--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Reflection/mir_tac.ML Tue Feb 03 16:50:41 2009 +0100
@@ -0,0 +1,168 @@
+(* Title: HOL/Reflection/mir_tac.ML
+ Author: Amine Chaieb, TU Muenchen
+*)
+
+structure Mir_Tac =
+struct
+
+val trace = ref false;
+fun trace_msg s = if !trace then tracing s else ();
+
+val mir_ss =
+let val ths = map thm ["real_of_int_inject", "real_of_int_less_iff", "real_of_int_le_iff"]
+in @{simpset} delsimps ths addsimps (map (fn th => th RS sym) ths)
+end;
+
+val nT = HOLogic.natT;
+ val nat_arith = map thm ["add_nat_number_of", "diff_nat_number_of",
+ "mult_nat_number_of", "eq_nat_number_of", "less_nat_number_of"];
+
+ val comp_arith = (map thm ["Let_def", "if_False", "if_True", "add_0",
+ "add_Suc", "add_number_of_left", "mult_number_of_left",
+ "Suc_eq_add_numeral_1"])@
+ (map (fn s => thm s RS sym) ["numeral_1_eq_1", "numeral_0_eq_0"])
+ @ @{thms arith_simps} @ nat_arith @ @{thms rel_simps}
+ val ths = [@{thm "mult_numeral_1"}, @{thm "mult_numeral_1_right"},
+ @{thm "real_of_nat_number_of"},
+ @{thm "real_of_nat_Suc"}, @{thm "real_of_nat_one"}, @{thm "real_of_one"},
+ @{thm "real_of_int_zero"}, @{thm "real_of_nat_zero"},
+ @{thm "Ring_and_Field.divide_zero"},
+ @{thm "divide_divide_eq_left"}, @{thm "times_divide_eq_right"},
+ @{thm "times_divide_eq_left"}, @{thm "divide_divide_eq_right"},
+ @{thm "diff_def"}, @{thm "minus_divide_left"}]
+val comp_ths = ths @ comp_arith @ simp_thms
+
+
+val zdvd_int = @{thm "zdvd_int"};
+val zdiff_int_split = @{thm "zdiff_int_split"};
+val all_nat = @{thm "all_nat"};
+val ex_nat = @{thm "ex_nat"};
+val number_of1 = @{thm "number_of1"};
+val number_of2 = @{thm "number_of2"};
+val split_zdiv = @{thm "split_zdiv"};
+val split_zmod = @{thm "split_zmod"};
+val mod_div_equality' = @{thm "mod_div_equality'"};
+val split_div' = @{thm "split_div'"};
+val Suc_plus1 = @{thm "Suc_plus1"};
+val imp_le_cong = @{thm "imp_le_cong"};
+val conj_le_cong = @{thm "conj_le_cong"};
+val nat_mod_add_eq = @{thm "mod_add1_eq"} RS sym;
+val nat_mod_add_left_eq = @{thm "mod_add_left_eq"} RS sym;
+val nat_mod_add_right_eq = @{thm "mod_add_right_eq"} RS sym;
+val int_mod_add_eq = @{thm "zmod_zadd1_eq"} RS sym;
+val int_mod_add_left_eq = @{thm "zmod_zadd_left_eq"} RS sym;
+val int_mod_add_right_eq = @{thm "zmod_zadd_right_eq"} RS sym;
+val nat_div_add_eq = @{thm "div_add1_eq"} RS sym;
+val int_div_add_eq = @{thm "zdiv_zadd1_eq"} RS sym;
+val ZDIVISION_BY_ZERO_MOD = @{thm "DIVISION_BY_ZERO"} RS conjunct2;
+val ZDIVISION_BY_ZERO_DIV = @{thm "DIVISION_BY_ZERO"} RS conjunct1;
+
+fun prepare_for_mir thy q fm =
+ let
+ val ps = Logic.strip_params fm
+ val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm)
+ val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm)
+ fun mk_all ((s, T), (P,n)) =
+ if 0 mem loose_bnos P then
+ (HOLogic.all_const T $ Abs (s, T, P), n)
+ else (incr_boundvars ~1 P, n-1)
+ fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t;
+ val rhs = hs
+(* val (rhs,irhs) = List.partition (relevant (rev ps)) hs *)
+ val np = length ps
+ val (fm',np) = foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n)))
+ (foldr HOLogic.mk_imp c rhs, np) ps
+ val (vs, _) = List.partition (fn t => q orelse (type_of t) = nT)
+ (OldTerm.term_frees fm' @ OldTerm.term_vars fm');
+ val fm2 = foldr mk_all2 fm' vs
+ in (fm2, np + length vs, length rhs) end;
+
+(*Object quantifier to meta --*)
