theory ComputeNumeral
imports ComputeHOL ComputeFloat
begin
(* equality for bit strings *)
lemmas biteq = eq_num_simps
(* x < y for bit strings *)
lemmas bitless = less_num_simps
(* x \<le> y for bit strings *)
lemmas bitle = le_num_simps
(* addition for bit strings *)
lemmas bitadd = add_num_simps
(* multiplication for bit strings *)
lemmas bitmul = mult_num_simps
lemmas bitarith = arith_simps
(* Normalization of nat literals *)
lemmas natnorm = one_eq_Numeral1_nat
fun natfac :: "nat \<Rightarrow> nat"
where "natfac n = (if n = 0 then 1 else n * (natfac (n - 1)))"
lemmas compute_natarith =
arith_simps rel_simps
diff_nat_numeral nat_numeral nat_0 nat_neg_numeral
numeral_1_eq_1 [symmetric]
numeral_1_eq_Suc_0 [symmetric]
Suc_numeral natfac.simps
lemmas number_norm = numeral_1_eq_1[symmetric]
lemmas compute_numberarith =
arith_simps rel_simps number_norm
lemmas compute_num_conversions =
real_of_nat_numeral real_of_nat_zero
nat_numeral nat_0 nat_neg_numeral
real_numeral real_of_int_zero
lemmas zpowerarith = zpower_numeral_even zpower_numeral_odd zpower_Pls int_pow_1
(* div, mod *)
lemmas compute_div_mod = div_0 mod_0 div_by_0 mod_by_0 div_by_1 mod_by_1
one_div_numeral one_mod_numeral minus_one_div_numeral minus_one_mod_numeral
one_div_minus_numeral one_mod_minus_numeral
numeral_div_numeral numeral_mod_numeral minus_numeral_div_numeral minus_numeral_mod_numeral
numeral_div_minus_numeral numeral_mod_minus_numeral
div_minus_minus mod_minus_minus Divides.adjust_div_eq of_bool_eq one_neq_zero
numeral_neq_zero neg_equal_0_iff_equal arith_simps arith_special divmod_trivial
divmod_steps divmod_cancel divmod_step_eq fst_conv snd_conv numeral_One
case_prod_beta rel_simps Divides.adjust_mod_def div_minus1_right mod_minus1_right
minus_minus numeral_times_numeral mult_zero_right mult_1_right
(* collecting all the theorems *)
lemma even_0_int: "even (0::int) = True"
by simp
lemma even_One_int: "even (numeral Num.One :: int) = False"
by simp
lemma even_Bit0_int: "even (numeral (Num.Bit0 x) :: int) = True"
by (simp only: even_numeral)
lemma even_Bit1_int: "even (numeral (Num.Bit1 x) :: int) = False"
by (simp only: odd_numeral)
lemmas compute_even = even_0_int even_One_int even_Bit0_int even_Bit1_int
lemmas compute_numeral = compute_if compute_let compute_pair compute_bool
compute_natarith compute_numberarith max_def min_def compute_num_conversions zpowerarith compute_div_mod compute_even
end