(* Title: Pure/old_goals.ML
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
Old-style 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
val the_context: unit -> theory
val premises: unit -> thm list
val prove_goal: theory -> string -> (thm list -> tactic list) -> thm
val prove_goalw: theory -> thm list -> string -> (thm list -> tactic list) -> thm
val topthm: unit -> thm
val result: unit -> thm
val uresult: unit -> thm
val getgoal: int -> term
val gethyps: int -> thm list
val prlev: int -> unit
val pr: unit -> unit
val prlim: int -> unit
val goal: theory -> string -> thm list
val goalw: theory -> thm list -> string -> thm list
val Goal: string -> thm list
val Goalw: thm list -> string -> thm list
val by: tactic -> unit
val back: unit -> unit
val choplev: int -> unit
val undo: unit -> unit
val qed: string -> unit
val qed_goal: string -> theory -> string -> (thm list -> tactic list) -> unit
val qed_goalw: string -> theory -> thm list -> string
-> (thm list -> tactic list) -> unit
val qed_spec_mp: string -> unit
val qed_goal_spec_mp: string -> theory -> string -> (thm list -> tactic list) -> unit
val qed_goalw_spec_mp: string -> theory -> thm list -> string
-> (thm list -> tactic list) -> unit
val no_qed: unit -> unit
val inst: string -> string -> thm -> thm
end;
signature OLD_GOALS =
sig
include GOALS
type proof
val chop: unit -> unit
val reset_goals: unit -> unit
val result_error_fn: (thm -> string -> thm) ref
val print_sign_exn: theory -> exn -> 'a
val prove_goalw_cterm: thm list->cterm->(thm list->tactic list)->thm
val prove_goalw_cterm_nocheck: thm list->cterm->(thm list->tactic list)->thm
val quick_and_dirty_prove_goalw_cterm: theory -> thm list -> cterm
-> (thm list -> tactic list) -> thm
val print_exn: exn -> 'a
val filter_goal: (term*term->bool) -> thm list -> int -> thm list
val goalw_cterm: thm list -> cterm -> thm list
val simple_prove_goal_cterm: cterm->(thm list->tactic list)->thm
val byev: tactic list -> unit
val save_proof: unit -> proof
val restore_proof: proof -> thm list
val push_proof: unit -> unit
val pop_proof: unit -> thm list
val rotate_proof: unit -> thm list
val bws: thm list -> unit
val bw: thm -> unit
val brs: thm list -> int -> unit
val br: thm -> int -> unit
val bes: thm list -> int -> unit
val be: thm -> int -> unit
val bds: thm list -> int -> unit
val bd: thm -> int -> unit
val ba: int -> unit
val ren: string -> int -> unit
val frs: thm list -> unit
val fr: thm -> unit
val fes: thm list -> unit
val fe: thm -> unit
val fds: thm list -> unit
val fd: thm -> unit
val fa: unit -> unit
end;
structure OldGoals: OLD_GOALS =
struct
val the_context = ML_Context.the_global_context;
(*** Goal package ***)
(*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 Seq.seq) list;
datatype proof = Proof of gstack list * thm list * (bool*thm->thm);
(*** References ***)
(*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". *)
fun init_mkresult _ = error "No goal has been supplied in subgoal module";
val curr_mkresult = ref (init_mkresult: bool*thm->thm);
(*List of previous goal stacks, for the undo operation. Set by setstate.
A list of lists!*)
val undo_list = ref([[(asm_rl, Seq.empty)]] : gstack list);
(* Stack of proof attempts *)
val proofstack = ref([]: proof list);
(*reset all refs*)
fun reset_goals () =
(curr_prems := []; curr_mkresult := init_mkresult;
undo_list := [[(asm_rl, Seq.empty)]]);
(*** Setting up goal-directed proof ***)
(*Generates the list of new theories when the proof state's theory changes*)
fun thy_error (thy,thy') =
let val names = Context.names_of thy' \\ Context.names_of thy
in case names of
[name] => "\nNew theory: " ^ name
| _ => "\nNew theories: " ^ space_implode ", " names
end;
(*Default action is to print an error message; could be suppressed for
special applications.*)
fun result_error_default state msg : thm =
Pretty.str "Bad final proof state:" :: Display.pretty_goals (!goals_limit) state @
[Pretty.str msg, Pretty.str "Proof failed!"] |> Pretty.chunks |> Pretty.string_of |> error;
val result_error_fn = ref result_error_default;
(*Common treatment of "goal" and "prove_goal":
Return assumptions, initial proof state, and function to make result.
