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src/Pure/goals.ML

author | wenzelm |

Fri, 29 Dec 2000 19:43:52 +0100 | |

changeset 10745 | 0f3537fad0f3 |

parent 10487 | 97d25c125c61 |

child 11554 | 685daff01da4 |

permissions | -rw-r--r-- |

proper error msg;

(* 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 reset_goals : unit -> unit val atomic_goal : theory -> string -> thm list val atomic_goalw : theory -> thm list -> string -> thm list val Goal : string -> thm list val Goalw : thm list -> string -> thm list 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 export_thy : theory -> thm -> thm val export : thm -> thm val Export : thm -> thm 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 current_goals_markers: (string * string * string) ref val print_current_goals_default: (int -> int -> thm -> unit) val print_current_goals_fn : (int -> int -> thm -> unit) ref val pop_proof : unit -> thm list val pr : unit -> unit val disable_pr : unit -> unit val enable_pr : unit -> unit val prlev : int -> unit val prlim : 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 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 prove_goalw_cterm_nocheck : 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_fn : (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 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); val dummy = trivial(read_cterm (Theory.sign_of ProtoPure.thy) ("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, 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 := [[(dummy, Seq.empty)]]); (*** 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 names = Sign.stamp_names_of sign' \\ Sign.stamp_names_of sign 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 = (writeln "Bad final proof state:"; print_goals (!goals_limit) state; writeln msg; error "Proof failed"); val result_error_fn = ref result_error_default; (* alternative to standard: this function does not discharge the hypotheses first. Is used for locales, in the following function prepare_proof *) fun varify th = let val {maxidx,...} = rep_thm th in th |> forall_intr_frees |> forall_elim_vars (maxidx + 1) |> Drule.strip_shyps_warning |> zero_var_indexes |> Thm.varifyT |> Thm.compress end; (** exporting a theorem out of a locale means turning all meta-hyps into assumptions and expand and cancel the locale definitions. export goes through all levels in case of nested locales, whereas export_thy just goes one up. **) fun get_top_scope_thms thy = let val sc = (Locale.get_scope_sg (Theory.sign_of thy)) in if (null sc) then (warning "No locale in theory"; []) else map (#prop o rep_thm) (map #2 (#thms(snd(hd sc)))) end; fun implies_intr_some_hyps thy A_set th = let val sign = Theory.sign_of thy; val used_As = A_set inter #hyps(rep_thm(th)); val ctl = map (cterm_of sign) used_As in foldl (fn (x, y) => Thm.implies_intr y x) (th, ctl) end; fun standard_some thy A_set th = let val {maxidx,...} = rep_thm th in th |> implies_intr_some_hyps thy A_set |> forall_intr_frees |> forall_elim_vars (maxidx + 1) |> Drule.strip_shyps_warning |> zero_var_indexes |> Thm.varifyT |> Thm.compress end; fun export_thy thy th = let val A_set = get_top_scope_thms thy in standard_some thy [] (Seq.hd ((REPEAT (FIRSTGOAL (rtac reflexive_thm))) (standard_some thy A_set th))) end; val export = standard o Seq.hd o (REPEAT (FIRSTGOAL (rtac reflexive_thm))) o standard; fun Export th = export_thy (the_context ()) th; (*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 {sign, t=horn,...} = rep_cterm 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(Logic.is_implies t orelse Logic.is_all t)) As; val (As,B) = if atoms then ([],horn) else (As,B); val cAs = map (cterm_of sign) As; val prems = map (rewrite_rule rths o forall_elim_vars(0) o assume) cAs; val cB = cterm_of sign B; val st0 = let val st = Drule.mk_triv_goal cB 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 = ath RS Drule.rev_triv_goal val {hyps,prop,sign=sign',...} = rep_thm th val final_th = if (null(hyps)) then standard th else varify th in if not check then final_th else if not (Sign.eq_sg(sign,sign')) then !result_error_fn state ("Signature of proof state has changed!" ^ sign_error (sign,sign')) else if ngoals>0 then !result_error_fn state (string_of_int ngoals ^ " unsolved goals!") else if (not (null hyps) andalso (not (Locale.in_locale hyps sign))) then !result_error_fn state ("Additional hypotheses:\n" ^ cat_lines (map (Sign.string_of_term sign) (filter (fn x => (not (Locale.in_locale [x] sign))) hyps))) else if Pattern.matches (#tsig(Sign.rep_sg sign)) (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 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 (Pretty.writeln o Display.pretty_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_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 (!Library.timing) statef) end handle e => (print_sign_exn_unit (#sign (rep_cterm chorn)) e; writeln ("The exception above was raised for\n" ^ 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 Library.timing false (prove_goalw_cterm_general true rths chorn) and prove_goalw_cterm_nocheck rths chorn = setmp Library.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 sign = Theory.sign_of thy val chorn = read_cterm sign (agoal,propT) in prove_goalw_cterm_general true rths chorn tacsf end handle ERROR => error (*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 []; (*** 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 goals of current level*) val current_goals_markers = ref ("", "", ""); fun print_current_goals_default n max th = let val ref (begin_state, end_state, begin_goal) = current_goals_markers; val ngoals = nprems_of th; in if begin_state = "" then () else writeln begin_state; writeln ("Level " ^ string_of_int n ^ (if ngoals > 0 then " (" ^ string_of_int ngoals ^ " subgoal" ^ (if ngoals <> 1 then "s" else "") ^ ")" else "")); Locale.print_goals_marker begin_goal max th; if end_state = "" then () else writeln end_state end; val print_current_goals_fn = ref print_current_goals_default; (* Print a level of the goal stack -- subject to quiet mode *) val quiet = ref false; fun disable_pr () = quiet := true; fun enable_pr () = quiet := false; fun print_top ((th, _), pairs) = if ! quiet then () else ! print_current_goals_fn (length pairs) (! goals_limit) th; (*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 = 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 = (enable_pr (); apply_fun (print_top o pop o (chop_level n))); fun pr () = (enable_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 (Theory.sign_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 (Locale.read_cterm(Theory.sign_of thy)(agoal,propT)) handle ERROR => error (*from type_assign, etc via prepare_proof*) ("The error(s) above occurred for " ^ quote agoal); val goalw = agoalw false; (*String version with no meta-rewrite-rules*) fun agoal atomic thy = agoalw atomic thy []; val goal = agoal false; (*now the versions that wrap the goal up in `Goal' to make it atomic*) val atomic_goalw = agoalw true; val atomic_goal = agoal true; (*implicit context versions*) fun Goal s = atomic_goal (Context.the_context ()) s; fun Goalw thms s = atomic_goalw (Context.the_context ()) thms s; (*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 eq_thm(th,th2) then warning "Warning: same as previous level" else if eq_thm_sg(th,th2) then () else warning ("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 (!Library.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 eq_thm(th,th2) then warning "Warning: same as previous choice at this level" else if eq_thm_sg(th,th2) then () else warning "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, TypeInfer.logicT)); (*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; (*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;