author | haftmann |
Thu, 22 Oct 2009 13:48:06 +0200 | |
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parent 33050 | fe166e8b9f07 |
child 33955 | fff6f11b1f09 |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/Groebner_Basis/groebner.ML |
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Author: Amine Chaieb, TU Muenchen |
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*) |
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signature GROEBNER = |
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sig |
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val ring_and_ideal_conv : |
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{idom: thm list, ring: cterm list * thm list, field: cterm list * thm list, |
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vars: cterm list, semiring: cterm list * thm list, ideal : thm list} -> |
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(cterm -> Rat.rat) -> (Rat.rat -> cterm) -> |
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conv -> conv -> |
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{ring_conv : conv, |
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simple_ideal: (cterm list -> cterm -> (cterm * cterm -> order) -> cterm list), |
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multi_ideal: cterm list -> cterm list -> cterm list -> (cterm * cterm) list, |
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poly_eq_ss: simpset, unwind_conv : conv} |
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val ring_tac: thm list -> thm list -> Proof.context -> int -> tactic |
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val ideal_tac: thm list -> thm list -> Proof.context -> int -> tactic |
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val algebra_tac: thm list -> thm list -> Proof.context -> int -> tactic |
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end |
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structure Groebner : GROEBNER = |
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struct |
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open Conv Normalizer Drule Thm; |
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fun is_comb ct = |
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(case Thm.term_of ct of |
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_ $ _ => true |
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| _ => false); |
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val concl = Thm.cprop_of #> Thm.dest_arg; |
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fun is_binop ct ct' = |
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(case Thm.term_of ct' of |
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c $ _ $ _ => term_of ct aconv c |
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| _ => false); |
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fun dest_binary ct ct' = |
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if is_binop ct ct' then Thm.dest_binop ct' |
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else raise CTERM ("dest_binary: bad binop", [ct, ct']) |
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fun inst_thm inst = Thm.instantiate ([], inst); |
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val rat_0 = Rat.zero; |
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val rat_1 = Rat.one; |
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val minus_rat = Rat.neg; |
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val denominator_rat = Rat.quotient_of_rat #> snd #> Rat.rat_of_int; |
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fun int_of_rat a = |
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case Rat.quotient_of_rat a of (i,1) => i | _ => error "int_of_rat: not an int"; |
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val lcm_rat = fn x => fn y => Rat.rat_of_int (Integer.lcm (int_of_rat x) (int_of_rat y)); |
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val (eqF_intr, eqF_elim) = |
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let val [th1,th2] = thms "PFalse" |
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in (fn th => th COMP th2, fn th => th COMP th1) end; |
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val (PFalse, PFalse') = |
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let val PFalse_eq = nth (thms "simp_thms") 13 |
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in (PFalse_eq RS iffD1, PFalse_eq RS iffD2) end; |
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(* Type for recording history, i.e. how a polynomial was obtained. *) |
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datatype history = |
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Start of int |
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| Mmul of (Rat.rat * int list) * history |
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| Add of history * history; |
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(* Monomial ordering. *) |
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fun morder_lt m1 m2= |
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let fun lexorder l1 l2 = |
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case (l1,l2) of |
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([],[]) => false |
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| (x1::o1,x2::o2) => x1 > x2 orelse x1 = x2 andalso lexorder o1 o2 |
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| _ => error "morder: inconsistent monomial lengths" |
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val n1 = Integer.sum m1 |
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val n2 = Integer.sum m2 in |
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n1 < n2 orelse n1 = n2 andalso lexorder m1 m2 |
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end; |
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fun morder_le m1 m2 = morder_lt m1 m2 orelse (m1 = m2); |
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fun morder_gt m1 m2 = morder_lt m2 m1; |
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(* Arithmetic on canonical polynomials. *) |
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fun grob_neg l = map (fn (c,m) => (minus_rat c,m)) l; |
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fun grob_add l1 l2 = |
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case (l1,l2) of |
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([],l2) => l2 |
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| (l1,[]) => l1 |
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| ((c1,m1)::o1,(c2,m2)::o2) => |
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if m1 = m2 then |
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let val c = c1+/c2 val rest = grob_add o1 o2 in |
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if c =/ rat_0 then rest else (c,m1)::rest end |
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else if morder_lt m2 m1 then (c1,m1)::(grob_add o1 l2) |
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else (c2,m2)::(grob_add l1 o2); |
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fun grob_sub l1 l2 = grob_add l1 (grob_neg l2); |
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fun grob_mmul (c1,m1) (c2,m2) = (c1*/c2, ListPair.map (op +) (m1, m2)); |
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fun grob_cmul cm pol = map (grob_mmul cm) pol; |
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fun grob_mul l1 l2 = |
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case l1 of |
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[] => [] |
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| (h1::t1) => grob_add (grob_cmul h1 l2) (grob_mul t1 l2); |
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fun grob_inv l = |
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case l of |
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[(c,vs)] => if (forall (fn x => x = 0) vs) then |
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if (c =/ rat_0) then error "grob_inv: division by zero" |
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else [(rat_1 // c,vs)] |
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else error "grob_inv: non-constant divisor polynomial" |
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| _ => error "grob_inv: non-constant divisor polynomial"; |
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fun grob_div l1 l2 = |
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case l2 of |
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[(c,l)] => if (forall (fn x => x = 0) l) then |
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if c =/ rat_0 then error "grob_div: division by zero" |
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else grob_cmul (rat_1 // c,l) l1 |
