author | wenzelm |
Thu, 19 Jan 2006 21:22:08 +0100 | |
changeset 18708 | 4b3dadb4fe33 |
parent 18127 | 9f03d8a9a81b |
child 18728 | 6790126ab5f6 |
permissions | -rw-r--r-- |
14620
1be590fd2422
Minor cleanup of headers and some speedup of the HOL4 import.
skalberg
parents:
14518
diff
changeset
|
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(* Title: HOL/Import/shuffler.ML |
14516 | 2 |
ID: $Id$ |
3 |
Author: Sebastian Skalberg, TU Muenchen |
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Package for proving two terms equal by normalizing (hence the |
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"shuffler" name). Uses the simplifier for the normalization. |
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*) |
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signature Shuffler = |
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sig |
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val debug : bool ref |
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val norm_term : theory -> term -> thm |
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val make_equal : theory -> term -> term -> thm option |
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val set_prop : theory -> term -> (string * thm) list -> (string * thm) option |
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val find_potential: theory -> term -> (string * thm) list |
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val gen_shuffle_tac: theory -> bool -> (string * thm) list -> int -> tactic |
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val shuffle_tac: (string * thm) list -> int -> tactic |
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val search_tac : (string * thm) list -> int -> tactic |
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val print_shuffles: theory -> unit |
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val add_shuffle_rule: thm -> theory -> theory |
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val shuffle_attr: theory attribute |
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||
18708 | 29 |
val setup : theory -> theory |
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end |
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structure Shuffler :> Shuffler = |
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struct |
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val debug = ref false |
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fun if_debug f x = if !debug then f x else () |
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val message = if_debug writeln |
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(*Prints exceptions readably to users*) |
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fun print_sign_exn_unit sign e = |
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case e of |
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THM (msg,i,thms) => |
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(writeln ("Exception THM " ^ string_of_int i ^ " raised:\n" ^ msg); |
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15570 | 45 |
List.app print_thm thms) |
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| THEORY (msg,thys) => |
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(writeln ("Exception THEORY raised:\n" ^ msg); |
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16428 | 48 |
List.app (writeln o Context.str_of_thy) thys) |
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| TERM (msg,ts) => |
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(writeln ("Exception TERM raised:\n" ^ msg); |
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15570 | 51 |
List.app (writeln o Sign.string_of_term sign) ts) |
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| TYPE (msg,Ts,ts) => |
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(writeln ("Exception TYPE raised:\n" ^ msg); |
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15570 | 54 |
List.app (writeln o Sign.string_of_typ sign) Ts; |
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List.app (writeln o Sign.string_of_term sign) ts) |
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14516 | 56 |
| e => raise e |
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(*Prints an exception, then fails*) |
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fun print_sign_exn sign e = (print_sign_exn_unit sign e; raise e) |
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val string_of_thm = Library.setmp print_mode [] string_of_thm; |
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val string_of_cterm = Library.setmp print_mode [] string_of_cterm; |
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14516 | 63 |
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fun mk_meta_eq th = |
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(case concl_of th of |
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Const("Trueprop",_) $ (Const("op =",_) $ _ $ _) => th RS eq_reflection |
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| Const("==",_) $ _ $ _ => th |
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| _ => raise THM("Not an equality",0,[th])) |
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handle _ => raise THM("Couldn't make meta equality",0,[th]) |
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fun mk_obj_eq th = |
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(case concl_of th of |
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Const("Trueprop",_) $ (Const("op =",_) $ _ $ _) => th |
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| Const("==",_) $ _ $ _ => th RS meta_eq_to_obj_eq |
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| _ => raise THM("Not an equality",0,[th])) |
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handle _ => raise THM("Couldn't make object equality",0,[th]) |
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structure ShuffleDataArgs: THEORY_DATA_ARGS = |
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struct |
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val name = "HOL/shuffles" |
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type T = thm list |
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val empty = [] |
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val copy = I |
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16428 | 84 |
val extend = I |
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fun merge _ = Library.gen_union Thm.eq_thm |
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fun print sg thms = |
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Pretty.writeln (Pretty.big_list "Shuffle theorems:" |
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(map Display.pretty_thm thms)) |
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end |
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structure ShuffleData = TheoryDataFun(ShuffleDataArgs) |
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val weaken = |
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let |
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val cert = cterm_of (sign_of ProtoPure.thy) |
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val P = Free("P",propT) |
