--- a/src/Pure/tctical.ML Fri Jul 24 11:55:34 2009 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,524 +0,0 @@
-(* Title: Pure/tctical.ML
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
-
-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 st =
- (tracing (msg ^ "\n" ^
- Pretty.string_of (Pretty.chunks
- (Display_Goal.pretty_goals_without_context (! Display_Goal.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
- (tracing (Pretty.string_of (Pretty.chunks
- (Display_Goal.pretty_goals_without_context (! Display_Goal.goals_limit) st @
- [Pretty.str "** 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 = Thm.nprems_of st
- val d = np-i (*distance from END*)
- val t = Thm.term_of (Thm.cprem_of st i)
- fun diff st' =
- Thm.nprems_of st' - d <= 0 (*the subgoal no longer exists*)
- orelse
- not (Pattern.aeconv (t, Thm.term_of (Thm.cprem_of st' (Thm.nprems_of st' - d))))
- 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 v = (Var v, free_of "METAHYP1_" v)
-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 = fold Term.add_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 maxidx = Thm.maxidx_of state
- val cterm = Thm.cterm_of (Thm.theory_of_thm state)
- val chyps = map cterm hyps
- val hypths = map assume chyps
- val subprems = map (Thm.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 (v, T) =
- if member (op =) concl_vars (v, T)
- then ((v, T), true, free_of "METAHYP2_" (v, T))
- else ((v, T), false, free_of "METAHYP2_" (v, map #2 params ---> T))
- (*Instantiate subgoal vars by Free applied to params*)
- fun mk_ctpair (v, in_concl, u) =
- if in_concl then (cterm (Var v), cterm u)
- else (cterm (Var v), cterm (list_comb (u, fparams)))
- (*Restore Vars with higher type and index*)
- fun mk_subgoal_swap_ctpair (((a, i), T), in_concl, u as Free (_, U)) =
- if in_concl then (cterm u, cterm (Var ((a, i), 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*)
- fold Term.add_vars (Logic.strip_imp_prems prop) []
- and concl_vars = Term.add_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 = Thm.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 (Thm.forall_elim_vars 0 o Thm.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: " ^ Syntax.string_of_typ_global thy ty;
- fun find_vars thy (Const (c, ty)) =
- if null (Term.add_tvarsT ty []) then I
- else 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;