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else error "grob_div: non-constant divisor polynomial" |
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| _ => error "grob_div: non-constant divisor polynomial"; |
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fun grob_pow vars l n = |
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if n < 0 then error "grob_pow: negative power" |
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else if n = 0 then [(rat_1,map (fn v => 0) vars)] |
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else grob_mul l (grob_pow vars l (n - 1)); |
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fun degree vn p = |
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case p of |
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[] => error "Zero polynomial" |
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| [(c,ns)] => nth ns vn |
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| (c,ns)::p' => Int.max (nth ns vn, degree vn p'); |
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fun head_deg vn p = let val d = degree vn p in |
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(d,fold (fn (c,r) => fn q => grob_add q [(c, map_index (fn (i,n) => if i = vn then 0 else n) r)]) (filter (fn (c,ns) => c <>/ rat_0 andalso nth ns vn = d) p) []) end; |
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val is_zerop = forall (fn (c,ns) => c =/ rat_0 andalso forall (curry (op =) 0) ns); |
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val grob_pdiv = |
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let fun pdiv_aux vn (n,a) p k s = |
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if is_zerop s then (k,s) else |
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let val (m,b) = head_deg vn s |
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in if m < n then (k,s) else |
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let val p' = grob_mul p [(rat_1, map_index (fn (i,v) => if i = vn then m - n else 0) |
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(snd (hd s)))] |
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in if a = b then pdiv_aux vn (n,a) p k (grob_sub s p') |
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else pdiv_aux vn (n,a) p (k + 1) (grob_sub (grob_mul a s) (grob_mul b p')) |
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end |
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end |
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in fn vn => fn s => fn p => pdiv_aux vn (head_deg vn p) p 0 s |
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end; |
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(* Monomial division operation. *) |
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fun mdiv (c1,m1) (c2,m2) = |
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(c1//c2, |
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map2 (fn n1 => fn n2 => if n1 < n2 then error "mdiv" else n1 - n2) m1 m2); |
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(* Lowest common multiple of two monomials. *) |
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fun mlcm (c1,m1) (c2,m2) = (rat_1, ListPair.map Int.max (m1, m2)); |
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(* Reduce monomial cm by polynomial pol, returning replacement for cm. *) |
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fun reduce1 cm (pol,hpol) = |
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case pol of |
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[] => error "reduce1" |
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| cm1::cms => ((let val (c,m) = mdiv cm cm1 in |
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(grob_cmul (minus_rat c,m) cms, |
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Mmul((minus_rat c,m),hpol)) end) |
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handle ERROR _ => error "reduce1"); |
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(* Try this for all polynomials in a basis. *) |
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fun tryfind f l = |
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case l of |
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[] => error "tryfind" |
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| (h::t) => ((f h) handle ERROR _ => tryfind f t); |
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fun reduceb cm basis = tryfind (fn p => reduce1 cm p) basis; |
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(* Reduction of a polynomial (always picking largest monomial possible). *) |
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fun reduce basis (pol,hist) = |
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case pol of |
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[] => (pol,hist) |
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| cm::ptl => ((let val (q,hnew) = reduceb cm basis in |
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reduce basis (grob_add q ptl,Add(hnew,hist)) end) |
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handle (ERROR _) => |
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(let val (q,hist') = reduce basis (ptl,hist) in |
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(cm::q,hist') end)); |
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(* Check for orthogonality w.r.t. LCM. *) |
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fun orthogonal l p1 p2 = |
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snd l = snd(grob_mmul (hd p1) (hd p2)); |
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(* Compute S-polynomial of two polynomials. *) |
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fun spoly cm ph1 ph2 = |
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case (ph1,ph2) of |
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(([],h),p) => ([],h) |
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| (p,([],h)) => ([],h) |
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| ((cm1::ptl1,his1),(cm2::ptl2,his2)) => |
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(grob_sub (grob_cmul (mdiv cm cm1) ptl1) |
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(grob_cmul (mdiv cm cm2) ptl2), |
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Add(Mmul(mdiv cm cm1,his1), |
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Mmul(mdiv (minus_rat(fst cm),snd cm) cm2,his2))); |
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(* Make a polynomial monic. *) |
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fun monic (pol,hist) = |
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if null pol then (pol,hist) else |
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let val (c',m') = hd pol in |
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(map (fn (c,m) => (c//c',m)) pol, |
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Mmul((rat_1 // c',map (K 0) m'),hist)) end; |
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(* The most popular heuristic is to order critical pairs by LCM monomial. *) |
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fun forder ((c1,m1),_) ((c2,m2),_) = morder_lt m1 m2; |
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fun poly_lt p q = |
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case (p,q) of |
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(p,[]) => false |
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| ([],q) => true |
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| ((c1,m1)::o1,(c2,m2)::o2) => |
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c1 </ c2 orelse |
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c1 =/ c2 andalso ((morder_lt m1 m2) orelse m1 = m2 andalso poly_lt o1 o2); |
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fun align ((p,hp),(q,hq)) = |
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if poly_lt p q then ((p,hp),(q,hq)) else ((q,hq),(p,hp)); |
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fun forall2 p l1 l2 = |
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case (l1,l2) of |
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([],[]) => true |
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| (h1::t1,h2::t2) => p h1 h2 andalso forall2 p t1 t2 |
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| _ => false; |
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fun poly_eq p1 p2 = |
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forall2 (fn (c1,m1) => fn (c2,m2) => c1 =/ c2 andalso (m1: int list) = m2) p1 p2; |
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fun memx ((p1,h1),(p2,h2)) ppairs = |
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not (exists (fn ((q1,_),(q2,_)) => poly_eq p1 q1 andalso poly_eq p2 q2) ppairs); |
