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src/Pure/goals.ML

author | paulson |

Tue, 22 Jul 1997 11:14:18 +0200 | |

changeset 3538 | ed9de44032e0 |

parent 3536 | 8fb4150e2ad3 |

child 3669 | 3384c6f1f095 |

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

Removal of the tactical STATE

(* 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 print_current_goals_fn : (int -> int -> thm -> unit) ref 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_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 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; writeln msg; raise 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. *) 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_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) then !result_error_fn state ("Additional hypotheses:\n" ^ cat_lines (map (Sign.string_of_term sign) hyps)) else if not (null xshyps) then !result_error_fn state ("Extra sort hypotheses: " ^ commas (map Sorts.str_of_sort xshyps)) else if Pattern.matches (#tsig(Sign.rep_sg sign)) (term_of chorn, prop) then standard 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 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(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*) fun print_current_goals_default n max th = (writeln ("Level " ^ string_of_int n); !print_goals_ref max th); val print_current_goals_fn = ref print_current_goals_default; (*Print a level of the goal stack.*) fun print_top ((th, _), pairs) = !print_current_goals_fn (length pairs) (!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(s) 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 writeln "Warning: same as previous level" else if eq_thm_sg(th,th2) then () else writeln ("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 writeln "Warning: same as previous choice at this level" else if eq_thm_sg(th,th2) then () else writeln "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;