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val Q = Free("Q",propT) |
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val PQ = Logic.mk_implies(P,Q) |
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val PPQ = Logic.mk_implies(P,PQ) |
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val cP = cert P |
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val cQ = cert Q |
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val cPQ = cert PQ |
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val cPPQ = cert PPQ |
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val th1 = assume cPQ |> implies_intr_list [cPQ,cP] |
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val th3 = assume cP |
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val th4 = implies_elim_list (assume cPPQ) [th3,th3] |
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|> implies_intr_list [cPPQ,cP] |
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in |
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equal_intr th4 th1 |> standard |
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end |
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val imp_comm = |
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let |
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val cert = cterm_of (sign_of ProtoPure.thy) |
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val P = Free("P",propT) |
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val Q = Free("Q",propT) |
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val R = Free("R",propT) |
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val PQR = Logic.mk_implies(P,Logic.mk_implies(Q,R)) |
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val QPR = Logic.mk_implies(Q,Logic.mk_implies(P,R)) |
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val cP = cert P |
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val cQ = cert Q |
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val cPQR = cert PQR |
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val cQPR = cert QPR |
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val th1 = implies_elim_list (assume cPQR) [assume cP,assume cQ] |
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|> implies_intr_list [cPQR,cQ,cP] |
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val th2 = implies_elim_list (assume cQPR) [assume cQ,assume cP] |
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|> implies_intr_list [cQPR,cP,cQ] |
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in |
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equal_intr th1 th2 |> standard |
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end |
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val def_norm = |
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let |
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val cert = cterm_of (sign_of ProtoPure.thy) |
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14854 | 135 |
val aT = TFree("'a",[]) |
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val bT = TFree("'b",[]) |
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val v = Free("v",aT) |
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val P = Free("P",aT-->bT) |
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val Q = Free("Q",aT-->bT) |
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val cvPQ = cert (list_all ([("v",aT)],Logic.mk_equals(P $ Bound 0,Q $ Bound 0))) |
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val cPQ = cert (Logic.mk_equals(P,Q)) |
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val cv = cert v |
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val rew = assume cvPQ |
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|> forall_elim cv |
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|> abstract_rule "v" cv |
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val (lhs,rhs) = Logic.dest_equals(concl_of rew) |
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val th1 = transitive (transitive |
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(eta_conversion (cert lhs) |> symmetric) |
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rew) |
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(eta_conversion (cert rhs)) |
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|> implies_intr cvPQ |
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val th2 = combination (assume cPQ) (reflexive cv) |
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|> forall_intr cv |
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|> implies_intr cPQ |
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in |
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equal_intr th1 th2 |> standard |
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end |
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val all_comm = |
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let |
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val cert = cterm_of (sign_of ProtoPure.thy) |
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14854 | 162 |
val xT = TFree("'a",[]) |
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val yT = TFree("'b",[]) |
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14516 | 164 |
val P = Free("P",xT-->yT-->propT) |
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val lhs = all xT $ (Abs("x",xT,all yT $ (Abs("y",yT,P $ Bound 1 $ Bound 0)))) |
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val rhs = all yT $ (Abs("y",yT,all xT $ (Abs("x",xT,P $ Bound 0 $ Bound 1)))) |
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val cl = cert lhs |
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val cr = cert rhs |
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val cx = cert (Free("x",xT)) |
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val cy = cert (Free("y",yT)) |
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val th1 = assume cr |
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|> forall_elim_list [cy,cx] |
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|> forall_intr_list [cx,cy] |
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|> implies_intr cr |
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val th2 = assume cl |
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|> forall_elim_list [cx,cy] |
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|> forall_intr_list [cy,cx] |
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|> implies_intr cl |
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in |
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equal_intr th1 th2 |> standard |
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end |
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val equiv_comm = |
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let |
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val cert = cterm_of (sign_of ProtoPure.thy) |
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val T = TFree("'a",[]) |
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val t = Free("t",T) |
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val u = Free("u",T) |
