(* Title: Pure/goals.ML
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
Goal stack package. The goal stack initially holds a dummy proof, and can
never become empty. Each goal stack consists of a list of levels. The
undo list is a list of goal stacks. Finally, there may be a stack of
pending proofs.
*)
signature GOALS =
sig
type proof
val ba : int -> unit
val back : unit -> unit
val bd : thm -> int -> unit
val bds : thm list -> int -> unit
val be : thm -> int -> unit
val bes : thm list -> int -> unit
val br : thm -> int -> unit
val brs : thm list -> int -> unit
val bw : thm -> unit
val bws : thm list -> unit
val by : tactic -> unit
val byev : tactic list -> unit
val chop : unit -> unit
val choplev : int -> unit
val fa : unit -> unit
val fd : thm -> unit
val fds : thm list -> unit
val fe : thm -> unit
val fes : thm list -> unit
val filter_goal : (term*term->bool) -> thm list -> int -> thm list
val fr : thm -> unit
val frs : thm list -> unit
val getgoal : int -> term
val gethyps : int -> thm list
val goal : theory -> string -> thm list
val goalw : theory -> thm list -> string -> thm list
val goalw_cterm : thm list -> cterm -> thm list
val pop_proof : unit -> thm list
val pr : unit -> unit
val prlev : int -> unit
val prlim : int -> unit
val pr_latex : unit -> unit
val printgoal_latex : int -> unit
val premises : unit -> thm list
val prin : term -> unit
val printyp : typ -> unit
val pprint_term : term -> pprint_args -> unit
val pprint_typ : typ -> pprint_args -> unit
val print_exn : exn -> 'a
val print_sign_exn : Sign.sg -> exn -> 'a
val proof_timing : bool ref
val prove_goal : theory -> string -> (thm list -> tactic list) -> thm
val prove_goalw : theory->thm list->string->(thm list->tactic list)->thm
val prove_goalw_cterm : thm list->cterm->(thm list->tactic list)->thm
val push_proof : unit -> unit
val read : string -> term
val ren : string -> int -> unit
val restore_proof : proof -> thm list
val result : unit -> thm
val result_error_ref : (thm -> string -> thm) ref
val rotate_proof : unit -> thm list
val uresult : unit -> thm
val save_proof : unit -> proof
val topthm : unit -> thm
val undo : unit -> unit
end;
structure Goals : GOALS =
struct
(*Each level of goal stack includes a proof state and alternative states,
the output of the tactic applied to the preceeding level. *)
type gstack = (thm * thm Sequence.seq) list;
datatype proof = Proof of gstack list * thm list * (bool*thm->thm);
(*** References ***)
(*Should process time be printed after proof steps?*)
val proof_timing = ref false;
(*Current assumption list -- set by "goal".*)
val curr_prems = ref([] : thm list);
(*Return assumption list -- useful if you didn't save "goal"'s result. *)
fun premises() = !curr_prems;
(*Current result maker -- set by "goal", used by "result". *)
val curr_mkresult =
ref((fn _=> error"No goal has been supplied in subgoal module")
: bool*thm->thm);
val dummy = trivial(read_cterm Sign.pure
("PROP No_goal_has_been_supplied",propT));
(*List of previous goal stacks, for the undo operation. Set by setstate.
