author | paulson |
Thu, 15 Nov 2001 16:12:49 +0100 | |
changeset 12196 | a3be6b3a9c0b |
parent 11868 | 56db9f3a6b3e |
child 12338 | de0f4a63baa5 |
permissions | -rw-r--r-- |
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(* Title: HOL/nat_simprocs.ML |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 2000 University of Cambridge |
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Simprocs for nat numerals. |
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*) |
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Goal "number_of v + (number_of v' + (k::nat)) = \ |
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\ (if neg (number_of v) then number_of v' + k \ |
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\ else if neg (number_of v') then number_of v + k \ |
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\ else number_of (bin_add v v') + k)"; |
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by (Simp_tac 1); |
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qed "nat_number_of_add_left"; |
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(** For combine_numerals **) |
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Goal "i*u + (j*u + k) = (i+j)*u + (k::nat)"; |
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by (asm_simp_tac (simpset() addsimps [add_mult_distrib]) 1); |
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qed "left_add_mult_distrib"; |
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(** For cancel_numerals **) |
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Goal "j <= (i::nat) ==> ((i*u + m) - (j*u + n)) = (((i-j)*u + m) - n)"; |
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by (asm_simp_tac (simpset() addsplits [nat_diff_split] |
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addsimps [add_mult_distrib]) 1); |
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qed "nat_diff_add_eq1"; |
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Goal "i <= (j::nat) ==> ((i*u + m) - (j*u + n)) = (m - ((j-i)*u + n))"; |
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by (asm_simp_tac (simpset() addsplits [nat_diff_split] |
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addsimps [add_mult_distrib]) 1); |
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qed "nat_diff_add_eq2"; |
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Goal "j <= (i::nat) ==> (i*u + m = j*u + n) = ((i-j)*u + m = n)"; |
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by (auto_tac (claset(), simpset() addsplits [nat_diff_split] |
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addsimps [add_mult_distrib])); |
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qed "nat_eq_add_iff1"; |
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Goal "i <= (j::nat) ==> (i*u + m = j*u + n) = (m = (j-i)*u + n)"; |
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by (auto_tac (claset(), simpset() addsplits [nat_diff_split] |
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addsimps [add_mult_distrib])); |
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qed "nat_eq_add_iff2"; |
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Goal "j <= (i::nat) ==> (i*u + m < j*u + n) = ((i-j)*u + m < n)"; |
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by (auto_tac (claset(), simpset() addsplits [nat_diff_split] |
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addsimps [add_mult_distrib])); |
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qed "nat_less_add_iff1"; |
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Goal "i <= (j::nat) ==> (i*u + m < j*u + n) = (m < (j-i)*u + n)"; |
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by (auto_tac (claset(), simpset() addsplits [nat_diff_split] |
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addsimps [add_mult_distrib])); |
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qed "nat_less_add_iff2"; |
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Goal "j <= (i::nat) ==> (i*u + m <= j*u + n) = ((i-j)*u + m <= n)"; |
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by (auto_tac (claset(), simpset() addsplits [nat_diff_split] |
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addsimps [add_mult_distrib])); |
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qed "nat_le_add_iff1"; |
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Goal "i <= (j::nat) ==> (i*u + m <= j*u + n) = (m <= (j-i)*u + n)"; |
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by (auto_tac (claset(), simpset() addsplits [nat_diff_split] |
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addsimps [add_mult_distrib])); |
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qed "nat_le_add_iff2"; |
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(** For cancel_numeral_factors **) |
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||
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Goal "(0::nat) < k ==> (k*m <= k*n) = (m<=n)"; |
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by Auto_tac; |
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qed "nat_mult_le_cancel1"; |
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||
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Goal "(0::nat) < k ==> (k*m < k*n) = (m<n)"; |
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by Auto_tac; |
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qed "nat_mult_less_cancel1"; |
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||
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Goal "(0::nat) < k ==> (k*m = k*n) = (m=n)"; |
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by Auto_tac; |
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qed "nat_mult_eq_cancel1"; |
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Goal "(0::nat) < k ==> (k*m) div (k*n) = (m div n)"; |
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by Auto_tac; |
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qed "nat_mult_div_cancel1"; |
