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src/Pure/tctical.ML

author | paulson |

Fri, 05 Oct 2007 09:59:03 +0200 | |

changeset 24854 | 0ebcd575d3c6 |

parent 24359 | 44556727197a |

child 26626 | c6231d64d264 |

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

filtering out some package theorems

(* Title: Pure/tctical.ML ID: $Id$ Author: Lawrence C Paulson, Cambridge University Computer Laboratory Copyright 1993 University of Cambridge Tacticals. *) infix 1 THEN THEN' THEN_ALL_NEW; infix 0 ORELSE APPEND INTLEAVE ORELSE' APPEND' INTLEAVE'; infix 0 THEN_ELSE; signature TACTICAL = sig type tactic = thm -> thm Seq.seq val THEN: tactic * tactic -> tactic val ORELSE: tactic * tactic -> tactic val APPEND: tactic * tactic -> tactic val INTLEAVE: tactic * tactic -> tactic val THEN_ELSE: tactic * (tactic*tactic) -> tactic val THEN': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic val ORELSE': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic val APPEND': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic val INTLEAVE': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic val all_tac: tactic val no_tac: tactic val DETERM: tactic -> tactic val COND: (thm -> bool) -> tactic -> tactic -> tactic val TRY: tactic -> tactic val EVERY: tactic list -> tactic val EVERY': ('a -> tactic) list -> 'a -> tactic val EVERY1: (int -> tactic) list -> tactic val FIRST: tactic list -> tactic val FIRST': ('a -> tactic) list -> 'a -> tactic val FIRST1: (int -> tactic) list -> tactic val RANGE: (int -> tactic) list -> int -> tactic val print_tac: string -> tactic val pause_tac: tactic val trace_REPEAT: bool ref val suppress_tracing: bool ref val tracify: bool ref -> tactic -> tactic val traced_tac: (thm -> (thm * thm Seq.seq) option) -> tactic val DETERM_UNTIL: (thm -> bool) -> tactic -> tactic val REPEAT_DETERM_N: int -> tactic -> tactic val REPEAT_DETERM: tactic -> tactic val REPEAT: tactic -> tactic val REPEAT_DETERM1: tactic -> tactic val REPEAT1: tactic -> tactic val FILTER: (thm -> bool) -> tactic -> tactic val CHANGED: tactic -> tactic val CHANGED_PROP: tactic -> tactic val ALLGOALS: (int -> tactic) -> tactic val SOMEGOAL: (int -> tactic) -> tactic val FIRSTGOAL: (int -> tactic) -> tactic val REPEAT_SOME: (int -> tactic) -> tactic val REPEAT_DETERM_SOME: (int -> tactic) -> tactic val REPEAT_FIRST: (int -> tactic) -> tactic val REPEAT_DETERM_FIRST: (int -> tactic) -> tactic val TRYALL: (int -> tactic) -> tactic val CSUBGOAL: ((cterm * int) -> tactic) -> int -> tactic val SUBGOAL: ((term * int) -> tactic) -> int -> tactic val CHANGED_GOAL: (int -> tactic) -> int -> tactic val THEN_ALL_NEW: (int -> tactic) * (int -> tactic) -> int -> tactic val REPEAT_ALL_NEW: (int -> tactic) -> int -> tactic val strip_context: term -> (string * typ) list * term list * term val metahyps_thms: int -> thm -> thm list option val METAHYPS: (thm list -> tactic) -> int -> tactic val PRIMSEQ: (thm -> thm Seq.seq) -> tactic val PRIMITIVE: (thm -> thm) -> tactic val SINGLE: tactic -> thm -> thm option val CONVERSION: conv -> int -> tactic end; structure Tactical : TACTICAL = struct (**** Tactics ****) (*A tactic maps a proof tree to a sequence of proof trees: if length of sequence = 0 then the tactic does not apply; if length > 1 then backtracking on the alternatives can occur.*) type tactic = thm -> thm Seq.seq; (*** LCF-style tacticals ***) (*the tactical THEN performs one tactic followed by another*) fun (tac1 THEN tac2) st = Seq.maps tac2 (tac1 st); (*The tactical ORELSE uses the first tactic that returns a nonempty sequence. Like in LCF, ORELSE commits to either tac1 or tac2 immediately. Does not backtrack to tac2 if tac1 was initially chosen. *) fun (tac1 ORELSE tac2) st = case Seq.pull(tac1 st) of NONE => tac2 st | sequencecell => Seq.make(fn()=> sequencecell); (*The tactical APPEND combines the results of two tactics. Like ORELSE, but allows backtracking on both tac1 and tac2. The tactic tac2 is not applied until needed.