author  haftmann 
Fri, 17 Apr 2009 08:34:51 +0200  
changeset 30939  207ec81543f6 
parent 30509  e19d5b459a61 
child 31070  ee1ebd405a37 
permissions  rwrr 
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(* Title: HOL/Decision_Procs/cooper_tac.ML 
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Author: Amine Chaieb, TU Muenchen 
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*) 

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structure Cooper_Tac = 

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struct 
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val trace = ref false; 

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fun trace_msg s = if !trace then tracing s else (); 

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val cooper_ss = @{simpset}; 

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val nT = HOLogic.natT; 

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val binarith = @{thms normalize_bin_simps}; 
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val comp_arith = binarith @ simp_thms 
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val zdvd_int = @{thm zdvd_int}; 
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val zdiff_int_split = @{thm zdiff_int_split}; 
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val all_nat = @{thm all_nat}; 
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val ex_nat = @{thm ex_nat}; 
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val number_of1 = @{thm number_of1}; 
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val number_of2 = @{thm number_of2}; 
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val split_zdiv = @{thm split_zdiv}; 
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val split_zmod = @{thm split_zmod}; 
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val mod_div_equality' = @{thm mod_div_equality'}; 
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val split_div' = @{thm split_div'}; 
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val Suc_plus1 = @{thm Suc_plus1}; 
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val imp_le_cong = @{thm imp_le_cong}; 
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val conj_le_cong = @{thm conj_le_cong}; 
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val mod_add_left_eq = @{thm mod_add_left_eq} RS sym; 
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val mod_add_right_eq = @{thm mod_add_right_eq} RS sym; 

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val mod_add_eq = @{thm mod_add_eq} RS sym; 
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val nat_div_add_eq = @{thm div_add1_eq} RS sym; 
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val int_div_add_eq = @{thm zdiv_zadd1_eq} RS sym; 
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fun prepare_for_linz q fm = 

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let 

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val ps = Logic.strip_params fm 

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val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm) 

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val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm) 

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fun mk_all ((s, T), (P,n)) = 

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if 0 mem loose_bnos P then 

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(HOLogic.all_const T $ Abs (s, T, P), n) 

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else (incr_boundvars ~1 P, n1) 

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fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t; 

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val rhs = hs 
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val np = length ps 
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val (fm',np) = foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n))) 

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(foldr HOLogic.mk_imp c rhs, np) ps 

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val (vs, _) = List.partition (fn t => q orelse (type_of t) = nT) 

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(OldTerm.term_frees fm' @ OldTerm.term_vars fm'); 
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val fm2 = foldr mk_all2 fm' vs 
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in (fm2, np + length vs, length rhs) end; 

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(*Object quantifier to meta *) 

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fun spec_step n th = if (n=0) then th else (spec_step (n1) th) RS spec ; 

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(* object implication to meta*) 

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fun mp_step n th = if (n=0) then th else (mp_step (n1) th) RS mp; 

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fun linz_tac ctxt q i = ObjectLogic.atomize_prems_tac i THEN (fn st => 
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let 
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val g = List.nth (prems_of st, i  1) 

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val thy = ProofContext.theory_of ctxt 

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(* Transform the term*) 

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val (t,np,nh) = prepare_for_linz q g 

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(* Some simpsets for dealing with mod div abs and nat*) 

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val mod_div_simpset = HOL_basic_ss 

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addsimps [refl,mod_add_eq, mod_add_left_eq, 
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mod_add_right_eq, 

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nat_div_add_eq, int_div_add_eq, 
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@{thm mod_self}, @{thm "zmod_self"}, 
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@{thm mod_by_0}, @{thm div_by_0}, 
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@{thm "zdiv_zero"}, @{thm "zmod_zero"}, @{thm "div_0"}, @{thm "mod_0"}, 
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@{thm "div_by_1"}, @{thm "mod_by_1"}, @{thm "div_1"}, @{thm "mod_1"}, 
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Suc_plus1] 
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addsimps @{thms add_ac} 
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addsimprocs [cancel_div_mod_nat_proc, cancel_div_mod_int_proc] 
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val simpset0 = HOL_basic_ss 
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addsimps [mod_div_equality', Suc_plus1] 

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addsimps comp_arith 

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addsplits [split_zdiv, split_zmod, split_div', @{thm "split_min"}, @{thm "split_max"}] 

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(* Simp rules for changing (n::int) to int n *) 

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val simpset1 = HOL_basic_ss 

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addsimps [nat_number_of_def, zdvd_int] @ map (fn r => r RS sym) 

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[@{thm int_int_eq}, @{thm zle_int}, @{thm zless_int}, @{thm zadd_int}, @{thm zmult_int}] 
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addsplits [zdiff_int_split] 
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(*simp rules for elimination of int n*) 

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val simpset2 = HOL_basic_ss 

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addsimps [@{thm nat_0_le}, @{thm all_nat}, @{thm ex_nat}, @{thm number_of1}, @{thm number_of2}, @{thm int_0}, @{thm int_1}] 
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addcongs [@{thm conj_le_cong}, @{thm imp_le_cong}] 

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(* simp rules for elimination of abs *) 
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val simpset3 = HOL_basic_ss addsplits [@{thm abs_split}] 
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val ct = cterm_of thy (HOLogic.mk_Trueprop t) 
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(* Theorem for the nat > int transformation *) 

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val pre_thm = Seq.hd (EVERY 

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[simp_tac mod_div_simpset 1, simp_tac simpset0 1, 

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TRY (simp_tac simpset1 1), TRY (simp_tac simpset2 1), 

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TRY (simp_tac simpset3 1), TRY (simp_tac cooper_ss 1)] 

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(trivial ct)) 

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fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i) 

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(* The result of the quantifier elimination *) 

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val (th, tac) = case (prop_of pre_thm) of 

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Const ("==>", _) $ (Const ("Trueprop", _) $ t1) $ _ => 

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let val pth = linzqe_oracle (cterm_of thy (Pattern.eta_long [] t1)) 
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in 
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((pth RS iffD2) RS pre_thm, 

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assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i)) 

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end 

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 _ => (pre_thm, assm_tac i) 

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in (rtac (((mp_step nh) o (spec_step np)) th) i 

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THEN tac) st 

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end handle Subscript => no_tac st); 

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fun linz_args meth = 

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let val parse_flag = 

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Args.$$$ "no_quantify" >> (K (K false)); 

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in 

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Method.simple_args 

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(Scan.optional (Args.$$$ "("  Scan.repeat1 parse_flag  Args.$$$ ")") [] >> 

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curry (Library.foldl op >) true) 

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(fn q => fn ctxt => meth ctxt q) 
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end; 
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fun linz_method ctxt q = SIMPLE_METHOD' (linz_tac ctxt q); 
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val setup = 

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Method.add_method ("cooper", 

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linz_args linz_method, 

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"decision procedure for linear integer arithmetic"); 

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end 