undo		: unit -> unit
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  end;
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structure Goals : GOALS =
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struct
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(*Each level of goal stack includes a proof state and alternative states,
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  the output of the tactic applied to the preceeding level.  *)
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type gstack = (thm * thm Sequence.seq) list;
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datatype proof = Proof of gstack list * thm list * (bool*thm->thm);
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(*** References ***)
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(*Should process time be printed after proof steps?*)
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val proof_timing = ref false;
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(*Current assumption list -- set by "goal".*)
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val curr_prems = ref([] : thm list);
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(*Return assumption list -- useful if you didn't save "goal"'s result. *)
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fun premises() = !curr_prems;
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(*Current result maker -- set by "goal", used by "result".  *)
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val curr_mkresult = 
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    ref((fn _=> error"No goal has been supplied in subgoal module") 
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       : bool*thm->thm);
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val dummy = trivial(read_cterm Sign.proto_pure 
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    ("PROP No_goal_has_been_supplied",propT));
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(*List of previous goal stacks, for the undo operation.  Set by setstate. 
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  A list of lists!*)
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val undo_list = ref([[(dummy, Sequence.null)]] : gstack list);
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(* Stack of proof attempts *)
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val proofstack = ref([]: proof list);
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(*** Setting up goal-directed proof ***)
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(*Generates the list of new theories when the proof state's signature changes*)
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fun sign_error (sign,sign') =
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  let val stamps = #stamps(Sign.rep_sg sign') \\ 
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                   #stamps(Sign.rep_sg sign)
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  in  case stamps of
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        [stamp] => "\nNew theory: " ^ !stamp
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      | _       => "\nNew theories: " ^ space_implode ", " (map ! stamps)
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  end;
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(*Default action is to print an error message; could be suppressed for
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  special applications.*)
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fun result_error_default state msg : thm = 
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  (writeln ("Bad final proof state:");
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   !print_goals_ref (!goals_limit) state;
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   error msg);
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val result_error_ref = ref result_error_default;
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(*Common treatment of "goal" and "prove_goal":
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  Return assumptions, initial proof state, and function to make result. *)
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fun prepare_proof rths chorn =
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  let val {sign, t=horn,...} = rep_cterm chorn;
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      val (_,As,B) = Logic.strip_horn(horn);
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      val cAs = map (cterm_of sign) As;
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      val prems = map (rewrite_rule rths o forall_elim_vars(0) o assume) cAs
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      and st0 = (rewrite_goals_rule rths o trivial) (cterm_of sign B)
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      (*discharges assumptions from state in the order they appear in goal;
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	checks (if requested) that resulting theorem is equivalent to goal. *)
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      fun mkresult (check,state) =
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        let val state = Sequence.hd (flexflex_rule state)
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	    		handle THM _ => state   (*smash flexflex pairs*)
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	    val ngoals = nprems_of state
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            val th = strip_shyps (implies_intr_list cAs state)
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            val {hyps,prop,sign=sign',...} = rep_thm th
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            val xshyps = extra_shyps th;
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        in  if not check then standard th
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	    else if not (Sign.eq_sg(sign,sign')) then !result_error_ref state
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		("Signature of proof state has changed!" ^
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		 sign_error (sign,sign'))
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            else if ngoals>0 then !result_error_ref state
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		(string_of_int ngoals ^ " unsolved goals!")