*) fun (tac1 APPEND tac2) st = Seq.append (tac1 st) (Seq.make(fn()=> Seq.pull (tac2 st))); (*Like APPEND, but interleaves results of tac1 and tac2.*) fun (tac1 INTLEAVE tac2) st = Seq.interleave(tac1 st, Seq.make(fn()=> Seq.pull (tac2 st))); (*Conditional tactic. tac1 ORELSE tac2 = tac1 THEN_ELSE (all_tac, tac2) tac1 THEN tac2 = tac1 THEN_ELSE (tac2, no_tac) *) fun (tac THEN_ELSE (tac1, tac2)) st = case Seq.pull(tac st) of NONE => tac2 st (*failed; try tactic 2*) | seqcell => Seq.maps tac1 (Seq.make(fn()=> seqcell)); (*succeeded; use tactic 1*) (*Versions for combining tactic-valued functions, as in SOMEGOAL (resolve_tac rls THEN' assume_tac) *) fun (tac1 THEN' tac2) x = tac1 x THEN tac2 x; fun (tac1 ORELSE' tac2) x = tac1 x ORELSE tac2 x; fun (tac1 APPEND' tac2) x = tac1 x APPEND tac2 x; fun (tac1 INTLEAVE' tac2) x = tac1 x INTLEAVE tac2 x; (*passes all proofs through unchanged; identity of THEN*) fun all_tac st = Seq.single st; (*passes no proofs through; identity of ORELSE and APPEND*) fun no_tac st = Seq.empty; (*Make a tactic deterministic by chopping the tail of the proof sequence*) fun DETERM tac = Seq.DETERM tac; (*Conditional tactical: testfun controls which tactic to use next. Beware: due to eager evaluation, both thentac and elsetac are evaluated.*) fun COND testfun thenf elsef = (fn prf => if testfun prf then thenf prf else elsef prf); (*Do the tactic or else do nothing*) fun TRY tac = tac ORELSE all_tac; (*** List-oriented tactics ***) local (*This version of EVERY avoids backtracking over repeated states*) fun EVY (trail, []) st = Seq.make (fn()=> SOME(st, Seq.make (fn()=> Seq.pull (evyBack trail)))) | EVY (trail, tac::tacs) st = case Seq.pull(tac st) of NONE => evyBack trail (*failed: backtrack*) | SOME(st',q) => EVY ((st',q,tacs)::trail, tacs) st' and evyBack [] = Seq.empty (*no alternatives*) | evyBack ((st',q,tacs)::trail) = case Seq.pull q of NONE => evyBack trail | SOME(st,q') => if Thm.eq_thm (st',st) then evyBack ((st',q',tacs)::trail) else EVY ((st,q',tacs)::trail, tacs) st in (* EVERY [tac1,...,tacn] equals tac1 THEN ... THEN tacn *) fun EVERY tacs = EVY ([], tacs); end; (* EVERY' [tac1,...,tacn] i equals tac1 i THEN ... THEN tacn i *) fun EVERY' tacs i = EVERY (map (fn f => f i) tacs); (*Apply every tactic to 1*) fun EVERY1 tacs = EVERY' tacs 1; (* FIRST [tac1,...,tacn] equals tac1 ORELSE ... ORELSE tacn *) fun FIRST tacs = fold_rev (curry op ORELSE) tacs no_tac; (* FIRST' [tac1,...,tacn] i equals tac1 i ORELSE ... ORELSE tacn i *) fun FIRST' tacs = fold_rev (curry op ORELSE') tacs (K no_tac); (*Apply first tactic to 1*) fun FIRST1 tacs = FIRST' tacs 1; (*Apply tactics on consecutive subgoals*) fun RANGE [] _ = all_tac | RANGE (tac :: tacs) i = RANGE tacs (i + 1) THEN tac i; (*** Tracing tactics ***) (*Print the current proof state and pass it on.*) fun print_tac msg = (fn st => (tracing msg; tracing ((Pretty.string_of o Pretty.chunks o Display.pretty_goals (! Display.goals_limit)) st); Seq.single st)); (*Pause until a line is typed -- if non-empty then fail. *) fun pause_tac st = (tracing "** Press RETURN to continue:"; if TextIO.inputLine TextIO.stdIn = SOME "\n" then Seq.single st else (tracing "Goodbye"; Seq.empty)); exception TRACE_EXIT of thm and TRACE_QUIT; (*Tracing flags*) val trace_REPEAT= ref false and suppress_tracing = ref false; (*Handle all tracing commands for current state and tactic *) fun exec_trace_command flag (tac, st) = case TextIO.inputLine TextIO.stdIn of SOME "\n" => tac st | SOME "f\n" => Seq.empty | SOME "o\n" => (flag:=false; tac st) | SOME "s\n" => (suppress_tracing:=true; tac st) | SOME "x\n" => (tracing "Exiting now"; raise (TRACE_EXIT st)) | SOME "quit\n" => raise TRACE_QUIT | _ => (tracing "Type RETURN to continue or...