A list of lists!*)
val undo_list = ref([[(dummy, Sequence.null)]] : gstack list);
(* Stack of proof attempts *)
val proofstack = ref([]: proof list);
(*** Setting up goal-directed proof ***)
(*Generates the list of new theories when the proof state's signature changes*)
fun sign_error (sign,sign') =
let val stamps = #stamps(Sign.rep_sg sign') \\
#stamps(Sign.rep_sg sign)
in case stamps of
[stamp] => "\nNew theory: " ^ !stamp
| _ => "\nNew theories: " ^ space_implode ", " (map ! stamps)
end;
(*Default action is to print an error message; could be suppressed for
special applications.*)
fun result_error_default state msg : thm =
(writeln ("Bad final proof state:");
!print_goals_ref (!goals_limit) state;
error msg);
val result_error_ref = ref result_error_default;
(*Common treatment of "goal" and "prove_goal":
Return assumptions, initial proof state, and function to make result. *)
fun prepare_proof rths chorn =
let val {sign, t=horn,...} = rep_cterm chorn;
val (_,As,B) = Logic.strip_horn(horn);
val cAs = map (cterm_of sign) As;
val prems = map (rewrite_rule rths o forall_elim_vars(0) o assume) cAs
and st0 = (rewrite_goals_rule rths o trivial) (cterm_of sign B)
(*discharges assumptions from state in the order they appear in goal;
checks (if requested) that resulting theorem is equivalent to goal. *)
fun mkresult (check,state) =
let val state = Sequence.hd (flexflex_rule state)
handle THM _ => state (*smash flexflex pairs*)
val ngoals = nprems_of state
val th = strip_shyps (implies_intr_list cAs state)
val {hyps,prop,sign=sign',...} = rep_thm th
val xshyps = extra_shyps th;
in if not check then th
else if not (Sign.eq_sg(sign,sign')) then !result_error_ref state
("Signature of proof state has changed!" ^
sign_error (sign,sign'))
else if ngoals>0 then !result_error_ref state
(string_of_int ngoals ^ " unsolved goals!")
else if not (null hyps) then !result_error_ref state
("Additional hypotheses:\n" ^
cat_lines (map (Sign.string_of_term sign) hyps))
else if not (null xshyps) then !result_error_ref state
("Extra sort hypotheses: " ^
commas (map Type.str_of_sort xshyps))
else if Pattern.matches (#tsig(Sign.rep_sg sign))
(term_of chorn, prop)
then standard th
else !result_error_ref state "proved a different theorem"
end
in
if Sign.eq_sg(sign, #sign(rep_thm st0))
then (prems, st0, mkresult)
else error ("Definitions would change the proof state's signature" ^
sign_error (sign, #sign(rep_thm st0)))
end
handle THM(s,_,_) => error("prepare_proof: exception THM was raised!\n" ^ s);
(*Prints exceptions readably to users*)
fun print_sign_exn_unit sign e =
case e of
THM (msg,i,thms) =>
(writeln ("Exception THM " ^ string_of_int i ^ " raised:\n" ^ msg);
seq print_thm thms)
| THEORY (msg,thys) =>
(writeln ("Exception THEORY raised:\n" ^ msg);
seq print_theory thys)
| TERM (msg,ts) =>
(writeln ("Exception TERM raised:\n" ^ msg);
seq (writeln o Sign.string_of_term sign) ts)
| TYPE (msg,Ts,ts) =>
(writeln ("Exception TYPE raised:\n" ^ msg);
seq (writeln o Sign.string_of_typ sign) Ts;
seq (writeln o Sign.string_of_term sign) ts)
| e => raise e;
(*Prints an exception, then fails*)
fun print_sign_exn sign e = (print_sign_exn_unit sign e; raise ERROR);
(** the prove_goal.... commands
Prove theorem using the listed tactics; check it has the specified form.
Augment signature with all type assignments of goal.
Syntax is similar to "goal" command for easy keyboard use. **)
(*Version taking the goal as a cterm*)
fun prove_goalw_cterm rths chorn tacsf =
let val (prems, st0, mkresult) = prepare_proof rths chorn
val tac = EVERY (tacsf prems)
fun statef() =
(case Sequence.pull (tac st0) of
Some(st,_) => st
| _ => error ("prove_goal: tactic failed"))
in mkresult (true, cond_timeit (!proof_timing) statef) end
handle e => (print_sign_exn_unit (#sign (rep_cterm chorn)) e;
error ("The exception above was raised for\n" ^
string_of_cterm chorn));
(*Version taking the goal as a string*)
fun prove_goalw thy rths agoal tacsf =
let val sign = sign_of thy
val chorn = read_cterm sign (agoal,propT)
in prove_goalw_cterm rths chorn tacsf end
handle ERROR => error (*from read_cterm?*)
("The error above occurred for " ^ quote agoal);
(*String version with no meta-rewrite-rules*)
fun prove_goal thy = prove_goalw thy [];
(*** Commands etc ***)
(*Return the current goal stack, if any, from undo_list*)
fun getstate() : gstack = case !undo_list of
[] => error"No current state in subgoal module"
| x::_ => x;
(*Pops the given goal stack*)
fun pop [] = error"Cannot go back past the beginning of the proof!"
| pop (pair::pairs) = (pair,pairs);
(*Print a level of the goal stack.*)
fun print_top ((th,_), pairs) =
(prs("Level " ^ string_of_int(length pairs) ^ "\n");
!print_goals_ref (!goals_limit) th);
(*Printing can raise exceptions, so the assignment occurs last.