"atomic" indicates if the goal should be wrapped up in the function
"Goal::prop=>prop" to avoid assumptions being returned separately.
*)
fun prepare_proof atomic rths chorn =
let
val _ = legacy_feature "Old goal command";
val thy = Thm.theory_of_cterm chorn;
val horn = Thm.term_of chorn;
val _ = Term.no_dummy_patterns horn handle TERM (msg, _) => error msg;
val (As, B) = Logic.strip_horn horn;
val atoms = atomic andalso
forall (fn t => not (can Logic.dest_implies t orelse can Logic.dest_all t)) As;
val (As,B) = if atoms then ([],horn) else (As,B);
val cAs = map (cterm_of thy) As;
val prems = map (rewrite_rule rths o Thm.forall_elim_vars 0 o Thm.assume) cAs;
val cB = cterm_of thy B;
val st0 = let val st = Goal.init cB |> fold Thm.weaken cAs
in rewrite_goals_rule rths st end
(*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 = Seq.hd (flexflex_rule state)
handle THM _ => state (*smash flexflex pairs*)
val ngoals = nprems_of state
val ath = implies_intr_list cAs state
val th = Goal.conclude ath
val thy' = Thm.theory_of_thm th
val {hyps, prop, ...} = Thm.rep_thm th
val final_th = standard th
in if not check then final_th
else if not (eq_thy(thy,thy')) then !result_error_fn state
("Theory of proof state has changed!" ^
thy_error (thy,thy'))
else if ngoals>0 then !result_error_fn state
(string_of_int ngoals ^ " unsolved goals!")
else if not (null hyps) then !result_error_fn state
("Additional hypotheses:\n" ^
cat_lines (map (Sign.string_of_term thy) hyps))
else if Pattern.matches thy
(Envir.beta_norm (term_of chorn), Envir.beta_norm prop)
then final_th
else !result_error_fn state "proved a different theorem"
end
in
if eq_thy(thy, Thm.theory_of_thm st0)
then (prems, st0, mkresult)
else error ("Definitions would change the proof state's theory" ^
thy_error (thy, Thm.theory_of_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 thy e =
case e of
THM (msg,i,thms) =>
(writeln ("Exception THM " ^ string_of_int i ^ " raised:\n" ^ msg);
List.app print_thm thms)
| THEORY (msg,thys) =>
(writeln ("Exception THEORY raised:\n" ^ msg);
List.app (writeln o Context.str_of_thy) thys)
| TERM (msg,ts) =>
(writeln ("Exception TERM raised:\n" ^ msg);
List.app (writeln o Sign.string_of_term thy) ts)
| TYPE (msg,Ts,ts) =>
(writeln ("Exception TYPE raised:\n" ^ msg);
List.app (writeln o Sign.string_of_typ thy) Ts;
List.app (writeln o Sign.string_of_term thy) ts)
| e => raise e;
(*Prints an exception, then fails*)
fun print_sign_exn thy e = (print_sign_exn_unit thy e; raise ERROR "");
(** the prove_goal.... commands
Prove theorem using the listed tactics; check it has the specified form.
Augment theory 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_general check rths chorn tacsf =
let val (prems, st0, mkresult) = prepare_proof false rths chorn
val tac = EVERY (tacsf prems)
fun statef() =
(case Seq.pull (tac st0) of
SOME(st,_) => st
| _ => error ("prove_goal: tactic failed"))
in mkresult (check, cond_timeit (!Output.timing) "" statef) end
handle e => (print_sign_exn_unit (Thm.theory_of_cterm chorn) e;
writeln ("The exception above was raised for\n" ^
Display.string_of_cterm chorn); raise e);
(*Two variants: one checking the result, one not.
Neither prints runtime messages: they are for internal packages.*)
fun prove_goalw_cterm rths chorn =
setmp Output.timing false (prove_goalw_cterm_general true rths chorn)
and prove_goalw_cterm_nocheck rths chorn =
setmp Output.timing false (prove_goalw_cterm_general false rths chorn);
(*Version taking the goal as a string*)
fun prove_goalw thy rths agoal tacsf =
let val chorn = Thm.read_cterm thy (agoal, propT)
in prove_goalw_cterm_general true rths chorn tacsf end
handle ERROR msg => cat_error msg (*from read_cterm?*)
("The error(s) above occurred for " ^ quote agoal);
(*String version with no meta-rewrite-rules*)
fun prove_goal thy = prove_goalw thy [];
(*quick and dirty version (conditional)*)
fun quick_and_dirty_prove_goalw_cterm thy rews ct tacs =
prove_goalw_cterm rews ct
(if ! quick_and_dirty then (K [SkipProof.cheat_tac thy]) else tacs);
(*** 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) =
let
val n = length pairs;
val m = (! goals_limit);
val ngoals = nprems_of th;
in
[Pretty.str ("Level " ^ string_of_int n ^
(if ngoals > 0 then " (" ^ string_of_int ngoals ^ " subgoal" ^
(if ngoals <> 1 then "s" else "") ^ ")"
else ""))] @
Display.pretty_goals m th
end |> Pretty.chunks |> Pretty.writeln;
(*Printing can raise exceptions, so the assignment occurs last.