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(* Buchberger's second criterion. *) |
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fun criterion2 basis (lcm,((p1,h1),(p2,h2))) opairs = |
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exists (fn g => not(poly_eq (fst g) p1) andalso not(poly_eq (fst g) p2) andalso |
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can (mdiv lcm) (hd(fst g)) andalso |
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not(memx (align (g,(p1,h1))) (map snd opairs)) andalso |
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not(memx (align (g,(p2,h2))) (map snd opairs))) basis; |
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(* Test for hitting constant polynomial. *) |
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fun constant_poly p = |
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length p = 1 andalso forall (fn x => x = 0) (snd(hd p)); |
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(* Grobner basis algorithm. *) |
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(* FIXME: try to get rid of mergesort? *) |
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fun merge ord l1 l2 = |
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case l1 of |
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[] => l2 |
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| h1::t1 => |
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case l2 of |
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[] => l1 |
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| h2::t2 => if ord h1 h2 then h1::(merge ord t1 l2) |
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else h2::(merge ord l1 t2); |
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fun mergesort ord l = |
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let |
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fun mergepairs l1 l2 = |
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case (l1,l2) of |
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([s],[]) => s |
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| (l,[]) => mergepairs [] l |
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| (l,[s1]) => mergepairs (s1::l) [] |
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| (l,(s1::s2::ss)) => mergepairs ((merge ord s1 s2)::l) ss |
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in if null l then [] else mergepairs [] (map (fn x => [x]) l) |
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end; |
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fun grobner_basis basis pairs = |
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case pairs of |
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[] => basis |
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| (l,(p1,p2))::opairs => |
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let val (sph as (sp,hist)) = monic (reduce basis (spoly l p1 p2)) |
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in |
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if null sp orelse criterion2 basis (l,(p1,p2)) opairs |
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then grobner_basis basis opairs |
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else if constant_poly sp then grobner_basis (sph::basis) [] |
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else |
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let |
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val rawcps = map (fn p => (mlcm (hd(fst p)) (hd sp),align(p,sph))) |
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basis |
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val newcps = filter (fn (l,(p,q)) => not(orthogonal l (fst p) (fst q))) |
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rawcps |
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in grobner_basis (sph::basis) |
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(merge forder opairs (mergesort forder newcps)) |
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end |
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end; |
23252 | 302 |
|
303 |
(* Interreduce initial polynomials. *) |
|
304 |
||
305 |
fun grobner_interreduce rpols ipols = |
|
306 |
case ipols of |
|
307 |
[] => map monic (rev rpols) |
|
308 |
| p::ps => let val p' = reduce (rpols @ ps) p in |
|
23579 | 309 |
if null (fst p') then grobner_interreduce rpols ps |
23252 | 310 |
else grobner_interreduce (p'::rpols) ps end; |
311 |
||
312 |
(* Overall function. *) |
|
313 |
||
314 |
fun grobner pols = |
|
33063 | 315 |
let val npols = map_index (fn (n, p) => (p, Start n)) pols |
23579 | 316 |
val phists = filter (fn (p,_) => not (null p)) npols |
23252 | 317 |
val bas = grobner_interreduce [] (map monic phists) |
25538 | 318 |
val prs0 = map_product pair bas bas |
23252 | 319 |
val prs1 = filter (fn ((x,_),(y,_)) => poly_lt x y) prs0 |
320 |
val prs2 = map (fn (p,q) => (mlcm (hd(fst p)) (hd(fst q)),(p,q))) prs1 |
|
321 |
val prs3 = |
|
322 |
filter (fn (l,(p,q)) => not(orthogonal l (fst p) (fst q))) prs2 in |
|
323 |
grobner_basis bas (mergesort forder prs3) end; |
|
324 |
||
325 |
(* Get proof of contradiction from Grobner basis. *) |
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|
23252 | 327 |
fun find p l = |
328 |
case l of |
|
329 |
[] => error "find" |
|
330 |
| (h::t) => if p(h) then h else find p t; |
|
331 |
||
332 |
fun grobner_refute pols = |
|
333 |
let val gb = grobner pols in |
|
334 |
snd(find (fn (p,h) => length p = 1 andalso forall (fn x=> x=0) (snd(hd p))) gb) |
|
335 |
end; |
|
336 |
||
337 |
(* Turn proof into a certificate as sum of multipliers. *) |
|
338 |
(* In principle this is very inefficient: in a heavily shared proof it may *) |
|
339 |
(* make the same calculation many times. Could put in a cache or something. *) |
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340 |
|
23252 | 341 |
fun resolve_proof vars prf = |
342 |
case prf of |
|
343 |
Start(~1) => [] |
|
344 |
| Start m => [(m,[(rat_1,map (K 0) vars)])] |
|
345 |
| Mmul(pol,lin) => |
|
346 |
let val lis = resolve_proof vars lin in |
|
347 |
map (fn (n,p) => (n,grob_cmul pol p)) lis end |
|
348 |
| Add(lin1,lin2) => |
|
349 |
let val lis1 = resolve_proof vars lin1 |
|
350 |
val lis2 = resolve_proof vars lin2 |
|
33042 | 351 |
val dom = distinct (op =) (union (op =) (map fst lis1) (map fst lis2)) |
23252 | 352 |
in |
23557 | 353 |
map (fn n => let val a = these (AList.lookup (op =) lis1 n) |
354 |
val b = these (AList.lookup (op =) lis2 n) |
|
355 |
in (n,grob_add a b) end) dom end; |
|
23252 | 356 |
|
357 |
(* Run the procedure and produce Weak Nullstellensatz certificate. *) |
|
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358 |
|
23252 | 359 |
fun grobner_weak vars pols = |
360 |
let val cert = resolve_proof vars (grobner_refute pols) |
|
361 |
val l = |
|
362 |
fold_rev (fold_rev (lcm_rat o denominator_rat o fst) o snd) cert (rat_1) in |
|
363 |
(l,map (fn (i,p) => (i,map (fn (d,m) => (l*/d,m)) p)) cert) end; |
|
364 |
||
365 |
(* Prove a polynomial is in ideal generated by others, using Grobner basis. *) |
|
366 |
||
367 |
fun grobner_ideal vars pols pol = |
|
368 |
let val (pol',h) = reduce (grobner pols) (grob_neg pol,Start(~1)) in |
|
24913 | 369 |
if not (null pol') then error "grobner_ideal: not in the ideal" else |
23252 | 370 |
resolve_proof vars h end; |
371 |
||
372 |
(* Produce Strong Nullstellensatz certificate for a power of pol. *) |
|
373 |
||
374 |
fun grobner_strong vars pols pol = |
|
375 |
let val vars' = @{cterm "True"}::vars |
|
376 |
val grob_z = [(rat_1,1::(map (fn x => 0) vars))] |
|
377 |
val grob_1 = [(rat_1,(map (fn x => 0) vars'))] |
|
378 |
fun augment p= map (fn (c,m) => (c,0::m)) p |
|
379 |
val pols' = map augment pols |
|
380 |
val pol' = augment pol |
|
381 |
val allpols = (grob_sub (grob_mul grob_z pol') grob_1)::pols' |
|
382 |
val (l,cert) = grobner_weak vars' allpols |
|
33029 | 383 |
val d = fold (fold (Integer.max o hd o snd) o snd) cert 0 |
23252 | 384 |
fun transform_monomial (c,m) = |
385 |
grob_cmul (c,tl m) (grob_pow vars pol (d - hd m)) |
|
386 |
fun transform_polynomial q = fold_rev (grob_add o transform_monomial) q [] |
|
387 |
val cert' = map (fn (c,q) => (c-1,transform_polynomial q)) |
|
388 |
(filter (fn (k,_) => k <> 0) cert) in |
|
389 |
(d,l,cert') end; |
|
390 |
||
391 |
||
392 |
(* Overall parametrized universal procedure for (semi)rings. *) |
|
393 |
(* We return an ideal_conv and the actual ring prover. *) |
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394 |
|
23252 | 395 |
fun refute_disj rfn tm = |
396 |
case term_of tm of |
|
397 |
Const("op |",_)$l$r => |
|
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398 |
compose_single(refute_disj rfn (dest_arg tm),2,compose_single(refute_disj rfn (dest_arg1 tm),2,disjE)) |
23252 | 399 |
| _ => rfn tm ; |
400 |
||
401 |
val notnotD = @{thm "notnotD"}; |