Can do setstate[(st,Sequence.null)] to set st as the state. *)
fun setstate newgoals =
(print_top (pop newgoals); undo_list := newgoals :: !undo_list);
(*Given a proof state transformation, return a command that updates
the goal stack*)
fun make_command com = setstate (com (pop (getstate())));
(*Apply a function on proof states to the current goal stack*)
fun apply_fun f = f (pop(getstate()));
(*Return the top theorem, representing the proof state*)
fun topthm () = apply_fun (fn ((th,_), _) => th);
(*Return the final result. *)
fun result () = !curr_mkresult (true, topthm());
(*Return the result UNCHECKED that it equals the goal -- for synthesis,
answer extraction, or other instantiation of Vars *)
fun uresult () = !curr_mkresult (false, topthm());
(*Get subgoal i from goal stack*)
fun getgoal i = List.nth (prems_of (topthm()), i-1)
handle Subscript => error"getgoal: Goal number out of range";
(*Return subgoal i's hypotheses as meta-level assumptions.
For debugging uses of METAHYPS*)
local exception GETHYPS of thm list
in
fun gethyps i =
(METAHYPS (fn hyps => raise (GETHYPS hyps)) i (topthm()); [])
handle GETHYPS hyps => hyps
end;
(*Which thms could apply to goal i? (debugs tactics involving filter_thms) *)
fun filter_goal could ths i = filter_thms could (999, getgoal i, ths);
(*For inspecting earlier levels of the backward proof*)
fun chop_level n (pair,pairs) =
let val level = length pairs
in if n<0 andalso ~n <= level
then List.drop (pair::pairs, ~n)
else if 0<=n andalso n<= level
then List.drop (pair::pairs, level - n)
else error ("Level number must lie between 0 and " ^
string_of_int level)
end;
(*Print the given level of the proof; prlev ~1 prints previous level*)
fun prlev n = apply_fun (print_top o pop o (chop_level n));
fun pr () = apply_fun print_top;
(*Set goals_limit and print again*)
fun prlim n = (goals_limit:=n; pr());
(** the goal.... commands
Read main goal. Set global variables curr_prems, curr_mkresult.
Initial subgoal and premises are rewritten using rths. **)
(*Version taking the goal as a cterm; if you have a term t and theory thy, use
goalw_cterm rths (cterm_of (sign_of thy) t); *)
fun goalw_cterm rths chorn =
let val (prems, st0, mkresult) = prepare_proof rths chorn
in undo_list := [];
setstate [ (st0, Sequence.null) ];
curr_prems := prems;
curr_mkresult := mkresult;
prems
end;
(*Version taking the goal as a string*)
fun goalw thy rths agoal =
goalw_cterm rths (read_cterm(sign_of thy)(agoal,propT))
handle ERROR => error (*from type_assign, etc via prepare_proof*)
("The error above occurred for " ^ quote agoal);
(*String version with no meta-rewrite-rules*)
fun goal thy = goalw thy [];
(*Proof step "by" the given tactic -- apply tactic to the proof state*)
fun by_com tac ((th,ths), pairs) : gstack =
(case Sequence.pull(tac th) of
None => error"by: tactic failed"
| Some(th2,ths2) =>
(if eq_thm(th,th2)
then warning "same as previous level"
else if eq_thm_sg(th,th2) then ()
else warning("signature of proof state has changed" ^
sign_error (#sign(rep_thm th), #sign(rep_thm th2)));
((th2,ths2)::(th,ths)::pairs)));
fun by tac = cond_timeit (!proof_timing)
(fn() => make_command (by_com tac));
(* byev[tac1,...,tacn] applies tac1 THEN ... THEN tacn.
Good for debugging proofs involving prove_goal.*)
val byev = by o EVERY;
(*Backtracking means find an alternative result from a tactic.