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            else if not (null hyps) then !result_error_ref state
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                ("Additional hypotheses:\n" ^ 
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                 cat_lines (map (Sign.string_of_term sign) hyps))
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	    else if not (null xshyps) then !result_error_ref state
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                ("Extra sort hypotheses: " ^
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                 commas (map Type.str_of_sort xshyps))
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	    else if Pattern.matches (#tsig(Sign.rep_sg sign)) 
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			            (term_of chorn, prop)
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		 then  standard th 
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	    else  !result_error_ref state "proved a different theorem"
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        end
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  in
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     if Sign.eq_sg(sign, #sign(rep_thm st0))
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     then (prems, st0, mkresult)
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     else error ("Definitions would change the proof state's signature" ^
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		 sign_error (sign, #sign(rep_thm st0)))
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  end
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  handle THM(s,_,_) => error("prepare_proof: exception THM was raised!\n" ^ s);
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(*Prints exceptions readably to users*)
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fun print_sign_exn_unit sign e = 
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  case e of
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     THM (msg,i,thms) =>
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	 (writeln ("Exception THM " ^ string_of_int i ^ " raised:\n" ^ msg);
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	  seq print_thm thms)
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   | THEORY (msg,thys) =>
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	 (writeln ("Exception THEORY raised:\n" ^ msg);
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	  seq print_theory thys)
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   | TERM (msg,ts) =>
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	 (writeln ("Exception TERM raised:\n" ^ msg);
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	  seq (writeln o Sign.string_of_term sign) ts)
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   | TYPE (msg,Ts,ts) =>
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	 (writeln ("Exception TYPE raised:\n" ^ msg);
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	  seq (writeln o Sign.string_of_typ sign) Ts;
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	  seq (writeln o Sign.string_of_term sign) ts)
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   | e => raise e;
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(*Prints an exception, then fails*)
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fun print_sign_exn sign e = (print_sign_exn_unit sign e; raise ERROR);
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(** the prove_goal.... commands
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    Prove theorem using the listed tactics; check it has the specified form.
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    Augment signature with all type assignments of goal.
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    Syntax is similar to "goal" command for easy keyboard use. **)
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(*Version taking the goal as a cterm*)
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fun prove_goalw_cterm rths chorn tacsf =
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  let val (prems, st0, mkresult) = prepare_proof rths chorn
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      val tac = EVERY (tacsf prems)
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      fun statef() = 
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	  (case Sequence.pull (tac st0) of 
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	       Some(st,_) => st
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	     | _ => error ("prove_goal: tactic failed"))
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  in  mkresult (true, cond_timeit (!proof_timing) statef)  end
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  handle e => (print_sign_exn_unit (#sign (rep_cterm chorn)) e;
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	       error ("The exception above was raised for\n" ^ 
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		      string_of_cterm chorn));
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(*Version taking the goal as a string*)
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fun prove_goalw thy rths agoal tacsf =
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  let val sign = sign_of thy
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      val chorn = read_cterm sign (agoal,propT)
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  in  prove_goalw_cterm rths chorn tacsf end
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  handle ERROR => error (*from read_cterm?*)
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		("The error above occurred for " ^ quote agoal);
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(*String version with no meta-rewrite-rules*)
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fun prove_goal thy = prove_goalw thy [];
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(*** Commands etc ***)
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(*Return the current goal stack, if any, from undo_list*)
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fun getstate() : gstack = case !undo_list of 
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      []   => error"No current state in subgoal module"
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    | x::_ => x;
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(*Pops the given goal stack*)
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fun pop [] = error"Cannot go back past the beginning of the proof!"
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  | pop (pair::pairs) = (pair,pairs);
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(*Print a level of the goal stack.*)
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fun print_top ((th,_), pairs) = 
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   (prs("Level " ^ string_of_int(length pairs) ^ "\n"); 
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    !print_goals_ref (!goals_limit) th);
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(*Printing can raise exceptions, so the assignment occurs last.
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  Can do   setstate[(st,Sequence.null)]  to set st as the state.  *)
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fun setstate newgoals = 
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  (print_top (pop newgoals);  undo_list := newgoals :: !undo_list);
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(*Given a proof state transformation, return a command that updates
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    the goal stack*)
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fun make_command com = setstate (com (pop (getstate())));
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(*Apply a function on proof states to the current goal stack*)
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fun apply_fun f = f (pop(getstate()));
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(*Return the top theorem, representing the proof state*)
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fun topthm () = apply_fun  (fn ((th,_), _) => th);
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(*Return the final result.  *)
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fun result () = !curr_mkresult (true, topthm());
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(*Return the result UNCHECKED that it equals the goal -- for synthesis,
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  answer extraction, or other instantiation of Vars *)
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fun uresult () = !curr_mkresult (false, topthm());
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(*Get subgoal i from goal stack*)
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fun getgoal i = 
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      (case  drop (i-1, prems_of (topthm()))  of
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	    [] => error"getgoal: Goal number out of range"
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	  | Q::_ => Q);
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(*Return subgoal i's hypotheses as meta-level assumptions.