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(** For cancel_factor **) |
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Goal "(k*m <= k*n) = ((0::nat) < k --> m<=n)"; |
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by Auto_tac; |
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qed "nat_mult_le_cancel_disj"; |
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Goal "(k*m < k*n) = ((0::nat) < k & m<n)"; |
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by Auto_tac; |
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qed "nat_mult_less_cancel_disj"; |
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Goal "(k*m = k*n) = (k = (0::nat) | m=n)"; |
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by Auto_tac; |
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qed "nat_mult_eq_cancel_disj"; |
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Goal "(k*m) div (k*n) = (if k = (0::nat) then 0 else m div n)"; |
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by (simp_tac (simpset() addsimps [nat_mult_div_cancel1]) 1); |
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qed "nat_mult_div_cancel_disj"; |
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structure Nat_Numeral_Simprocs = |
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struct |
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(*Maps n to #n for n = 0, 1, 2*) |
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val numeral_syms = |
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[numeral_0_eq_0 RS sym, numeral_1_eq_1 RS sym, numeral_2_eq_2 RS sym]; |
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val numeral_sym_ss = HOL_ss addsimps numeral_syms; |
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|
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fun rename_numerals th = |
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114 |
simplify numeral_sym_ss (Thm.transfer (the_context ()) th); |
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115 |
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116 |
(*Utilities*) |
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117 |
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10693 | 118 |
fun mk_numeral n = HOLogic.number_of_const HOLogic.natT $ HOLogic.mk_bin n; |
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(*Decodes a unary or binary numeral to a NATURAL NUMBER*) |
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fun dest_numeral (Const ("0", _)) = 0 |
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| dest_numeral (Const ("Suc", _) $ t) = 1 + dest_numeral t |
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| dest_numeral (Const("Numeral.number_of", _) $ w) = |
10890 | 124 |
(BasisLibrary.Int.max (0, HOLogic.dest_binum w) |
125 |
handle TERM _ => raise TERM("Nat_Numeral_Simprocs.dest_numeral:1", [w])) |
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| dest_numeral t = raise TERM("Nat_Numeral_Simprocs.dest_numeral:2", [t]); |
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fun find_first_numeral past (t::terms) = |
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((dest_numeral t, t, rev past @ terms) |
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handle TERM _ => find_first_numeral (t::past) terms) |
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131 |
| find_first_numeral past [] = raise TERM("find_first_numeral", []); |
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val zero = mk_numeral 0; |
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val mk_plus = HOLogic.mk_binop "op +"; |
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136 |
(*Thus mk_sum[t] yields t+0; longer sums don't have a trailing zero*) |
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fun mk_sum [] = zero |
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| mk_sum [t,u] = mk_plus (t, u) |
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| mk_sum (t :: ts) = mk_plus (t, mk_sum ts); |
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141 |
(*this version ALWAYS includes a trailing zero*) |
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142 |
fun long_mk_sum [] = HOLogic.zero |
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| long_mk_sum (t :: ts) = mk_plus (t, mk_sum ts); |
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val dest_plus = HOLogic.dest_bin "op +" HOLogic.natT; |
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(*extract the outer Sucs from a term and convert them to a binary numeral*) |
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148 |
fun dest_Sucs (k, Const ("Suc", _) $ t) = dest_Sucs (k+1, t) |
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| dest_Sucs (0, t) = t |
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| dest_Sucs (k, t) = mk_plus (mk_numeral k, t); |
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|
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fun dest_sum t = |
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let val (t,u) = dest_plus t |
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154 |
in dest_sum t @ dest_sum u end |
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handle TERM _ => [t]; |
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|
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fun dest_Sucs_sum t = dest_sum (dest_Sucs (0,t)); |
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158 |
|
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159 |
|
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(** Other simproc items **) |
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161 |
|
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val trans_tac = Int_Numeral_Simprocs.trans_tac; |
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|
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val bin_simps = [numeral_0_eq_0 RS sym, numeral_1_eq_1 RS sym, |
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add_nat_number_of, nat_number_of_add_left, |