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val ctu = cert (Logic.mk_equals(t,u)) |
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val cut = cert (Logic.mk_equals(u,t)) |
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val th1 = assume ctu |> symmetric |> implies_intr ctu |
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val th2 = assume cut |> symmetric |> implies_intr cut |
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in |
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equal_intr th1 th2 |> standard |
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end |
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(* This simplification procedure rewrites !!x y. P x y |
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deterministicly, in order for the normalization function, defined |
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below, to handle nested quantifiers robustly *) |
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local |
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exception RESULT of int |
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fun find_bound n (Bound i) = if i = n then raise RESULT 0 |
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else if i = n+1 then raise RESULT 1 |
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else () |
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| find_bound n (t $ u) = (find_bound n t; find_bound n u) |
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| find_bound n (Abs(_,_,t)) = find_bound (n+1) t |
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| find_bound _ _ = () |
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fun swap_bound n (Bound i) = if i = n then Bound (n+1) |
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else if i = n+1 then Bound n |
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else Bound i |
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| swap_bound n (t $ u) = (swap_bound n t $ swap_bound n u) |
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| swap_bound n (Abs(x,xT,t)) = Abs(x,xT,swap_bound (n+1) t) |
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| swap_bound n t = t |
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fun rew_th sg (xv as (x,xT)) (yv as (y,yT)) t = |
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let |
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val lhs = list_all ([xv,yv],t) |
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val rhs = list_all ([yv,xv],swap_bound 0 t) |
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val rew = Logic.mk_equals (lhs,rhs) |
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val init = trivial (cterm_of sg rew) |
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in |
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17959 | 226 |
(all_comm RS init handle e => (message "rew_th"; OldGoals.print_exn e)) |
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end |
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fun quant_rewrite sg assumes (t as Const("all",T1) $ (Abs(x,xT,Const("all",T2) $ Abs(y,yT,body)))) = |
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let |
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val res = (find_bound 0 body;2) handle RESULT i => i |
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in |
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case res of |
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0 => SOME (rew_th sg (x,xT) (y,yT) body) |
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| 1 => if string_ord(y,x) = LESS |
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then |
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let |
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val newt = Const("all",T1) $ (Abs(y,xT,Const("all",T2) $ Abs(x,yT,body))) |
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val t_th = reflexive (cterm_of sg t) |
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val newt_th = reflexive (cterm_of sg newt) |
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in |
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15531 | 242 |
SOME (transitive t_th newt_th) |
14516 | 243 |
end |
15531 | 244 |
else NONE |
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| _ => error "norm_term (quant_rewrite) internal error" |
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end |
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15531 | 247 |
| quant_rewrite _ _ _ = (warning "quant_rewrite: Unknown lhs"; NONE) |
14516 | 248 |
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fun freeze_thaw_term t = |
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let |
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val tvars = term_tvars t |
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val tfree_names = add_term_tfree_names(t,[]) |
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val (type_inst,_) = |
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15570 | 254 |
Library.foldl (fn ((inst,used),(w as (v,_),S)) => |
14516 | 255 |
let |
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val v' = variant used v |
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in |
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((w,TFree(v',S))::inst,v'::used) |
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end) |
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(([],tfree_names),tvars) |
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val t' = subst_TVars type_inst t |
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in |
|
14518
c3019a66180f
Added a number of explicit type casts and delayed evaluations (all seemingly
skalberg
parents:
14516
diff
changeset
|
263 |
(t',map (fn (w,TFree(v,S)) => (v,TVar(w,S)) |
c3019a66180f
Added a number of explicit type casts and delayed evaluations (all seemingly
skalberg
parents:
14516
diff
changeset
|
264 |
| _ => error "Internal error in Shuffler.freeze_thaw") type_inst) |
14516 | 265 |
end |
266 |
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fun inst_tfrees sg [] thm = thm |
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| inst_tfrees sg ((name,U)::rest) thm = |
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let |
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val cU = ctyp_of sg U |
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15794
5de27a5fc5ed
Adapted to new interface of instantiation and unification / matching functions.
berghofe
parents:
15661
diff
changeset
|
271 |
val tfrees = add_term_tfrees (prop_of thm,[]) |
18127 | 272 |
val (rens, thm') = varifyT' |
15794
5de27a5fc5ed
Adapted to new interface of instantiation and unification / matching functions.
berghofe
parents:
15661
diff
changeset
|
273 |
(gen_rem (op = o apfst fst) (tfrees, name)) thm |
14516 | 274 |
val mid = |
275 |
case rens of |
|
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[] => thm' |
|
15794
5de27a5fc5ed
Adapted to new interface of instantiation and unification / matching functions.
berghofe
parents:
15661
diff
changeset
|
277 |
| [((_, S), idx)] => instantiate |
5de27a5fc5ed
Adapted to new interface of instantiation and unification / matching functions.