|
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402 |
fun mk_binop ct x y = capply (capply ct x) y |
23252 | 403 |
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404 |
val mk_comb = capply; |
23252 | 405 |
fun is_neg t = |
406 |
case term_of t of |
|
407 |
(Const("Not",_)$p) => true |
|
408 |
| _ => false; |
|
409 |
fun is_eq t = |
|
410 |
case term_of t of |
|
411 |
(Const("op =",_)$_$_) => true |
|
412 |
| _ => false; |
|
413 |
||
414 |
fun end_itlist f l = |
|
415 |
case l of |
|
416 |
[] => error "end_itlist" |
|
417 |
| [x] => x |
|
418 |
| (h::t) => f h (end_itlist f t); |
|
419 |
||
420 |
val list_mk_binop = fn b => end_itlist (mk_binop b); |
|
421 |
||
422 |
val list_dest_binop = fn b => |
|
423 |
let fun h acc t = |
|
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424 |
((let val (l,r) = dest_binary b t in h (h acc r) l end) |
23252 | 425 |
handle CTERM _ => (t::acc)) (* Why had I handle _ => ? *) |
426 |
in h [] |
|
427 |
end; |
|
428 |
||
429 |
val strip_exists = |
|
430 |
let fun h (acc, t) = |
|
431 |
case (term_of t) of |
|
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432 |
Const("Ex",_)$Abs(x,T,p) => h (dest_abs NONE (dest_arg t) |>> (fn v => v::acc)) |
23252 | 433 |
| _ => (acc,t) |
434 |
in fn t => h ([],t) |
|
435 |
end; |
|
436 |
||
437 |
fun is_forall t = |
|
438 |
case term_of t of |
|
439 |
(Const("All",_)$Abs(_,_,_)) => true |
|
440 |
| _ => false; |
|
441 |
||
442 |
val mk_object_eq = fn th => th COMP meta_eq_to_obj_eq; |
|
443 |
val bool_simps = @{thms "bool_simps"}; |
|
444 |
val nnf_simps = @{thms "nnf_simps"}; |
|
445 |
val nnf_conv = Simplifier.rewrite (HOL_basic_ss addsimps bool_simps addsimps nnf_simps) |
|
23557 | 446 |
val weak_dnf_conv = Simplifier.rewrite (HOL_basic_ss addsimps @{thms "weak_dnf_simps"}); |
23252 | 447 |
val initial_conv = |
448 |
Simplifier.rewrite |
|
449 |
(HOL_basic_ss addsimps nnf_simps |
|
450 |
addsimps [not_all, not_ex] addsimps map (fn th => th RS sym) (ex_simps @ all_simps)); |
|
451 |
||
452 |
val specl = fold_rev (fn x => fn th => instantiate' [] [SOME x] (th RS spec)); |
|
453 |
||
454 |
val cTrp = @{cterm "Trueprop"}; |
|
455 |
val cConj = @{cterm "op &"}; |
|
456 |
val (cNot,false_tm) = (@{cterm "Not"}, @{cterm "False"}); |
|
23557 | 457 |
val assume_Trueprop = mk_comb cTrp #> assume; |
23252 | 458 |
val list_mk_conj = list_mk_binop cConj; |
459 |
val conjs = list_dest_binop cConj; |
|
460 |
val mk_neg = mk_comb cNot; |
|
461 |
||
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462 |
fun striplist dest = |
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|
463 |
let |
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|
464 |
fun h acc x = case try dest x of |
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465 |
SOME (a,b) => h (h acc b) a |
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466 |
| NONE => x::acc |
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|
467 |
in h [] end; |
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|
468 |
fun list_mk_binop b = foldr1 (fn (s,t) => Thm.capply (Thm.capply b s) t); |
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|
469 |
|
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|
470 |
val eq_commute = mk_meta_eq @{thm eq_commute}; |
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|
471 |
|
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|
472 |
fun sym_conv eq = |
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|
473 |
let val (l,r) = Thm.dest_binop eq |
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|
474 |
in instantiate' [SOME (ctyp_of_term l)] [SOME l, SOME r] eq_commute |
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|
475 |
end; |
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|
476 |
|
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|
477 |
(* FIXME : copied from cqe.ML -- complex QE*) |
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|
478 |
fun conjuncts ct = |
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|
479 |
case term_of ct of |
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480 |
@{term "op &"}$_$_ => (Thm.dest_arg1 ct)::(conjuncts (Thm.dest_arg ct)) |
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481 |
| _ => [ct]; |
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|
482 |
|
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|
483 |
fun fold1 f = foldr1 (uncurry f); |
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|
484 |
|
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|
485 |
val list_conj = fold1 (fn c => fn c' => Thm.capply (Thm.capply @{cterm "op &"} c) c') ; |
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|
486 |
|
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|
487 |
fun mk_conj_tab th = |
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|
488 |
let fun h acc th = |
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|
489 |
case prop_of th of |
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|
490 |
@{term "Trueprop"}$(@{term "op &"}$p$q) => |
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|
491 |
h (h acc (th RS conjunct2)) (th RS conjunct1) |
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492 |
| @{term "Trueprop"}$p => (p,th)::acc |
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|
493 |
in fold (Termtab.insert Thm.eq_thm) (h [] th) Termtab.empty end; |
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|
494 |
|
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|
495 |
fun is_conj (@{term "op &"}$_$_) = true |
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|
496 |
| is_conj _ = false; |
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|
497 |
|
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|
498 |
fun prove_conj tab cjs = |
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|
499 |
case cjs of |
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|
500 |
[c] => if is_conj (term_of c) then prove_conj tab (conjuncts c) else tab c |
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|
501 |
| c::cs => conjI OF [prove_conj tab [c], prove_conj tab cs]; |
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|
502 |
|
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|
503 |
fun conj_ac_rule eq = |
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(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
504 |
let |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
505 |
val (l,r) = Thm.dest_equals eq |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
506 |
val ctabl = mk_conj_tab (assume (Thm.capply @{cterm Trueprop} l)) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
507 |
val ctabr = mk_conj_tab (assume (Thm.capply @{cterm Trueprop} r)) |
33035 | 508 |
fun tabl c = the (Termtab.lookup ctabl (term_of c)) |
509 |
fun tabr c = the (Termtab.lookup ctabr (term_of c)) |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
510 |
val thl = prove_conj tabl (conjuncts r) |> implies_intr_hyps |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
511 |
val thr = prove_conj tabr (conjuncts l) |> implies_intr_hyps |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
512 |
val eqI = instantiate' [] [SOME l, SOME r] @{thm iffI} |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
513 |
in implies_elim (implies_elim eqI thl) thr |> mk_meta_eq end; |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
514 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
515 |
(* END FIXME.*) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
516 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
517 |
(* Conversion for the equivalence of existential statements where |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
518 |
EX quantifiers are rearranged differently *) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
519 |
fun ext T = cterm_rule (instantiate' [SOME T] []) @{cpat Ex} |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
520 |
fun mk_ex v t = Thm.capply (ext (ctyp_of_term v)) (Thm.cabs v t) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
521 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
522 |
fun choose v th th' = case concl_of th of |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
523 |
@{term Trueprop} $ (Const("Ex",_)$_) => |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
524 |
let |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
525 |
val p = (funpow 2 Thm.dest_arg o cprop_of) th |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
526 |
val T = (hd o Thm.dest_ctyp o ctyp_of_term) p |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
527 |
val th0 = fconv_rule (Thm.beta_conversion true) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
528 |
(instantiate' [SOME T] [SOME p, (SOME o Thm.dest_arg o cprop_of) th'] exE) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
529 |