+fun spec_step n th = if (n=0) then th else (spec_step (n-1) th) RS spec ;
+
+(* object implication to meta---*)
+fun mp_step n th = if (n=0) then th else (mp_step (n-1) th) RS mp;
+
+
+fun mir_tac ctxt q i =
+ (ObjectLogic.atomize_prems_tac i)
+ THEN (simp_tac (HOL_basic_ss addsimps [@{thm "abs_ge_zero"}] addsimps simp_thms) i)
+ THEN (REPEAT_DETERM (split_tac [@{thm "split_min"}, @{thm "split_max"},@{thm "abs_split"}] i))
+ THEN (fn st =>
+ let
+ val g = List.nth (prems_of st, i - 1)
+ val thy = ProofContext.theory_of ctxt
+ (* Transform the term*)
+ val (t,np,nh) = prepare_for_mir thy q g
+ (* Some simpsets for dealing with mod div abs and nat*)
+ val mod_div_simpset = HOL_basic_ss
+ addsimps [refl,nat_mod_add_eq,
+ @{thm "mod_self"}, @{thm "zmod_self"},
+ @{thm "zdiv_zero"},@{thm "zmod_zero"},@{thm "div_0"}, @{thm "mod_0"},
+ @{thm "zdiv_1"}, @{thm "zmod_1"}, @{thm "div_1"}, @{thm "mod_1"},
+ @{thm "Suc_plus1"}]
+ addsimps @{thms add_ac}
+ addsimprocs [cancel_div_mod_proc]
+ val simpset0 = HOL_basic_ss
+ addsimps [mod_div_equality', Suc_plus1]
+ addsimps comp_ths
+ addsplits [@{thm "split_zdiv"}, @{thm "split_zmod"}, @{thm "split_div'"}, @{thm "split_min"}, @{thm "split_max"}]
+ (* Simp rules for changing (n::int) to int n *)
+ val simpset1 = HOL_basic_ss
+ addsimps [@{thm "nat_number_of_def"}, @{thm "zdvd_int"}] @ map (fn r => r RS sym)
+ [@{thm "int_int_eq"}, @{thm "zle_int"}, @{thm "zless_int"}, @{thm "zadd_int"},
+ @{thm "zmult_int"}]
+ addsplits [@{thm "zdiff_int_split"}]
+ (*simp rules for elimination of int n*)
+
+ val simpset2 = HOL_basic_ss
+ addsimps [@{thm "nat_0_le"}, @{thm "all_nat"}, @{thm "ex_nat"}, @{thm "number_of1"},
+ @{thm "number_of2"}, @{thm "int_0"}, @{thm "int_1"}]
+ addcongs [@{thm "conj_le_cong"}, @{thm "imp_le_cong"}]
+ (* simp rules for elimination of abs *)
+ val ct = cterm_of thy (HOLogic.mk_Trueprop t)
+ (* Theorem for the nat --> int transformation *)
+ val pre_thm = Seq.hd (EVERY
+ [simp_tac mod_div_simpset 1, simp_tac simpset0 1,
+ TRY (simp_tac simpset1 1), TRY (simp_tac simpset2 1), TRY (simp_tac mir_ss 1)]
+ (trivial ct))
+ fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i)
+ (* The result of the quantifier elimination *)
+ val (th, tac) = case (prop_of pre_thm) of
+ Const ("==>", _) $ (Const ("Trueprop", _) $ t1) $ _ =>
+ let val pth =
+ (* If quick_and_dirty then run without proof generation as oracle*)
+ if !quick_and_dirty
+ then mirfr_oracle (false, cterm_of thy (Pattern.eta_long [] t1))
+ else mirfr_oracle (true, cterm_of thy (Pattern.eta_long [] t1))
+ in
+ (trace_msg ("calling procedure with term:\n" ^
+ Syntax.string_of_term ctxt t1);
+ ((pth RS iffD2) RS pre_thm,
+ assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i)))
+ end
+ | _ => (pre_thm, assm_tac i)
+ in (rtac (((mp_step nh) o (spec_step np)) th) i
+ THEN tac) st
+ end handle Subscript => no_tac st);
+
+fun mir_args meth =
+ let val parse_flag =
+ Args.$$$ "no_quantify" >> (K (K false));
+ in
+ Method.simple_args
+ (Scan.optional (Args.$$$ "(" |-- Scan.repeat1 parse_flag --| Args.$$$ ")") [] >>
+ curry (Library.foldl op |>) true)
+ (fn q => fn ctxt => meth ctxt q 1)
+ end;
+
+fun mir_method ctxt q i = Method.METHOD (fn facts =>
+ Method.insert_tac facts 1 THEN mir_tac ctxt q i);
+
+val setup =
+ Method.add_method ("mir",
+ mir_args mir_method,
+ "decision procedure for MIR arithmetic");
+
+
+end