berghofe
parents:
15661
diff
changeset
|
278 |
([(ctyp_of sg (TVar (idx, S)), cU)], []) thm' |
14516 | 279 |
| _ => error "Shuffler.inst_tfrees internal error" |
280 |
in |
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281 |
inst_tfrees sg rest mid |
|
282 |
end |
|
283 |
||
284 |
fun is_Abs (Abs _) = true |
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| is_Abs _ = false |
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286 |
||
287 |
fun eta_redex (t $ Bound 0) = |
|
288 |
let |
|
289 |
fun free n (Bound i) = i = n |
|
290 |
| free n (t $ u) = free n t orelse free n u |
|
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| free n (Abs(_,_,t)) = free (n+1) t |
|
292 |
| free n _ = false |
|
293 |
in |
|
294 |
not (free 0 t) |
|
295 |
end |
|
296 |
| eta_redex _ = false |
|
297 |
||
298 |
fun eta_contract sg assumes origt = |
|
299 |
let |
|
300 |
val (typet,Tinst) = freeze_thaw_term origt |
|
301 |
val (init,thaw) = freeze_thaw (reflexive (cterm_of sg typet)) |
|
302 |
val final = inst_tfrees sg Tinst o thaw |
|
303 |
val t = #1 (Logic.dest_equals (prop_of init)) |
|
304 |
val _ = |
|
305 |
let |
|
306 |
val lhs = #1 (Logic.dest_equals (prop_of (final init))) |
|
307 |
in |
|
308 |
if not (lhs aconv origt) |
|
15661
9ef583b08647
reverted renaming of Some/None in comments and strings;
wenzelm
parents:
15574
diff
changeset
|
309 |
then (writeln "Something is utterly wrong: (orig,lhs,frozen type,t,tinst)"; |
14516 | 310 |
writeln (string_of_cterm (cterm_of sg origt)); |
311 |
writeln (string_of_cterm (cterm_of sg lhs)); |
|
312 |
writeln (string_of_cterm (cterm_of sg typet)); |
|
313 |
writeln (string_of_cterm (cterm_of sg t)); |
|
314 |
app (fn (n,T) => writeln (n ^ ": " ^ (string_of_ctyp (ctyp_of sg T)))) Tinst; |
|
315 |
writeln "done") |
|
316 |
else () |
|
317 |
end |
|
318 |
in |
|
319 |
case t of |
|
320 |
Const("all",_) $ (Abs(x,xT,Const("==",eqT) $ P $ Q)) => |
|
321 |
((if eta_redex P andalso eta_redex Q |
|
322 |
then |
|
323 |
let |
|
324 |
val cert = cterm_of sg |
|
325 |
val v = Free(variant (add_term_free_names(t,[])) "v",xT) |
|
326 |
val cv = cert v |
|
327 |
val ct = cert t |
|
328 |
val th = (assume ct) |
|
329 |
|> forall_elim cv |
|
330 |
|> abstract_rule x cv |
|
331 |
val ext_th = eta_conversion (cert (Abs(x,xT,P))) |
|
332 |
val th' = transitive (symmetric ext_th) th |
|
333 |
val cu = cert (prop_of th') |
|
334 |
val uth = combination (assume cu) (reflexive cv) |
|
335 |
val uth' = (beta_conversion false (cert (Abs(x,xT,Q) $ v))) |
|
336 |
|> transitive uth |
|
337 |
|> forall_intr cv |
|
338 |
|> implies_intr cu |
|
339 |
val rew_th = equal_intr (th' |> implies_intr ct) uth' |
|
340 |
val res = final rew_th |
|
341 |
val lhs = (#1 (Logic.dest_equals (prop_of res))) |
|
342 |
in |
|
15531 | 343 |
SOME res |
14516 | 344 |
end |
15531 | 345 |
else NONE) |
17959 | 346 |
handle e => OldGoals.print_exn e) |
17440
df77edc4f5d0
fixed HOL-light/Isabelle syntax incompatability via more protect_xxx functions
obua
parents:
17188
diff
changeset
|
347 |
| _ => NONE |
df77edc4f5d0
fixed HOL-light/Isabelle syntax incompatability via more protect_xxx functions
obua
parents:
17188
diff
changeset
|
348 |
end |
14516 | 349 |
|
350 |
fun beta_fun sg assume t = |
|
15531 | 351 |
SOME (beta_conversion true (cterm_of sg t)) |
14516 | 352 |
|
17188 | 353 |
val meta_sym_rew = thm "refl" |
354 |
||
355 |