val pv = (Thm.rhs_of o Thm.beta_conversion true) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
530 |
(Thm.capply @{cterm Trueprop} (Thm.capply p v)) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
531 |
val th1 = forall_intr v (implies_intr pv th') |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
532 |
in implies_elim (implies_elim th0 th) th1 end |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
533 |
| _ => error "" |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
534 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
535 |
fun simple_choose v th = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
536 |
choose v (assume ((Thm.capply @{cterm Trueprop} o mk_ex v) ((Thm.dest_arg o hd o #hyps o Thm.crep_thm) th))) th |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
537 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
538 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
539 |
fun mkexi v th = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
540 |
let |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
541 |
val p = Thm.cabs v (Thm.dest_arg (Thm.cprop_of th)) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
542 |
in implies_elim |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
543 |
(fconv_rule (Thm.beta_conversion true) (instantiate' [SOME (ctyp_of_term v)] [SOME p, SOME v] @{thm exI})) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
544 |
th |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
545 |
end |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
546 |
fun ex_eq_conv t = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
547 |
let |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
548 |
val (p0,q0) = Thm.dest_binop t |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
549 |
val (vs',P) = strip_exists p0 |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
550 |
val (vs,_) = strip_exists q0 |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
551 |
val th = assume (Thm.capply @{cterm Trueprop} P) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
552 |
val th1 = implies_intr_hyps (fold simple_choose vs' (fold mkexi vs th)) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
553 |
val th2 = implies_intr_hyps (fold simple_choose vs (fold mkexi vs' th)) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
554 |
val p = (Thm.dest_arg o Thm.dest_arg1 o cprop_of) th1 |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
555 |
val q = (Thm.dest_arg o Thm.dest_arg o cprop_of) th1 |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
556 |
in implies_elim (implies_elim (instantiate' [] [SOME p, SOME q] iffI) th1) th2 |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
557 |
|> mk_meta_eq |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
558 |
end; |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
559 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
560 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
561 |
fun getname v = case term_of v of |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
562 |
Free(s,_) => s |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
563 |
| Var ((s,_),_) => s |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
564 |
| _ => "x" |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
565 |
fun mk_eq s t = Thm.capply (Thm.capply @{cterm "op == :: bool => _"} s) t |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
566 |
fun mkeq s t = Thm.capply @{cterm Trueprop} (Thm.capply (Thm.capply @{cterm "op = :: bool => _"} s) t) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
567 |
fun mk_exists v th = arg_cong_rule (ext (ctyp_of_term v)) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
568 |
(Thm.abstract_rule (getname v) v th) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
569 |
val simp_ex_conv = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
570 |
Simplifier.rewrite (HOL_basic_ss addsimps @{thms simp_thms(39)}) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
571 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
572 |
fun frees t = Thm.add_cterm_frees t []; |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
573 |
fun free_in v t = member op aconvc (frees t) v; |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
574 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
575 |
val vsubst = let |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
576 |
fun vsubst (t,v) tm = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
577 |
(Thm.rhs_of o Thm.beta_conversion false) (Thm.capply (Thm.cabs v tm) t) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
578 |
in fold vsubst end; |
23252 | 579 |
|
580 |
||
581 |
(** main **) |
|
582 |
||
583 |
fun ring_and_ideal_conv |
|
30866 | 584 |
{vars, semiring = (sr_ops, sr_rules), ring = (r_ops, r_rules), |
585 |
field = (f_ops, f_rules), idom, ideal} |
|
23252 | 586 |
dest_const mk_const ring_eq_conv ring_normalize_conv = |
587 |
let |
|
588 |
val [add_pat, mul_pat, pow_pat, zero_tm, one_tm] = sr_ops; |
|
589 |
val [ring_add_tm, ring_mul_tm, ring_pow_tm] = |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
590 |
map dest_fun2 [add_pat, mul_pat, pow_pat]; |
23252 | 591 |
|
592 |
val (ring_sub_tm, ring_neg_tm) = |
|
593 |
(case r_ops of |
|
30866 | 594 |
[sub_pat, neg_pat] => (dest_fun2 sub_pat, dest_fun neg_pat) |
595 |
|_ => (@{cterm "True"}, @{cterm "True"})); |
|
596 |
||
597 |
val (field_div_tm, field_inv_tm) = |
|
598 |
(case f_ops of |
|
599 |
[div_pat, inv_pat] => (dest_fun2 div_pat, dest_fun inv_pat) |
|
600 |
| _ => (@{cterm "True"}, @{cterm "True"})); |
|
23252 | 601 |
|
602 |
val [idom_thm, neq_thm] = idom; |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
603 |
val [idl_sub, idl_add0] = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
604 |
if length ideal = 2 then ideal else [eq_commute, eq_commute] |
30866 | 605 |
fun ring_dest_neg t = |
606 |
let val (l,r) = dest_comb t |
|
607 |
in if Term.could_unify(term_of l,term_of ring_neg_tm) then r |
|
608 |
else raise CTERM ("ring_dest_neg", [t]) |
|
609 |
end |
|
23252 | 610 |
|
611 |
val ring_mk_neg = fn tm => mk_comb (ring_neg_tm) (tm); |
|
30866 | 612 |
fun field_dest_inv t = |
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
613 |
let val (l,r) = dest_comb t in |
30866 | 614 |
if Term.could_unify(term_of l, term_of field_inv_tm) then r |
615 |
else raise CTERM ("field_dest_inv", [t]) |
|
23252 | 616 |
end |
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
617 |
val ring_dest_add = dest_binary ring_add_tm; |
23252 | 618 |
val ring_mk_add = mk_binop ring_add_tm; |
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
619 |
val ring_dest_sub = dest_binary ring_sub_tm; |
23252 | 620 |
val ring_mk_sub = mk_binop ring_sub_tm; |
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
621 |
val ring_dest_mul = dest_binary ring_mul_tm; |
23252 | 622 |
val ring_mk_mul = mk_binop ring_mul_tm; |
30866 | 623 |
val field_dest_div = dest_binary field_div_tm; |
624 |
val field_mk_div = mk_binop field_div_tm; |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
625 |
val ring_dest_pow = dest_binary ring_pow_tm; |
23252 | 626 |
val ring_mk_pow = mk_binop ring_pow_tm ; |
627 |
fun grobvars tm acc = |
|
628 |
if can dest_const tm then acc |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
629 |
else if can ring_dest_neg tm then grobvars (dest_arg tm) acc |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
630 |
else if can ring_dest_pow tm then grobvars (dest_arg1 tm) acc |
23252 | 631 |
else if can ring_dest_add tm orelse can ring_dest_sub tm |
632 |
orelse can ring_dest_mul tm |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
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diff
changeset
|
633 |
then grobvars (dest_arg1 tm) (grobvars (dest_arg tm) acc) |
30866 | 634 |
else if can field_dest_inv tm |
635 |
then |
|
636 |
let val gvs = grobvars (dest_arg tm) [] |
|
637 |
in if null gvs then acc else tm::acc |
|
638 |
end |
|
639 |
else if can field_dest_div tm then |
|
640 |
let val lvs = grobvars (dest_arg1 tm) acc |
|
641 |
val gvs = grobvars (dest_arg tm) [] |
|
642 |
in if null gvs then lvs else tm::acc |
|
643 |
end |
|
23252 | 644 |
else tm::acc ; |
645 |
||
646 |
fun grobify_term vars tm = |
|
647 |
((if not (member (op aconvc) vars tm) then raise CTERM ("Not a variable", [tm]) else |
|
648 |
[(rat_1,map (fn i => if i aconvc tm then 1 else 0) vars)]) |
|
649 |
handle CTERM _ => |
|
650 |
((let val x = dest_const tm |
|
651 |
in if x =/ rat_0 then [] else [(x,map (fn v => 0) vars)] |
|
652 |
end) |
|
653 |
handle ERROR _ => |
|
654 |
((grob_neg(grobify_term vars (ring_dest_neg tm))) |
|
655 |
handle CTERM _ => |
|
656 |
( |
|
30866 | 657 |
(grob_inv(grobify_term vars (field_dest_inv tm))) |
658 |
handle CTERM _ => |
|
23252 | 659 |
((let val (l,r) = ring_dest_add tm |
660 |
in grob_add (grobify_term vars l) (grobify_term vars r) |
|