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  For debugging uses of METAHYPS*)
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local exception GETHYPS of thm list
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in
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fun gethyps i = 
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    (METAHYPS (fn hyps => raise (GETHYPS hyps)) i (topthm());  [])
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    handle GETHYPS hyps => hyps
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end;
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(*Which thms could apply to goal i? (debugs tactics involving filter_thms) *)
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fun filter_goal could ths i = filter_thms could (999, getgoal i, ths);
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(*For inspecting earlier levels of the backward proof*)
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fun chop_level n (pair,pairs) = 
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  let val level = length pairs
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  in  if n<0 andalso ~n <= level
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      then  drop (~n, pair::pairs) 
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      else if 0<=n andalso n<= level
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      then  drop (level - n, pair::pairs) 
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      else  error ("Level number must lie between 0 and " ^ 
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		   string_of_int level)
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  end;
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(*Print the given level of the proof*)
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fun prlev n = apply_fun (print_top o pop o (chop_level n));
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fun pr () = apply_fun print_top;
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(** the goal.... commands
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    Read main goal.  Set global variables curr_prems, curr_mkresult. 
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    Initial subgoal and premises are rewritten using rths. **)
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(*Version taking the goal as a cterm; if you have a term t and theory thy, use
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    goalw_cterm rths (cterm_of (sign_of thy) t);      *)
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fun goalw_cterm rths chorn = 
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  let val (prems, st0, mkresult) = prepare_proof rths chorn
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  in  undo_list := [];
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      setstate [ (st0, Sequence.null) ];  
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      curr_prems := prems;
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      curr_mkresult := mkresult;
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      prems
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  end;
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(*Version taking the goal as a string*)
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fun goalw thy rths agoal = 
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  goalw_cterm rths (read_cterm(sign_of thy)(agoal,propT))
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  handle ERROR => error (*from type_assign, etc via prepare_proof*)
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	    ("The error above occurred for " ^ quote agoal);
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(*String version with no meta-rewrite-rules*)
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fun goal thy = goalw thy [];
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(*Proof step "by" the given tactic -- apply tactic to the proof state*)
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fun by_com tac ((th,ths), pairs) : gstack =
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  (case  Sequence.pull(tac th)  of
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     None      => error"by: tactic failed"
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   | Some(th2,ths2) => 
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       (if eq_thm(th,th2) 
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	  then warning "same as previous level"
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	  else if eq_thm_sg(th,th2) then ()
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	  else warning("signature of proof state has changed" ^
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		       sign_error (#sign(rep_thm th), #sign(rep_thm th2)));
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       ((th2,ths2)::(th,ths)::pairs)));
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fun by tac = cond_timeit (!proof_timing) 
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    (fn() => make_command (by_com tac));
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(* byev[tac1,...,tacn] applies tac1 THEN ... THEN tacn.
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   Good for debugging proofs involving prove_goal.*)
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val byev = by o EVERY;
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(*Backtracking means find an alternative result from a tactic.