fun equals_fun sg assume t = |
|
356 |
case t of |
|
357 |
Const("op ==",_) $ u $ v => if Term.term_ord (u,v) = LESS then SOME (meta_sym_rew) else NONE |
|
358 |
| _ => NONE |
|
359 |
||
14516 | 360 |
fun eta_expand sg assumes origt = |
361 |
let |
|
362 |
val (typet,Tinst) = freeze_thaw_term origt |
|
363 |
val (init,thaw) = freeze_thaw (reflexive (cterm_of sg typet)) |
|
364 |
val final = inst_tfrees sg Tinst o thaw |
|
365 |
val t = #1 (Logic.dest_equals (prop_of init)) |
|
366 |
val _ = |
|
367 |
let |
|
368 |
val lhs = #1 (Logic.dest_equals (prop_of (final init))) |
|
369 |
in |
|
370 |
if not (lhs aconv origt) |
|
15661
9ef583b08647
reverted renaming of Some/None in comments and strings;
wenzelm
parents:
15574
diff
changeset
|
371 |
then (writeln "Something is utterly wrong: (orig,lhs,frozen type,t,tinst)"; |
14516 | 372 |
writeln (string_of_cterm (cterm_of sg origt)); |
373 |
writeln (string_of_cterm (cterm_of sg lhs)); |
|
374 |
writeln (string_of_cterm (cterm_of sg typet)); |
|
375 |
writeln (string_of_cterm (cterm_of sg t)); |
|
376 |
app (fn (n,T) => writeln (n ^ ": " ^ (string_of_ctyp (ctyp_of sg T)))) Tinst; |
|
377 |
writeln "done") |
|
378 |
else () |
|
379 |
end |
|
380 |
in |
|
381 |
case t of |
|
382 |
Const("==",T) $ P $ Q => |
|
383 |
if is_Abs P orelse is_Abs Q |
|
384 |
then (case domain_type T of |
|
385 |
Type("fun",[aT,bT]) => |
|
386 |
let |
|
387 |
val cert = cterm_of sg |
|
388 |
val vname = variant (add_term_free_names(t,[])) "v" |
|
389 |
val v = Free(vname,aT) |
|
390 |
val cv = cert v |
|
391 |
val ct = cert t |
|
392 |
val th1 = (combination (assume ct) (reflexive cv)) |
|
393 |
|> forall_intr cv |
|
394 |
|> implies_intr ct |
|
395 |
val concl = cert (concl_of th1) |
|
396 |
val th2 = (assume concl) |
|
397 |
|> forall_elim cv |
|
398 |
|> abstract_rule vname cv |
|
399 |
val (lhs,rhs) = Logic.dest_equals (prop_of th2) |
|
400 |
val elhs = eta_conversion (cert lhs) |
|
401 |
val erhs = eta_conversion (cert rhs) |
|
402 |
val th2' = transitive |
|
403 |
(transitive (symmetric elhs) th2) |
|
404 |
erhs |
|
405 |
val res = equal_intr th1 (th2' |> implies_intr concl) |
|
406 |
val res' = final res |
|
407 |
in |
|
15531 | 408 |
SOME res' |
14516 | 409 |
end |
15531 | 410 |
| _ => NONE) |
411 |
else NONE |
|
412 |
| _ => (error ("Bad eta_expand argument" ^ (string_of_cterm (cterm_of sg t))); NONE) |
|
14516 | 413 |
end |
17959 | 414 |
handle e => (writeln "eta_expand internal error"; OldGoals.print_exn e) |
14516 | 415 |
|
14854 | 416 |
fun mk_tfree s = TFree("'"^s,[]) |
14516 | 417 |
val xT = mk_tfree "a" |
418 |
val yT = mk_tfree "b" |
|
419 |
val P = Var(("P",0),xT-->yT-->propT) |
|
420 |
val Q = Var(("Q",0),xT-->yT) |
|
421 |
val R = Var(("R",0),xT-->yT) |
|
422 |
val S = Var(("S",0),xT) |
|
17188 | 423 |
val S' = Var(("S'",0),xT) |
14516 | 424 |
in |
425 |
fun beta_simproc sg = Simplifier.simproc_i |
|
426 |
sg |
|
427 |
"Beta-contraction" |
|
428 |
[Abs("x",xT,Q) $ S] |
|
429 |
beta_fun |
|
430 |
||
17188 | 431 |
fun equals_simproc sg = Simplifier.simproc_i |
432 |
sg |
|
433 |
"Ordered rewriting of meta equalities" |
|
434 |
[Const("op ==",xT) $ S $ S'] |
|
435 |
equals_fun |
|
436 |
||
14516 | 437 |
fun quant_simproc sg = Simplifier.simproc_i |
438 |
sg |
|
439 |
"Ordered rewriting of nested quantifiers" |
|
440 |
[all xT $ (Abs("x",xT,all yT $ (Abs("y",yT,P $ Bound 1 $ Bound 0))))] |