661 |
end) |
|
662 |
handle CTERM _ => |
|
663 |
((let val (l,r) = ring_dest_sub tm |
|
664 |
in grob_sub (grobify_term vars l) (grobify_term vars r) |
|
665 |
end) |
|
666 |
handle CTERM _ => |
|
667 |
((let val (l,r) = ring_dest_mul tm |
|
668 |
in grob_mul (grobify_term vars l) (grobify_term vars r) |
|
669 |
end) |
|
670 |
handle CTERM _ => |
|
30866 | 671 |
( (let val (l,r) = field_dest_div tm |
23252 | 672 |
in grob_div (grobify_term vars l) (grobify_term vars r) |
673 |
end) |
|
30866 | 674 |
handle CTERM _ => |
23252 | 675 |
((let val (l,r) = ring_dest_pow tm |
676 |
in grob_pow vars (grobify_term vars l) ((term_of #> HOLogic.dest_number #> snd) r) |
|
677 |
end) |
|
678 |
handle CTERM _ => error "grobify_term: unknown or invalid term"))))))))); |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
679 |
val eq_tm = idom_thm |> concl |> dest_arg |> dest_arg |> dest_fun2; |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
680 |
val dest_eq = dest_binary eq_tm; |
23252 | 681 |
|
682 |
fun grobify_equation vars tm = |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
683 |
let val (l,r) = dest_binary eq_tm tm |
23252 | 684 |
in grob_sub (grobify_term vars l) (grobify_term vars r) |
685 |
end; |
|
686 |
||
687 |
fun grobify_equations tm = |
|
688 |
let |
|
689 |
val cjs = conjs tm |
|
690 |
val rawvars = fold_rev (fn eq => fn a => |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
691 |
grobvars (dest_arg1 eq) (grobvars (dest_arg eq) a)) cjs [] |
29269
5c25a2012975
moved term order operations to structure TermOrd (cf. Pure/term_ord.ML);
wenzelm
parents:
27671
diff
changeset
|
692 |
val vars = sort (fn (x, y) => TermOrd.term_ord(term_of x,term_of y)) |
23252 | 693 |
(distinct (op aconvc) rawvars) |
694 |
in (vars,map (grobify_equation vars) cjs) |
|
695 |
end; |
|
696 |
||
697 |
val holify_polynomial = |
|
698 |
let fun holify_varpow (v,n) = |
|
23579 | 699 |
if n = 1 then v else ring_mk_pow v (Numeral.mk_cnumber @{ctyp "nat"} n) (* FIXME *) |
23252 | 700 |
fun holify_monomial vars (c,m) = |
24630
351a308ab58d
simplified type int (eliminated IntInf.int, integer);
wenzelm
parents:
23579
diff
changeset
|
701 |
let val xps = map holify_varpow (filter (fn (_,n) => n <> 0) (vars ~~ m)) |
23252 | 702 |
in end_itlist ring_mk_mul (mk_const c :: xps) |
703 |
end |
|
704 |
fun holify_polynomial vars p = |
|
23579 | 705 |
if null p then mk_const (rat_0) |
23252 | 706 |
else end_itlist ring_mk_add (map (holify_monomial vars) p) |
707 |
in holify_polynomial |
|
708 |
end ; |
|
709 |
val idom_rule = simplify (HOL_basic_ss addsimps [idom_thm]); |
|
710 |
fun prove_nz n = eqF_elim |
|
711 |
(ring_eq_conv(mk_binop eq_tm (mk_const n) (mk_const(rat_0)))); |
|
712 |
val neq_01 = prove_nz (rat_1); |
|
713 |
fun neq_rule n th = [prove_nz n, th] MRS neq_thm; |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
714 |
fun mk_add th1 = combination(arg_cong_rule ring_add_tm th1); |
23252 | 715 |
|
716 |
fun refute tm = |
|
23557 | 717 |
if tm aconvc false_tm then assume_Trueprop tm else |
29800
f73a68c9d810
Now catch ERROR exception thrown by find and friends
chaieb
parents:
29269
diff
changeset
|
718 |
((let |
23557 | 719 |
val (nths0,eths0) = List.partition (is_neg o concl) (HOLogic.conj_elims (assume_Trueprop tm)) |
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
720 |
val nths = filter (is_eq o dest_arg o concl) nths0 |
23252 | 721 |
val eths = filter (is_eq o concl) eths0 |
722 |
in |
|
723 |
if null eths then |
|
724 |
let |
|
23557 | 725 |
val th1 = end_itlist (fn th1 => fn th2 => idom_rule(HOLogic.conj_intr th1 th2)) nths |
23252 | 726 |
val th2 = Conv.fconv_rule |
727 |
((arg_conv #> arg_conv) |
|
728 |
(binop_conv ring_normalize_conv)) th1 |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
729 |
val conc = th2 |> concl |> dest_arg |
23252 | 730 |
val (l,r) = conc |> dest_eq |
731 |
in implies_intr (mk_comb cTrp tm) |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
732 |
(equal_elim (arg_cong_rule cTrp (eqF_intr th2)) |
23252 | 733 |
(reflexive l |> mk_object_eq)) |
734 |
end |
|
735 |
else |
|
736 |
let |
|
737 |
val (vars,l,cert,noteqth) =( |
|
738 |
if null nths then |
|
739 |
let val (vars,pols) = grobify_equations(list_mk_conj(map concl eths)) |
|
740 |
val (l,cert) = grobner_weak vars pols |
|
741 |
in (vars,l,cert,neq_01) |
|
742 |
end |
|
743 |
else |
|
744 |
let |
|
23557 | 745 |
val nth = end_itlist (fn th1 => fn th2 => idom_rule(HOLogic.conj_intr th1 th2)) nths |
23252 | 746 |
val (vars,pol::pols) = |
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
747 |
grobify_equations(list_mk_conj(dest_arg(concl nth)::map concl eths)) |
23252 | 748 |
val (deg,l,cert) = grobner_strong vars pols pol |
749 |
val th1 = Conv.fconv_rule((arg_conv o arg_conv)(binop_conv ring_normalize_conv)) nth |
|
24630
351a308ab58d
simplified type int (eliminated IntInf.int, integer);
wenzelm
parents:
23579
diff
changeset
|
750 |
val th2 = funpow deg (idom_rule o HOLogic.conj_intr th1) neq_01 |
23252 | 751 |
in (vars,l,cert,th2) |
752 |
end) |
|
753 |
val cert_pos = map (fn (i,p) => (i,filter (fn (c,m) => c >/ rat_0) p)) cert |
|
754 |
val cert_neg = map (fn (i,p) => (i,map (fn (c,m) => (minus_rat c,m)) |
|
755 |
(filter (fn (c,m) => c </ rat_0) p))) cert |
|
756 |
val herts_pos = map (fn (i,p) => (i,holify_polynomial vars p)) cert_pos |
|
757 |
val herts_neg = map (fn (i,p) => (i,holify_polynomial vars p)) cert_neg |
|
758 |
fun thm_fn pols = |
|
759 |
if null pols then reflexive(mk_const rat_0) else |
|
760 |
end_itlist mk_add |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
761 |
(map (fn (i,p) => arg_cong_rule (mk_comb ring_mul_tm p) |
24630
351a308ab58d
simplified type int (eliminated IntInf.int, integer);
wenzelm
parents:
23579
diff
changeset
|
762 |
(nth eths i |> mk_meta_eq)) pols) |
23252 | 763 |
val th1 = thm_fn herts_pos |
764 |
val th2 = thm_fn herts_neg |
|
23557 | 765 |
val th3 = HOLogic.conj_intr(mk_add (symmetric th1) th2 |> mk_object_eq) noteqth |
23252 | 766 |
val th4 = Conv.fconv_rule ((arg_conv o arg_conv o binop_conv) ring_normalize_conv) |
767 |
(neq_rule l th3) |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
768 |
val (l,r) = dest_eq(dest_arg(concl th4)) |
23252 | 769 |
in implies_intr (mk_comb cTrp tm) |
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
770 |
(equal_elim (arg_cong_rule cTrp (eqF_intr th4)) |
23252 | 771 |
(reflexive l |> mk_object_eq)) |
772 |
end |
|
29800
f73a68c9d810
Now catch ERROR exception thrown by find and friends
chaieb
parents:
29269
diff
changeset
|
773 |
end) handle ERROR _ => raise CTERM ("Gorbner-refute: unable to refute",[tm])) |
23252 | 774 |
|
775 |
fun ring tm = |
|
776 |
let |
|
777 |
fun mk_forall x p = |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
778 |
mk_comb (cterm_rule (instantiate' [SOME (ctyp_of_term x)] []) @{cpat "All:: (?'a => bool) => _"}) (cabs x p) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
779 |
val avs = add_cterm_frees tm [] |
23252 | 780 |
val P' = fold mk_forall avs tm |
781 |
val th1 = initial_conv(mk_neg P') |
|
782 |
val (evs,bod) = strip_exists(concl th1) in |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
783 |
if is_forall bod then raise CTERM("ring: non-universal formula",[tm]) |
23252 | 784 |
else |
785 |
let |
|
786 |
val th1a = weak_dnf_conv bod |
|
787 |
val boda = concl th1a |
|
788 |
val th2a = refute_disj refute boda |
|
789 |
val th2b = [mk_object_eq th1a, (th2a COMP notI) COMP PFalse'] MRS trans |
|
790 |
val th2 = fold (fn v => fn th => (forall_intr v th) COMP allI) evs (th2b RS PFalse) |
|
791 |
val th3 = equal_elim |
|
792 |
(Simplifier.rewrite (HOL_basic_ss addsimps [not_ex RS sym]) |
|
793 |
(th2 |> cprop_of)) th2 |
|
794 |
in specl avs |
|
795 |
([[[mk_object_eq th1, th3 RS PFalse'] MRS trans] MRS PFalse] MRS notnotD) |
|
796 |
end |
|
797 |
end |
|
798 |
fun ideal tms tm ord = |
|
799 |
let |
|
800 |
val rawvars = fold_rev grobvars (tm::tms) [] |
|
801 |
val vars = sort ord (distinct (fn (x,y) => (term_of x) aconv (term_of y)) rawvars) |
|
802 |
val pols = map (grobify_term vars) tms |
|
803 |
val pol = grobify_term vars tm |
|
804 |
val cert = grobner_ideal vars pols pol |
|
33063 | 805 |
in map_range (fn n => these (AList.lookup (op =) cert n) |> holify_polynomial vars) |
806 |
(length pols) |
|
23252 | 807 |
end |
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
808 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
809 |
fun poly_eq_conv t = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
810 |
let val (a,b) = Thm.dest_binop t |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
811 |
in fconv_rule (arg_conv (arg1_conv ring_normalize_conv)) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
812 |
(instantiate' [] [SOME a, SOME b] idl_sub) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
813 |
end |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
