author  hoelzl 
Wed, 11 Mar 2009 10:58:18 +0100  
changeset 30439  57c68b3af2ea 
parent 30242  aea5d7fa7ef5 
child 30509  e19d5b459a61 
permissions  rwrr 
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(* Title: HOL/Decision_Procs/mir_tac.ML 
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Author: Amine Chaieb, TU Muenchen 
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*) 

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structure Mir_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 mir_ss = 
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let val ths = map thm ["real_of_int_inject", "real_of_int_less_iff", "real_of_int_le_iff"] 
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in @{simpset} delsimps ths addsimps (map (fn th => th RS sym) ths) 
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end; 
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val nT = HOLogic.natT; 
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val nat_arith = map thm ["add_nat_number_of", "diff_nat_number_of", 
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"mult_nat_number_of", "eq_nat_number_of", "less_nat_number_of"]; 
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val comp_arith = (map thm ["Let_def", "if_False", "if_True", "add_0", 
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"add_Suc", "add_number_of_left", "mult_number_of_left", 
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"Suc_eq_add_numeral_1"])@ 
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(map (fn s => thm s RS sym) ["numeral_1_eq_1", "numeral_0_eq_0"]) 
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@ @{thms arith_simps} @ nat_arith @ @{thms rel_simps} 
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val ths = [@{thm "mult_numeral_1"}, @{thm "mult_numeral_1_right"}, 
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@{thm "real_of_nat_number_of"}, 
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@{thm "real_of_nat_Suc"}, @{thm "real_of_nat_one"}, @{thm "real_of_one"}, 
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@{thm "real_of_int_zero"}, @{thm "real_of_nat_zero"}, 
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@{thm "Ring_and_Field.divide_zero"}, 
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@{thm "divide_divide_eq_left"}, @{thm "times_divide_eq_right"}, 
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@{thm "times_divide_eq_left"}, @{thm "divide_divide_eq_right"}, 
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@{thm "diff_def"}, @{thm "minus_divide_left"}] 
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val comp_ths = ths @ comp_arith @ 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_eq = @{thm "mod_add_eq"} RS sym; 
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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 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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val ZDIVISION_BY_ZERO_MOD = @{thm "DIVISION_BY_ZERO"} RS conjunct2; 
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val ZDIVISION_BY_ZERO_DIV = @{thm "DIVISION_BY_ZERO"} RS conjunct1; 
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fun prepare_for_mir thy 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 (rhs,irhs) = List.partition (relevant (rev ps)) 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 mir_tac ctxt q i = 
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(ObjectLogic.atomize_prems_tac i) 
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THEN (simp_tac (HOL_basic_ss addsimps [@{thm "abs_ge_zero"}] addsimps simp_thms) i) 
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THEN (REPEAT_DETERM (split_tac [@{thm "split_min"}, @{thm "split_max"},@{thm "abs_split"}] i)) 

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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_mir thy 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, 
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@{thm "mod_self"}, @{thm "zmod_self"}, 
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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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@{thm "Suc_plus1"}] 
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addsimps @{thms add_ac} 

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addsimprocs [cancel_div_mod_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_ths 
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addsplits [@{thm "split_zdiv"}, @{thm "split_zmod"}, @{thm "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 [@{thm "nat_number_of_def"}, @{thm "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"}, 

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@{thm "zmult_int"}] 

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addsplits [@{thm "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"}, 
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@{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 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), TRY (simp_tac mir_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 = 
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(* If quick_and_dirty then run without proof generation as oracle*) 
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if !quick_and_dirty 
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then mirfr_oracle (false, cterm_of thy (Pattern.eta_long [] t1)) 

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else mirfr_oracle (true, cterm_of thy (Pattern.eta_long [] t1)) 

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in 
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(trace_msg ("calling procedure with term:\n" ^ 
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Syntax.string_of_term ctxt t1); 
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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 mir_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 1) 
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end; 
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fun mir_method ctxt q i = Method.METHOD (fn facts => 
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Method.insert_tac facts 1 THEN mir_tac ctxt q i); 
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val setup = 
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Method.add_method ("mir", 
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mir_args mir_method, 
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"decision procedure for MIR arithmetic"); 
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end 