|
441 |
quant_rewrite |
|
442 |
fun eta_expand_simproc sg = Simplifier.simproc_i |
|
443 |
sg |
|
444 |
"Smart eta-expansion by equivalences" |
|
445 |
[Logic.mk_equals(Q,R)] |
|
446 |
eta_expand |
|
447 |
fun eta_contract_simproc sg = Simplifier.simproc_i |
|
448 |
sg |
|
449 |
"Smart handling of eta-contractions" |
|
450 |
[all xT $ (Abs("x",xT,Logic.mk_equals(Q $ Bound 0,R $ Bound 0)))] |
|
451 |
eta_contract |
|
452 |
end |
|
453 |
||
454 |
(* Disambiguates the names of bound variables in a term, returning t |
|
455 |
== t' where all the names of bound variables in t' are unique *) |
|
456 |
||
457 |
fun disamb_bound sg t = |
|
458 |
let |
|
459 |
||
460 |
fun F (t $ u,idx) = |
|
461 |
let |
|
462 |
val (t',idx') = F (t,idx) |
|
463 |
val (u',idx'') = F (u,idx') |
|
464 |
in |
|
465 |
(t' $ u',idx'') |
|
466 |
end |
|
467 |
| F (Abs(x,xT,t),idx) = |
|
468 |
let |
|
469 |
val x' = "x" ^ (LargeInt.toString idx) (* amazing *) |
|
470 |
val (t',idx') = F (t,idx+1) |
|
471 |
in |
|
472 |
(Abs(x',xT,t'),idx') |
|
473 |
end |
|
474 |
| F arg = arg |
|
475 |
val (t',_) = F (t,0) |
|
476 |
val ct = cterm_of sg t |
|
477 |
val ct' = cterm_of sg t' |
|
478 |
val res = transitive (reflexive ct) (reflexive ct') |
|
479 |
val _ = message ("disamb_term: " ^ (string_of_thm res)) |
|
480 |
in |
|
481 |
res |
|
482 |
end |
|
483 |
||
484 |
(* Transforms a term t to some normal form t', returning the theorem t |
|
485 |
== t'. This is originally a help function for make_equal, but might |
|
486 |
be handy in its own right, for example for indexing terms. *) |
|
487 |
||
488 |
fun norm_term thy t = |
|
489 |
let |
|
490 |
val sg = sign_of thy |
|
491 |
||
492 |
val norms = ShuffleData.get thy |
|
17892 | 493 |
val ss = Simplifier.theory_context thy empty_ss |
494 |
setmksimps single |
|
495 |
addsimps (map (Thm.transfer sg) norms) |
|
14516 | 496 |
fun chain f th = |
497 |
let |
|
17440
df77edc4f5d0
fixed HOL-light/Isabelle syntax incompatability via more protect_xxx functions
obua
parents:
17188
diff
changeset
|
498 |
val rhs = snd (dest_equals (cprop_of th)) |
df77edc4f5d0
fixed HOL-light/Isabelle syntax incompatability via more protect_xxx functions
obua
parents:
17188
diff
changeset
|
499 |
in |
14516 | 500 |
transitive th (f rhs) |
501 |
end |
|
502 |
||
503 |
val th = |
|
504 |
t |> disamb_bound sg |
|
505 |
|> chain (Simplifier.full_rewrite |
|
506 |
(ss addsimprocs [quant_simproc sg,eta_expand_simproc sg,eta_contract_simproc sg])) |
|
507 |
|> chain eta_conversion |
|
508 |
|> strip_shyps |
|
509 |
val _ = message ("norm_term: " ^ (string_of_thm th)) |
|
510 |
in |
|
511 |
th |
|
17463 | 512 |
end |
14516 | 513 |
handle e => (writeln "norm_term internal error"; print_sign_exn (sign_of thy) e) |
514 |
||
515 |
||
516 |
(* Closes a theorem with respect to free and schematic variables (does |
|
517 |
not touch type variables, though). *) |
|
518 |
||
519 |
fun close_thm th = |
|
520 |
let |
|
521 |
val sg = sign_of_thm th |
|
522 |
val c = prop_of th |
|
14854 | 523 |
val vars = add_term_frees (c,add_term_vars(c,[])) |
14516 | 524 |
in |
14854 | 525 |
Drule.forall_intr_list (map (cterm_of sg) vars) th |
14516 | 526 |
end |
17959 | 527 |
handle e => (writeln "close_thm internal error"; OldGoals.print_exn e) |
14516 | 528 |
|
529 |
(* Normalizes a theorem's conclusion using norm_term. *) |
|
530 |
||
531 |
fun norm_thm thy th = |
|
532 |