814 |
val poly_eq_simproc = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
815 |
let |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
816 |
fun proc phi ss t = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
817 |
let val th = poly_eq_conv t |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
818 |
in if Thm.is_reflexive th then NONE else SOME th |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
819 |
end |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
820 |
in make_simproc {lhss = [Thm.lhs_of idl_sub], |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
821 |
name = "poly_eq_simproc", proc = proc, identifier = []} |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
822 |
end; |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
823 |
val poly_eq_ss = HOL_basic_ss addsimps simp_thms |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
824 |
addsimprocs [poly_eq_simproc] |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
825 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
826 |
local |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
827 |
fun is_defined v t = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
828 |
let |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
829 |
val mons = striplist(dest_binary ring_add_tm) t |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
830 |
in member (op aconvc) mons v andalso |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
831 |
forall (fn m => v aconvc m |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
832 |
orelse not(member (op aconvc) (Thm.add_cterm_frees m []) v)) mons |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
833 |
end |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
834 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
835 |
fun isolate_variable vars tm = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
836 |
let |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
837 |
val th = poly_eq_conv tm |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
838 |
val th' = (sym_conv then_conv poly_eq_conv) tm |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
839 |
val (v,th1) = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
840 |
case find_first(fn v=> is_defined v (Thm.dest_arg1 (Thm.rhs_of th))) vars of |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
841 |
SOME v => (v,th') |
33035 | 842 |
| NONE => (the (find_first |
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
843 |
(fn v => is_defined v (Thm.dest_arg1 (Thm.rhs_of th'))) vars) ,th) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
844 |
val th2 = transitive th1 |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
845 |
(instantiate' [] [(SOME o Thm.dest_arg1 o Thm.rhs_of) th1, SOME v] |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
846 |
idl_add0) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
847 |
in fconv_rule(funpow 2 arg_conv ring_normalize_conv) th2 |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
848 |
end |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
849 |
in |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
850 |
fun unwind_polys_conv tm = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
851 |
let |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
852 |
val (vars,bod) = strip_exists tm |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
853 |
val cjs = striplist (dest_binary @{cterm "op &"}) bod |
33035 | 854 |
val th1 = (the (get_first (try (isolate_variable vars)) cjs) |
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
855 |
handle Option => raise CTERM ("unwind_polys_conv",[tm])) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
856 |
val eq = Thm.lhs_of th1 |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
857 |
val bod' = list_mk_binop @{cterm "op &"} (eq::(remove op aconvc eq cjs)) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
858 |
val th2 = conj_ac_rule (mk_eq bod bod') |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
859 |
val th3 = transitive th2 |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
860 |
(Drule.binop_cong_rule @{cterm "op &"} th1 |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
861 |
(reflexive (Thm.dest_arg (Thm.rhs_of th2)))) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
862 |
val v = Thm.dest_arg1(Thm.dest_arg1(Thm.rhs_of th3)) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
863 |
val vars' = (remove op aconvc v vars) @ [v] |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
864 |
val th4 = fconv_rule (arg_conv simp_ex_conv) (mk_exists v th3) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
865 |
val th5 = ex_eq_conv (mk_eq tm (fold mk_ex (remove op aconvc v vars) (Thm.lhs_of th4))) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
866 |
in transitive th5 (fold mk_exists (remove op aconvc v vars) th4) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
867 |
end; |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
868 |
end |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
869 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
870 |
local |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
871 |
fun scrub_var v m = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
872 |
let |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
873 |
val ps = striplist ring_dest_mul m |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
874 |
val ps' = remove op aconvc v ps |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
875 |
in if null ps' then one_tm else fold1 ring_mk_mul ps' |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
876 |
end |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
877 |
fun find_multipliers v mons = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
878 |
let |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
879 |
val mons1 = filter (fn m => free_in v m) mons |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
880 |
val mons2 = map (scrub_var v) mons1 |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
881 |
in if null mons2 then zero_tm else fold1 ring_mk_add mons2 |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
882 |
end |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
883 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
884 |
fun isolate_monomials vars tm = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
885 |
let |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
886 |
val (cmons,vmons) = |
33049
c38f02fdf35d
curried inter as canonical list operation (beware of argument order)
haftmann
parents:
33039
diff
changeset
|
887 |
List.partition (fn m => null (inter (op aconvc) vars (frees m))) |
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
888 |
(striplist ring_dest_add tm) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
889 |
val cofactors = map (fn v => find_multipliers v vmons) vars |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
890 |
val cnc = if null cmons then zero_tm |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
891 |
else Thm.capply ring_neg_tm |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
892 |
(list_mk_binop ring_add_tm cmons) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
893 |
in (cofactors,cnc) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
894 |
end; |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
895 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
896 |
fun isolate_variables evs ps eq = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
897 |
let |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
898 |
val vars = filter (fn v => free_in v eq) evs |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
899 |
val (qs,p) = isolate_monomials vars eq |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
900 |
val rs = ideal (qs @ ps) p |
29269
5c25a2012975
moved term order operations to structure TermOrd (cf. Pure/term_ord.ML);
wenzelm
parents:
27671
diff
changeset
|
901 |
(fn (s,t) => TermOrd.term_ord (term_of s, term_of t)) |
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
902 |
in (eq,Library.take (length qs, rs) ~~ vars) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
903 |
end; |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
904 |
fun subst_in_poly i p = Thm.rhs_of (ring_normalize_conv (vsubst i p)); |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
905 |
in |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
906 |
fun solve_idealism evs ps eqs = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
907 |
if null evs then [] else |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
908 |
let |
33035 | 909 |
val (eq,cfs) = get_first (try (isolate_variables evs ps)) eqs |> the |
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
910 |
val evs' = subtract op aconvc evs (map snd cfs) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
911 |