Can do setstate[(st,Seq.empty)] 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 = Logic.get_goal (prop_of (topthm())) i;
(*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;
(*Prints exceptions nicely at top level;
raises the exception in order to have a polymorphic type!*)
fun print_exn e = (print_sign_exn_unit (Thm.theory_of_thm (topthm())) e; raise e);
(*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 thy t); *)
fun agoalw_cterm atomic rths chorn =
let val (prems, st0, mkresult) = prepare_proof atomic rths chorn
in undo_list := [];
setstate [ (st0, Seq.empty) ];
curr_prems := prems;
curr_mkresult := mkresult;
prems
end;
val goalw_cterm = agoalw_cterm false;
(*Version taking the goal as a string*)
fun agoalw atomic thy rths agoal =
agoalw_cterm atomic rths (Thm.read_cterm thy (agoal, propT))
handle ERROR msg => cat_error msg (*from type_assign, etc via prepare_proof*)
("The error(s) above occurred for " ^ quote agoal);
val goalw = agoalw false;
fun goal thy = goalw thy [];
(*now the versions that wrap the goal up in `Goal' to make it atomic*)
fun Goalw thms s = agoalw true (ML_Context.the_global_context ()) thms s;
val Goal = Goalw [];
(*simple version with minimal amount of checking and postprocessing*)
fun simple_prove_goal_cterm G f =
let
val _ = legacy_feature "Old goal command";
val As = Drule.strip_imp_prems G;
val B = Drule.strip_imp_concl G;
val asms = map Assumption.assume As;
fun check NONE = error "prove_goal: tactic failed"
| check (SOME (thm, _)) = (case nprems_of thm of
0 => thm
| i => !result_error_fn thm (string_of_int i ^ " unsolved goals!"))
in
standard (implies_intr_list As
(check (Seq.pull (EVERY (f asms) (trivial B)))))
end;
(*Proof step "by" the given tactic -- apply tactic to the proof state*)
fun by_com tac ((th,ths), pairs) : gstack =
(case Seq.pull(tac th) of
NONE => error"by: tactic failed"
| SOME(th2,ths2) =>
(if Thm.eq_thm(th,th2)
then warning "Warning: same as previous level"
else if Thm.eq_thm_thy(th,th2) then ()
else warning ("Warning: theory of proof state has changed" ^
thy_error (Thm.theory_of_thm th, Thm.theory_of_thm th2));
((th2,ths2)::(th,ths)::pairs)));
fun by tac = cond_timeit (!Output.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 Seq.pull thstr of
NONE => (writeln"Going back a level..."; backtrack pairs)
| SOME(th2,thstr2) =>
(if Thm.eq_thm(th,th2)
then warning "Warning: same as previous choice at this level"
else if Thm.eq_thm_thy(th,th2) then ()
else warning "Warning: theory 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));
(** theorem bindings **)
fun qed name = ML_Context.ml_store_thm (name, result ());
fun qed_goal name thy goal tacsf = ML_Context.ml_store_thm (name, prove_goal thy goal tacsf);
fun qed_goalw name thy rews goal tacsf =
ML_Context.ml_store_thm (name, prove_goalw thy rews goal tacsf);
fun qed_spec_mp name =
ML_Context.ml_store_thm (name, ObjectLogic.rulify_no_asm (result ()));
fun qed_goal_spec_mp name thy s p =
bind_thm (name, ObjectLogic.rulify_no_asm (prove_goal thy s p));
fun qed_goalw_spec_mp name thy defs s p =
bind_thm (name, ObjectLogic.rulify_no_asm (prove_goalw thy defs s p));
fun no_qed () = ();
(*shorthand for instantiating just one variable in the current theory*)
fun inst x t = read_instantiate_sg (ML_Context.the_global_context()) [(x,t)];
end;
structure Goals: GOALS = OldGoals;
open Goals;