let |
|
533 |
val c = prop_of th |
|
534 |
in |
|
535 |
equal_elim (norm_term thy c) th |
|
536 |
end |
|
537 |
||
538 |
(* make_equal sg t u tries to construct the theorem t == u under the |
|
15531 | 539 |
signature sg. If it succeeds, SOME (t == u) is returned, otherwise |
540 |
NONE is returned. *) |
|
14516 | 541 |
|
542 |
fun make_equal sg t u = |
|
543 |
let |
|
544 |
val t_is_t' = norm_term sg t |
|
545 |
val u_is_u' = norm_term sg u |
|
546 |
val th = transitive t_is_t' (symmetric u_is_u') |
|
15531 | 547 |
val _ = message ("make_equal: SOME " ^ (string_of_thm th)) |
14516 | 548 |
in |
15531 | 549 |
SOME th |
14516 | 550 |
end |
15531 | 551 |
handle e as THM _ => (message "make_equal: NONE";NONE) |
14516 | 552 |
|
553 |
fun match_consts ignore t (* th *) = |
|
554 |
let |
|
555 |
fun add_consts (Const (c, _), cs) = |
|
556 |
if c mem_string ignore |
|
557 |
then cs |
|
558 |
else c ins_string cs |
|
559 |
| add_consts (t $ u, cs) = add_consts (t, add_consts (u, cs)) |
|
560 |
| add_consts (Abs (_, _, t), cs) = add_consts (t, cs) |
|
561 |
| add_consts (_, cs) = cs |
|
562 |
val t_consts = add_consts(t,[]) |
|
563 |
in |
|
564 |
fn (name,th) => |
|
565 |
let |
|
566 |
val th_consts = add_consts(prop_of th,[]) |
|
567 |
in |
|
568 |
eq_set(t_consts,th_consts) |
|
569 |
end |
|
570 |
end |
|
571 |
||
572 |
val collect_ignored = |
|
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
573 |
foldr (fn (thm,cs) => |
14516 | 574 |
let |
575 |
val (lhs,rhs) = Logic.dest_equals (prop_of thm) |
|
576 |
val ignore_lhs = term_consts lhs \\ term_consts rhs |
|
577 |
val ignore_rhs = term_consts rhs \\ term_consts lhs |
|
578 |
in |
|
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
579 |
foldr (op ins_string) cs (ignore_lhs @ ignore_rhs) |
14516 | 580 |
end) |
581 |
||
582 |
(* set_prop t thms tries to make a theorem with the proposition t from |
|
583 |
one of the theorems thms, by shuffling the propositions around. If it |
|
15531 | 584 |
succeeds, SOME theorem is returned, otherwise NONE. *) |
14516 | 585 |
|
586 |
fun set_prop thy t = |
|
587 |
let |
|
588 |
val sg = sign_of thy |
|
14854 | 589 |
val vars = add_term_frees (t,add_term_vars (t,[])) |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
590 |
val closed_t = foldr (fn (v,body) => let val vT = type_of v |
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
591 |
in all vT $ (Abs("x",vT,abstract_over(v,body))) end) t vars |
14516 | 592 |
val rew_th = norm_term thy closed_t |
593 |
val rhs = snd (dest_equals (cprop_of rew_th)) |
|
594 |
||
595 |
val shuffles = ShuffleData.get thy |
|
15531 | 596 |
fun process [] = NONE |
14516 | 597 |
| process ((name,th)::thms) = |
598 |
let |
|
16428 | 599 |
val norm_th = varifyT (norm_thm thy (close_thm (Thm.transfer sg th))) |
14516 | 600 |
val triv_th = trivial rhs |
601 |
val _ = message ("Shuffler.set_prop: Gluing together " ^ (string_of_thm norm_th) ^ " and " ^ (string_of_thm triv_th)) |
|
17188 | 602 |
val mod_th = case Seq.pull (bicompose false (*true*) (false,norm_th,0) 1 triv_th) of |
15531 | 603 |
SOME(th,_) => SOME th |
604 |
| NONE => NONE |
|
14516 | 605 |
in |
606 |
case mod_th of |
|
15531 | 607 |
SOME mod_th => |
14516 | 608 |
let |
609 |
val closed_th = equal_elim (symmetric rew_th) mod_th |
|
610 |
in |
|
611 |
message ("Shuffler.set_prop succeeded by " ^ name); |
|
15531 | 612 |