If none at this level, try earlier levels*)
fun backtrack [] = error"back: no alternatives"
| backtrack ((th,thstr) :: pairs) =
(case Sequence.pull thstr of
None => (writeln"Going back a level..."; backtrack pairs)
| Some(th2,thstr2) =>
(if eq_thm(th,th2)
then warning "same as previous choice at this level"
else if eq_thm_sg(th,th2) then ()
else warning "signature of proof state has changed";
(th2,thstr2)::pairs));
fun back() = setstate (backtrack (getstate()));
(*Chop back to previous level of the proof*)
fun choplev n = make_command (chop_level n);
(*Chopping back the goal stack*)
fun chop () = make_command (fn (_,pairs) => pairs);
(*Restore the previous proof state; discard current state. *)
fun undo() = case !undo_list of
[] => error"No proof state"
| [_] => error"Already at initial state"
| _::newundo => (undo_list := newundo; pr()) ;
(*** Managing the proof stack ***)
fun save_proof() = Proof(!undo_list, !curr_prems, !curr_mkresult);
fun restore_proof(Proof(ul,prems,mk)) =
(undo_list:= ul; curr_prems:= prems; curr_mkresult := mk; prems);
fun top_proof() = case !proofstack of
[] => error("Stack of proof attempts is empty!")
| p::ps => (p,ps);
(* push a copy of the current proof state on to the stack *)
fun push_proof() = (proofstack := (save_proof() :: !proofstack));
(* discard the top proof state of the stack *)
fun pop_proof() =
let val (p,ps) = top_proof()
val prems = restore_proof p
in proofstack := ps; pr(); prems end;
(* rotate the stack so that the top element goes to the bottom *)
fun rotate_proof() = let val (p,ps) = top_proof()
in proofstack := ps@[save_proof()];
restore_proof p;
pr();
!curr_prems
end;
(** Shortcuts for commonly-used tactics **)
fun bws rls = by (rewrite_goals_tac rls);
fun bw rl = bws [rl];
fun brs rls i = by (resolve_tac rls i);
fun br rl = brs [rl];
fun bes rls i = by (eresolve_tac rls i);
fun be rl = bes [rl];
fun bds rls i = by (dresolve_tac rls i);
fun bd rl = bds [rl];
fun ba i = by (assume_tac i);
fun ren str i = by (rename_tac str i);
(** Shortcuts to work on the first applicable subgoal **)
fun frs rls = by (FIRSTGOAL (trace_goalno_tac (resolve_tac rls)));
fun fr rl = frs [rl];
fun fes rls = by (FIRSTGOAL (trace_goalno_tac (eresolve_tac rls)));
fun fe rl = fes [rl];
fun fds rls = by (FIRSTGOAL (trace_goalno_tac (dresolve_tac rls)));
fun fd rl = fds [rl];
fun fa() = by (FIRSTGOAL (trace_goalno_tac assume_tac));
(** Reading and printing terms wrt the current theory **)
fun top_sg() = #sign(rep_thm(topthm()));
fun read s = term_of (read_cterm (top_sg())
(s, (TVar(("DUMMY",0),[]))));
(*Print a term under the current signature of the proof state*)
fun prin t = writeln (Sign.string_of_term (top_sg()) t);
fun printyp T = writeln (Sign.string_of_typ (top_sg()) T);
fun pprint_term t = Sign.pprint_term (top_sg()) t;
fun pprint_typ T = Sign.pprint_typ (top_sg()) T;
(* Redirect output of function f:unit->unit to LaTeX *)
fun redirect_to_latex f =
let
val s = ref ""
val old_prs_fn = !prs_fn
in
(prs_fn := (fn a => s := !s ^ a);
f ();
latex (!s);
prs_fn := old_prs_fn)
end;
(* Display current proof state in xdvi window *)
fun pr_latex () = redirect_to_latex pr;
(* Display goal n of current proof state in xdvi window *)
fun printgoal_latex n = redirect_to_latex (fn () => prin(getgoal n));
(*Prints exceptions nicely at top level;
raises the exception in order to have a polymorphic type!*)
fun print_exn e = (print_sign_exn_unit (top_sg()) e; raise e);
end;
open Goals;