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src/Pure/old_goals.ML

author | wenzelm |

Sat, 21 Jan 2006 23:02:14 +0100 | |

changeset 18728 | 6790126ab5f6 |

parent 18678 | dd0c569fa43d |

child 19053 | 358c0eb6d785 |

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

simplified type attribute;

(* 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 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 disable_pr: unit -> unit val enable_pr: unit -> unit 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 chop: unit -> unit val undo: unit -> unit val bind_thm: string * thm -> unit val bind_thms: string * thm list -> 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 thms_containing: xstring list -> (string * thm) list end; signature OLD_GOALS = sig include GOALS val legacy: bool ref type proof 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 legacy = ref false; fun warn_obsolete () = if ! legacy then () else warning "Obsolete goal command encountered"; (*** 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); val dummy = Thm.trivial (read_cterm 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 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 _ = warn_obsolete (); val {thy, 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 thy) As; val prems = map (rewrite_rule rths o 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 {hyps,prop,thy=thy',...} = 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 (#thy (rep_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 = 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 -- 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 ! Display.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 = 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 = (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 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 (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 (Context.the_context ()) thms s; val Goal = Goalw []; (*simple version with minimal amount of checking and postprocessing*) fun simple_prove_goal_cterm G f = let val _ = warn_obsolete (); val As = Drule.strip_imp_prems G; val B = Drule.strip_imp_concl G; val asms = map (Goal.norm_hhf o Thm.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 eq_thm(th,th2) then warning "Warning: same as previous level" else if 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 eq_thm(th,th2) then warning "Warning: same as previous choice at this level" else if 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 database operations **) (* store *) fun bind_thm (name, thm) = ThmDatabase.ml_store_thm (name, standard thm); fun bind_thms (name, thms) = ThmDatabase.ml_store_thms (name, map standard thms); fun qed name = ThmDatabase.ml_store_thm (name, result ()); fun qed_goal name thy goal tacsf = ThmDatabase.ml_store_thm (name, prove_goal thy goal tacsf); fun qed_goalw name thy rews goal tacsf = ThmDatabase.ml_store_thm (name, prove_goalw thy rews goal tacsf); fun qed_spec_mp name = ThmDatabase.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 () = (); (* retrieve *) fun thms_containing raw_consts = let val thy = Thm.theory_of_thm (topthm ()); val consts = map (Sign.intern_const thy) raw_consts; in (case List.filter (is_none o Sign.const_type thy) consts of [] => () | cs => error ("thms_containing: undeclared consts " ^ commas_quote cs)); PureThy.thms_containing_consts thy consts end; end; structure Goals: GOALS = OldGoals; open Goals;