SOME (name,forall_elim_list (map (cterm_of sg) vars) closed_th) |
14516 | 613 |
end |
15531 | 614 |
| NONE => process thms |
14516 | 615 |
end |
616 |
handle e as THM _ => process thms |
|
617 |
in |
|
618 |
fn thms => |
|
619 |
case process thms of |
|
15531 | 620 |
res as SOME (name,th) => if (prop_of th) aconv t |
14516 | 621 |
then res |
622 |
else error "Internal error in set_prop" |
|
15531 | 623 |
| NONE => NONE |
14516 | 624 |
end |
17959 | 625 |
handle e => (writeln "set_prop internal error"; OldGoals.print_exn e) |
14516 | 626 |
|
627 |
fun find_potential thy t = |
|
628 |
let |
|
629 |
val shuffles = ShuffleData.get thy |
|
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
630 |
val ignored = collect_ignored [] shuffles |
14516 | 631 |
val rel_consts = term_consts t \\ ignored |
632 |
val pot_thms = PureThy.thms_containing_consts thy rel_consts |
|
633 |
in |
|
15570 | 634 |
List.filter (match_consts ignored t) pot_thms |
14516 | 635 |
end |
636 |
||
637 |
fun gen_shuffle_tac thy search thms i st = |
|
638 |
let |
|
639 |
val _ = message ("Shuffling " ^ (string_of_thm st)) |
|
15570 | 640 |
val t = List.nth(prems_of st,i-1) |
14516 | 641 |
val set = set_prop thy t |
642 |
fun process_tac thms st = |
|
643 |
case set thms of |
|
15531 | 644 |
SOME (_,th) => Seq.of_list (compose (th,i,st)) |
645 |
| NONE => Seq.empty |
|
14516 | 646 |
in |
647 |
(process_tac thms APPEND (if search |
|
648 |
then process_tac (find_potential thy t) |
|
649 |
else no_tac)) st |
|
650 |
end |
|
651 |
||
652 |
fun shuffle_tac thms i st = |
|
653 |
gen_shuffle_tac (the_context()) false thms i st |
|
654 |
||
655 |
fun search_tac thms i st = |
|
656 |
gen_shuffle_tac (the_context()) true thms i st |
|
657 |
||
658 |
fun shuffle_meth (thms:thm list) ctxt = |
|
659 |
let |
|
660 |
val thy = ProofContext.theory_of ctxt |
|
661 |
in |
|
662 |
Method.SIMPLE_METHOD' HEADGOAL (gen_shuffle_tac thy false (map (pair "") thms)) |
|
663 |
end |
|
664 |
||
665 |
fun search_meth ctxt = |
|
666 |
let |
|
667 |
val thy = ProofContext.theory_of ctxt |
|
668 |
val prems = ProofContext.prems_of ctxt |
|
669 |
in |
|
670 |
Method.SIMPLE_METHOD' HEADGOAL (gen_shuffle_tac thy true (map (pair "premise") prems)) |
|
671 |
end |
|
672 |
||
673 |
val print_shuffles = ShuffleData.print |
|
674 |
||
675 |
fun add_shuffle_rule thm thy = |
|
676 |
let |
|
677 |
val shuffles = ShuffleData.get thy |
|
678 |
in |
|
679 |
if exists (curry Thm.eq_thm thm) shuffles |
|
680 |
then (warning ((string_of_thm thm) ^ " already known to the shuffler"); |
|
681 |
thy) |
|
682 |
else ShuffleData.put (thm::shuffles) thy |
|
683 |
end |
|
684 |
||
685 |
fun shuffle_attr (thy,thm) = (add_shuffle_rule thm thy,thm) |
|
686 |
||
18708 | 687 |
val setup = |
688 |
Method.add_method ("shuffle_tac",Method.thms_ctxt_args shuffle_meth,"solve goal by shuffling terms around") #> |
|
689 |
Method.add_method ("search_tac",Method.ctxt_args search_meth,"search for suitable theorems") #> |
|
690 |
ShuffleData.init #> |
|
691 |
add_shuffle_rule weaken #> |
|
692 |
add_shuffle_rule equiv_comm #> |
|
693 |
add_shuffle_rule imp_comm #> |
|
694 |
add_shuffle_rule Drule.norm_hhf_eq #> |
|
695 |
add_shuffle_rule Drule.triv_forall_equality #> |
|
696 |
Attrib.add_attributes [("shuffle_rule", (Attrib.no_args shuffle_attr,K Attrib.undef_local_attribute),"tell the shuffler about the theorem")] |
|
697 |
||
14516 | 698 |
end |