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  If none at this level, try earlier levels*)
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fun backtrack [] = error"back: no alternatives"
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  | backtrack ((th,thstr) :: pairs) =
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     (case Sequence.pull thstr of
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	  None      => (writeln"Going back a level..."; backtrack pairs)
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	| Some(th2,thstr2) =>  
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	   (if eq_thm(th,th2) 
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	      then warning "same as previous choice at this level"
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	      else if eq_thm_sg(th,th2) then ()
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	      else warning "signature of proof state has changed";
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	    (th2,thstr2)::pairs));
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fun back() = setstate (backtrack (getstate()));
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(*Chop back to previous level of the proof*)
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fun choplev n = make_command (chop_level n);
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(*Chopping back the goal stack*)
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fun chop () = make_command (fn (_,pairs) => pairs);
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(*Restore the previous proof state;  discard current state. *)
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fun undo() = case !undo_list of
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      [] => error"No proof state"
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    | [_] => error"Already at initial state"
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    | _::newundo =>  (undo_list := newundo;  pr()) ;
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(*** Managing the proof stack ***)
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fun save_proof() = Proof(!undo_list, !curr_prems, !curr_mkresult);
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fun restore_proof(Proof(ul,prems,mk)) =
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 (undo_list:= ul;  curr_prems:= prems;  curr_mkresult := mk;  prems);
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fun top_proof() = case !proofstack of
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	[] => error("Stack of proof attempts is empty!")
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    | p::ps => (p,ps);
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(*  push a copy of the current proof state on to the stack *)
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fun push_proof() = (proofstack := (save_proof() :: !proofstack));
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(* discard the top proof state of the stack *)
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fun pop_proof() = 
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  let val (p,ps) = top_proof()
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      val prems = restore_proof p
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  in proofstack := ps;  pr();  prems end;
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(* rotate the stack so that the top element goes to the bottom *)
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fun rotate_proof() = let val (p,ps) = top_proof()
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		    in proofstack := ps@[save_proof()];
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		       restore_proof p;
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		       pr();
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		       !curr_prems
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		    end;
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(** Shortcuts for commonly-used tactics **)
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fun bws rls = by (rewrite_goals_tac rls);
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fun bw rl = bws [rl];
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fun brs rls i = by (resolve_tac rls i);
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fun br rl = brs [rl];
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fun bes rls i = by (eresolve_tac rls i);
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fun be rl = bes [rl];
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fun bds rls i = by (dresolve_tac rls i);
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fun bd rl = bds [rl];
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fun ba i = by (assume_tac i);
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fun ren str i = by (rename_tac str i);
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(** Shortcuts to work on the first applicable subgoal **)
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fun frs rls = by (FIRSTGOAL (trace_goalno_tac (resolve_tac rls)));
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fun fr rl = frs [rl];
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fun fes rls = by (FIRSTGOAL (trace_goalno_tac (eresolve_tac rls)));
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fun fe rl = fes [rl];
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fun fds rls = by (FIRSTGOAL (trace_goalno_tac (dresolve_tac rls)));
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fun fd rl = fds [rl];
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fun fa() = by (FIRSTGOAL (trace_goalno_tac assume_tac));
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(** Reading and printing terms wrt the current theory **)
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fun top_sg() = #sign(rep_thm(topthm()));
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fun read s = term_of (read_cterm (top_sg())
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			                   (s, (TVar(("DUMMY",0),[]))));
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(*Print a term under the current signature of the proof state*)
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fun prin t = writeln (Sign.string_of_term (top_sg()) t);
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fun printyp T = writeln (Sign.string_of_typ (top_sg()) T);
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fun pprint_term t = Sign.pprint_term (top_sg()) t;
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fun pprint_typ T = Sign.pprint_typ (top_sg()) T;
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(* Redirect output of function f:unit->unit to LaTeX *)
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fun redirect_to_latex f =
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	let
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		val s = ref ""
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		val old_prs_fn = !prs_fn
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	in
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		(prs_fn := (fn a => s := !s ^ a);
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		f ();
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		latex (!s);
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		prs_fn := old_prs_fn)
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	end;
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(* Display current proof state in xdvi window *)
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fun pr_latex () = redirect_to_latex pr;
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(* Display goal n of current proof state in xdvi window *)
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fun printgoal_latex n = redirect_to_latex (fn () => prin(getgoal n));
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(*Prints exceptions nicely at top level; 
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  raises the exception in order to have a polymorphic type!*)
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fun print_exn e = (print_sign_exn_unit (top_sg()) e;  raise e);
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end;
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open Goals;