\n\ \ f - to fail here\n\ \ o - to switch tracing off\n\ \ s - to suppress tracing until next entry to a tactical\n\ \ x - to exit at this point\n\ \ quit - to abort this tracing run\n\ \** Well? " ; exec_trace_command flag (tac, st)); (*Extract from a tactic, a thm->thm seq function that handles tracing*) fun tracify flag tac st = if !flag andalso not (!suppress_tracing) then (Display.print_goals (! Display.goals_limit) st; tracing "** Press RETURN to continue:"; exec_trace_command flag (tac,st)) else tac st; (*Create a tactic whose outcome is given by seqf, handling TRACE_EXIT*) fun traced_tac seqf st = (suppress_tracing := false; Seq.make (fn()=> seqf st handle TRACE_EXIT st' => SOME(st', Seq.empty))); (*Deterministic DO..UNTIL: only retains the first outcome; tail recursive. Forces repitition until predicate on state is fulfilled.*) fun DETERM_UNTIL p tac = let val tac = tracify trace_REPEAT tac fun drep st = if p st then SOME (st, Seq.empty) else (case Seq.pull(tac st) of NONE => NONE | SOME(st',_) => drep st') in traced_tac drep end; (*Deterministic REPEAT: only retains the first outcome; uses less space than REPEAT; tail recursive. If non-negative, n bounds the number of repetitions.*) fun REPEAT_DETERM_N n tac = let val tac = tracify trace_REPEAT tac fun drep 0 st = SOME(st, Seq.empty) | drep n st = (case Seq.pull(tac st) of NONE => SOME(st, Seq.empty) | SOME(st',_) => drep (n-1) st') in traced_tac (drep n) end; (*Allows any number of repetitions*) val REPEAT_DETERM = REPEAT_DETERM_N ~1; (*General REPEAT: maintains a stack of alternatives; tail recursive*) fun REPEAT tac = let val tac = tracify trace_REPEAT tac fun rep qs st = case Seq.pull(tac st) of NONE => SOME(st, Seq.make(fn()=> repq qs)) | SOME(st',q) => rep (q::qs) st' and repq [] = NONE | repq(q::qs) = case Seq.pull q of NONE => repq qs | SOME(st,q) => rep (q::qs) st in traced_tac (rep []) end; (*Repeat 1 or more times*) fun REPEAT_DETERM1 tac = DETERM tac THEN REPEAT_DETERM tac; fun REPEAT1 tac = tac THEN REPEAT tac; (** Filtering tacticals **) fun FILTER pred tac st = Seq.filter pred (tac st); (*Accept only next states that change the theorem somehow*) fun CHANGED tac st = let fun diff st' = not (Thm.eq_thm (st, st')); in Seq.filter diff (tac st) end; (*Accept only next states that change the theorem's prop field (changes to signature, hyps, etc. don't count)*) fun CHANGED_PROP tac st = let fun diff st' = not (Thm.eq_thm_prop (st, st')); in Seq.filter diff (tac st) end; (*** Tacticals based on subgoal numbering ***) (*For n subgoals, performs tac(n) THEN ... THEN tac(1) Essential to work backwards since tac(i) may add/delete subgoals at i. *) fun ALLGOALS tac st = let fun doall 0 = all_tac | doall n = tac(n) THEN doall(n-1) in doall(nprems_of st)st end; (*For n subgoals, performs tac(n) ORELSE ... ORELSE tac(1) *) fun SOMEGOAL tac st = let fun find 0 = no_tac | find n = tac(n) ORELSE find(n-1) in find(nprems_of st)st end; (*For n subgoals, performs tac(1) ORELSE ... ORELSE tac(n). More appropriate than SOMEGOAL in some cases.