val eqs' = map (subst_in_poly cfs) (remove op aconvc eq eqs) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
912 |
in cfs @ solve_idealism evs' ps eqs' |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
913 |
end; |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
914 |
end; |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
915 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
916 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
917 |
in {ring_conv = ring, simple_ideal = ideal, multi_ideal = solve_idealism, |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
918 |
poly_eq_ss = poly_eq_ss, unwind_conv = unwind_polys_conv} |
23252 | 919 |
end; |
920 |
||
921 |
||
922 |
fun find_term bounds tm = |
|
923 |
(case term_of tm of |
|
924 |
Const ("op =", T) $ _ $ _ => |
|
925 |
if domain_type T = HOLogic.boolT then find_args bounds tm |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
926 |
else dest_arg tm |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
927 |
| Const ("Not", _) $ _ => find_term bounds (dest_arg tm) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
928 |
| Const ("All", _) $ _ => find_body bounds (dest_arg tm) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
929 |
| Const ("Ex", _) $ _ => find_body bounds (dest_arg tm) |
23252 | 930 |
| Const ("op &", _) $ _ $ _ => find_args bounds tm |
931 |
| Const ("op |", _) $ _ $ _ => find_args bounds tm |
|
932 |
| Const ("op -->", _) $ _ $ _ => find_args bounds tm |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
933 |
| @{term "op ==>"} $_$_ => find_args bounds tm |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
934 |
| Const("op ==",_)$_$_ => find_args bounds tm |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
935 |
| @{term Trueprop}$_ => find_term bounds (dest_arg tm) |
23252 | 936 |
| _ => raise TERM ("find_term", [])) |
937 |
and find_args bounds tm = |
|
938 |
let val (t, u) = Thm.dest_binop tm |
|
939 |
in (find_term bounds t handle TERM _ => find_term bounds u) end |
|
940 |
and find_body bounds b = |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
941 |
let val (_, b') = dest_abs (SOME (Name.bound bounds)) b |
23252 | 942 |
in find_term (bounds + 1) b' end; |
943 |
||
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
944 |
|
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
945 |
fun get_ring_ideal_convs ctxt form = |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
946 |
case try (find_term 0) form of |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
947 |
NONE => NONE |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
948 |
| SOME tm => |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
949 |
(case NormalizerData.match ctxt tm of |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
950 |
NONE => NONE |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
951 |
| SOME (res as (theory, {is_const, dest_const, |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
952 |
mk_const, conv = ring_eq_conv})) => |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
953 |
SOME (ring_and_ideal_conv theory |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
954 |
dest_const (mk_const (ctyp_of_term tm)) (ring_eq_conv ctxt) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
955 |
(semiring_normalize_wrapper ctxt res))) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
956 |
|
23579 | 957 |
fun ring_solve ctxt form = |
23252 | 958 |
(case try (find_term 0 (* FIXME !? *)) form of |
959 |
NONE => reflexive form |
|
960 |
| SOME tm => |
|
961 |
(case NormalizerData.match ctxt tm of |
|
962 |
NONE => reflexive form |
|
963 |
| SOME (res as (theory, {is_const, dest_const, mk_const, conv = ring_eq_conv})) => |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
964 |
#ring_conv (ring_and_ideal_conv theory |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
965 |
dest_const (mk_const (ctyp_of_term tm)) (ring_eq_conv ctxt) |
23330
01c09922ce59
Conversion for computation on constants now depends on the context
chaieb
parents:
23259
diff
changeset
|
966 |
(semiring_normalize_wrapper ctxt res)) form)); |
23252 | 967 |
|
23579 | 968 |
fun ring_tac add_ths del_ths ctxt = |
969 |
ObjectLogic.full_atomize_tac |
|
27671 | 970 |
THEN' asm_full_simp_tac (Simplifier.context ctxt (fst (NormalizerData.get ctxt)) delsimps del_ths addsimps add_ths) |
23579 | 971 |
THEN' CSUBGOAL (fn (p, i) => |
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
972 |
rtac (let val form = (ObjectLogic.dest_judgment p) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
973 |
in case get_ring_ideal_convs ctxt form of |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
974 |
NONE => reflexive form |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
975 |
| SOME thy => #ring_conv thy form |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
976 |
end) i |
23579 | 977 |
handle TERM _ => no_tac |
978 |
| CTERM _ => no_tac |
|
979 |
| THM _ => no_tac); |
|
23334 | 980 |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
981 |
local |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
982 |
fun lhs t = case term_of t of |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
983 |
Const("op =",_)$_$_ => Thm.dest_arg1 t |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
984 |
| _=> raise CTERM ("ideal_tac - lhs",[t]) |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
985 |
fun exitac NONE = no_tac |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
986 |
| exitac (SOME y) = rtac (instantiate' [SOME (ctyp_of_term y)] [NONE,SOME y] exI) 1 |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
987 |
in |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
988 |
fun ideal_tac add_ths del_ths ctxt = |
27671 | 989 |
asm_full_simp_tac |
990 |
(Simplifier.context ctxt (fst (NormalizerData.get ctxt)) delsimps del_ths addsimps add_ths) |
|
991 |
THEN' |
|
25251
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
992 |
CSUBGOAL (fn (p, i) => |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
993 |
case get_ring_ideal_convs ctxt p of |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
994 |
NONE => no_tac |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
995 |
| SOME thy => |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
changeset
|
996 |
let |
759bffe1d416
(1) signatures updated according to normalizer_data.ML (added field ideal in entry);
chaieb
parents:
24913
diff
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997 |
fun poly_exists_tac {asms = asms, concl = concl, prems = prems, |
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998 |
params = params, context = ctxt, schematics = scs} = |
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999 |
let |
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1000 |
val (evs,bod) = strip_exists (Thm.dest_arg concl) |
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1001 |
val ps = map_filter (try (lhs o Thm.dest_arg)) asms |
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1002 |
val cfs = (map swap o #multi_ideal thy evs ps) |
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1003 |
(map Thm.dest_arg1 (conjuncts bod)) |
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1004 |
val ws = map (exitac o AList.lookup op aconvc cfs) evs |
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1005 |
in EVERY (rev ws) THEN Method.insert_tac prems 1 |
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1006 |
THEN ring_tac add_ths del_ths ctxt 1 |
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1007 |
end |
27671 | 1008 |
in |
1009 |
clarify_tac @{claset} i |
|
1010 |
THEN ObjectLogic.full_atomize_tac i |
|
1011 |
THEN asm_full_simp_tac (Simplifier.context ctxt (#poly_eq_ss thy)) i |
|
1012 |
THEN clarify_tac @{claset} i |
|
25251
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1013 |
THEN (REPEAT (CONVERSION (#unwind_conv thy) i)) |
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1014 |
THEN SUBPROOF poly_exists_tac ctxt i |
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1015 |
end |
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1016 |
handle TERM _ => no_tac |
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1017 |
| CTERM _ => no_tac |
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1018 |
| THM _ => no_tac); |
23252 | 1019 |
end; |
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1020 |
|
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1021 |
fun algebra_tac add_ths del_ths ctxt i = |
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1022 |
ring_tac add_ths del_ths ctxt i ORELSE ideal_tac add_ths del_ths ctxt i |
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|
1023 |
|
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1024 |
|
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|
1025 |
|
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|
1026 |
end; |