*) fun FIRSTGOAL tac st = let fun find (i,n) = if i>n then no_tac else tac(i) ORELSE find (i+1,n) in find(1, nprems_of st)st end; (*Repeatedly solve some using tac. *) fun REPEAT_SOME tac = REPEAT1 (SOMEGOAL (REPEAT1 o tac)); fun REPEAT_DETERM_SOME tac = REPEAT_DETERM1 (SOMEGOAL (REPEAT_DETERM1 o tac)); (*Repeatedly solve the first possible subgoal using tac. *) fun REPEAT_FIRST tac = REPEAT1 (FIRSTGOAL (REPEAT1 o tac)); fun REPEAT_DETERM_FIRST tac = REPEAT_DETERM1 (FIRSTGOAL (REPEAT_DETERM1 o tac)); (*For n subgoals, tries to apply tac to n,...1 *) fun TRYALL tac = ALLGOALS (TRY o tac); (*Make a tactic for subgoal i, if there is one. *) fun CSUBGOAL goalfun i st = (case SOME (Thm.cprem_of st i) handle THM _ => NONE of SOME goal => goalfun (goal, i) st | NONE => Seq.empty); fun SUBGOAL goalfun = CSUBGOAL (fn (goal, i) => goalfun (Thm.term_of goal, i)); (*Returns all states that have changed in subgoal i, counted from the LAST subgoal. For stac, for example.*) fun CHANGED_GOAL tac i st = let val np = nprems_of st val d = np-i (*distance from END*) val t = List.nth(prems_of st, i-1) fun diff st' = nprems_of st' - d <= 0 (*the subgoal no longer exists*) orelse not (Pattern.aeconv (t, List.nth(prems_of st', nprems_of st' - d - 1))) in Seq.filter diff (tac i st) end handle Subscript => Seq.empty (*no subgoal i*); fun (tac1 THEN_ALL_NEW tac2) i st = st |> (tac1 i THEN (fn st' => Seq.INTERVAL tac2 i (i + nprems_of st' - nprems_of st) st')); (*repeatedly dig into any emerging subgoals*) fun REPEAT_ALL_NEW tac = tac THEN_ALL_NEW (TRY o (fn i => REPEAT_ALL_NEW tac i)); (*Strips assumptions in goal yielding ( [x1,...,xm], [H1,...,Hn], B ) H1,...,Hn are the hypotheses; x1...xm are variants of the parameters. Main difference from strip_assums concerns parameters: it replaces the bound variables by free variables. *) fun strip_context_aux (params, Hs, Const("==>", _) $ H $ B) = strip_context_aux (params, H::Hs, B) | strip_context_aux (params, Hs, Const("all",_)$Abs(a,T,t)) = let val (b,u) = Syntax.variant_abs(a,T,t) in strip_context_aux ((b,T)::params, Hs, u) end | strip_context_aux (params, Hs, B) = (rev params, rev Hs, B); fun strip_context A = strip_context_aux ([],[],A); (**** METAHYPS -- tactical for using hypotheses as meta-level assumptions METAHYPS (fn prems => tac prems) i converts subgoal i, of the form !!x1...xm. [| A1;...;An] ==> A into a new proof state A==>A, supplying A1,...,An as meta-level assumptions (in "prems"). The parameters x1,...,xm become free variables. If the resulting proof state is [| B1;...;Bk] ==> C (possibly assuming A1,...,An) then it is lifted back into the original context, yielding k subgoals. Replaces unknowns in the context by Frees having the prefix METAHYP_ New unknowns in [| B1;...;Bk] ==> C are lifted over x1,...,xm. DOES NOT HANDLE TYPE UNKNOWNS. ****) local (*Left-to-right replacements: ctpairs = [...,(vi,ti),...]. Instantiates distinct free variables by terms of same type.*) fun free_instantiate ctpairs = forall_elim_list (map snd ctpairs) o forall_intr_list (map fst ctpairs); fun free_of s ((a,i), T) = Free(s ^ (case i of 0 => a | _ => a ^ "_" ^ string_of_int i), T) fun mk_inst (var as Var(v,T)) = (var, free_of "METAHYP1_" (v,T)) in (*Common code for METAHYPS and metahyps_thms*) fun metahyps_split_prem prem = let (*find all vars in the hyps -- should find tvars also!*) val hyps_vars = List.foldr add_term_vars [] (Logic.strip_assums_hyp prem) val insts = map mk_inst hyps_vars (*replace the hyps_vars by Frees*) val prem' = subst_atomic insts prem val (params,hyps,concl) = strip_context prem' in (insts,params,hyps,concl) end; fun metahyps_aux_tac tacf (prem,gno) state = let val (insts,params,hyps,concl) = metahyps_split_prem prem val {thy = sign,maxidx,...} = rep_thm state val cterm = cterm_of sign val chyps = map cterm hyps val hypths = map assume chyps val subprems = map (forall_elim_vars 0) hypths val fparams = map Free params val cparams = map cterm fparams fun swap_ctpair (t,u) = (cterm u, cterm t) (*Subgoal variables: make Free; lift type over params*) fun mk_subgoal_inst concl_vars (var as Var(v,T)) = if member (op =) concl_vars var then (var, true, free_of "METAHYP2_" (v,T)) else (var, false, free_of "METAHYP2_" (v, map #2 params --->T)) (*Instantiate subgoal vars by Free applied to params*) fun mk_ctpair (t,in_concl,u) = if in_concl then (cterm t, cterm u) else (cterm t, cterm (list_comb (u,fparams))) (*Restore Vars with higher type and index*) fun mk_subgoal_swap_ctpair (t as Var((a,i),_), in_concl, u as Free(_,U)) = if in_concl then (cterm u, cterm t) else (cterm u, cterm(Var((a, i+maxidx), U))) (*Embed B in the original context of params and hyps*) fun embed B = list_all_free (params, Logic.list_implies (hyps, B)) (*Strip the context using elimination rules*) fun elim Bhyp = implies_elim_list (forall_elim_list cparams Bhyp) hypths (*A form of lifting that discharges assumptions.*) fun relift st = let val prop = Thm.prop_of st val subgoal_vars = (*Vars introduced in the subgoals*) List.foldr add_term_vars [] (Logic.strip_imp_prems prop) and concl_vars = add_term_vars (Logic.strip_imp_concl prop, []) val subgoal_insts = map (mk_subgoal_inst concl_vars) subgoal_vars val st' = Thm.instantiate ([], map mk_ctpair subgoal_insts) st val emBs = map (cterm o embed) (prems_of st') val Cth = implies_elim_list st' (map (elim o assume) emBs) in (*restore the unknowns to the hypotheses*) free_instantiate (map swap_ctpair insts @ map mk_subgoal_swap_ctpair subgoal_insts) (*discharge assumptions from state in same order*) (implies_intr_list emBs (forall_intr_list cparams (implies_intr_list chyps Cth))) end (*function to replace the current subgoal*) fun next st = bicompose false (false, relift st, nprems_of st) gno state in Seq.maps next (tacf subprems (trivial (cterm concl))) end; end; (*Returns the theorem list that METAHYPS would supply to its tactic*) fun metahyps_thms i state = let val prem = Logic.nth_prem (i, Thm.prop_of state) and cterm = cterm_of (Thm.theory_of_thm state) val (_,_,hyps,_) = metahyps_split_prem prem in SOME (map (forall_elim_vars 0 o assume o cterm) hyps) end handle TERM ("nth_prem", [A]) => NONE; local fun print_vars_terms thy (n,thm) = let fun typed ty = " has type: " ^ Sign.string_of_typ thy ty; fun find_vars thy (Const (c, ty)) = (case Term.typ_tvars ty of [] => I | _ => insert (op =) (c ^ typed ty)) | find_vars thy (Var (xi, ty)) = insert (op =) (Term.string_of_vname xi ^ typed ty) | find_vars _ (Free _) = I | find_vars _ (Bound _) = I | find_vars thy (Abs (_, _, t)) = find_vars thy t | find_vars thy (t1 $ t2) = find_vars thy t1 #> find_vars thy t1; val prem = Logic.nth_prem (n, Thm.prop_of thm) val tms = find_vars thy prem [] in (warning "Found schematic vars in assumptions:"; warning (cat_lines tms)) end; in fun METAHYPS tacf n thm = SUBGOAL (metahyps_aux_tac tacf) n thm handle THM("assume: variables",_,_) => (print_vars_terms (theory_of_thm thm) (n,thm); Seq.empty) end; (*Makes a tactic whose effect on a state is given by thmfun: thm->thm seq.*) fun PRIMSEQ thmfun st = thmfun st handle THM _ => Seq.empty; (*Makes a tactic whose effect on a state is given by thmfun: thm->thm.*) fun PRIMITIVE thmfun = PRIMSEQ (Seq.single o thmfun); (*Inverse (more or less) of PRIMITIVE*) fun SINGLE tacf = Option.map fst o Seq.pull o tacf (*Conversions as tactics*) fun CONVERSION cv i st = Seq.single (Conv.gconv_rule cv i st) handle THM _ => Seq.empty | CTERM _ => Seq.empty | TERM _ => Seq.empty | TYPE _ => Seq.empty; end; open Tactical;