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diff_nat_number_of, le_nat_number_of_eq_not_less, |
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less_nat_number_of, mult_nat_number_of, |
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thm "Let_number_of", nat_number_of] @ |
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bin_arith_simps @ bin_rel_simps; |
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|
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fun prep_simproc (name, pats, proc) = Simplifier.mk_simproc name pats proc; |
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fun prep_pat s = Thm.read_cterm (Theory.sign_of (the_context ())) |
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(s, HOLogic.termT); |
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val prep_pats = map prep_pat; |
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|
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|
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177 |
(*** CancelNumerals simprocs ***) |
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|
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val one = mk_numeral 1; |
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val mk_times = HOLogic.mk_binop "op *"; |
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|
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fun mk_prod [] = one |
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| mk_prod [t] = t |
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| mk_prod (t :: ts) = if t = one then mk_prod ts |
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else mk_times (t, mk_prod ts); |
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186 |
|
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val dest_times = HOLogic.dest_bin "op *" HOLogic.natT; |
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|
188 |
|
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189 |
fun dest_prod t = |
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let val (t,u) = dest_times t |
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191 |
in dest_prod t @ dest_prod u end |
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192 |
handle TERM _ => [t]; |
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193 |
|
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|
194 |
(*DON'T do the obvious simplifications; that would create special cases*) |
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195 |
fun mk_coeff (k,t) = mk_times (mk_numeral k, t); |
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|
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197 |
(*Express t as a product of (possibly) a numeral with other factors, sorted*) |
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198 |
fun dest_coeff t = |
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199 |
let val ts = sort Term.term_ord (dest_prod t) |
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|
200 |
val (n, _, ts') = find_first_numeral [] ts |
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201 |
handle TERM _ => (1, one, ts) |
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|
202 |
in (n, mk_prod ts') end; |
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|
203 |
|
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204 |
(*Find first coefficient-term THAT MATCHES u*) |
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205 |
fun find_first_coeff past u [] = raise TERM("find_first_coeff", []) |
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|
206 |
| find_first_coeff past u (t::terms) = |
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207 |
let val (n,u') = dest_coeff t |
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|
208 |
in if u aconv u' then (n, rev past @ terms) |
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|
209 |
else find_first_coeff (t::past) u terms |
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|
210 |
end |
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|
211 |
handle TERM _ => find_first_coeff (t::past) u terms; |
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|
212 |
|
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|
213 |
|
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|
214 |
(*Simplify 1*n and n*1 to n*) |
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|
215 |
val add_0s = map rename_numerals [add_0, add_0_right]; |
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|
216 |
val mult_1s = map rename_numerals [mult_1, mult_1_right]; |
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|
217 |
|
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|
218 |
(*Final simplification: cancel + and *; replace Numeral0 by 0 and Numeral1 by 1*) |
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|
219 |
val simplify_meta_eq = |
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|
220 |
Int_Numeral_Simprocs.simplify_meta_eq |
11868
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|
221 |
[numeral_0_eq_0, numeral_1_eq_Suc_0, add_0, add_0_right, |
9436
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|
222 |
mult_0, mult_0_right, mult_1, mult_1_right]; |
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|
223 |
|
10536 | 224 |
|
11377
0f16ad464c62
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diff
changeset
|
225 |
(** Restricted version of dest_Sucs_sum for nat_combine_numerals: |
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|
226 |
Simprocs never apply unless the original expression contains at least one |
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|
227 |
numeral in a coefficient position. |
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diff
changeset
|
228 |
**) |
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|
229 |
|
12196 | 230 |
fun ignore_Sucs (Const ("Suc", _) $ t) = ignore_Sucs t |
231 |
| ignore_Sucs t = t; |
|
232 |
||
11377
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|
233 |
fun is_numeral (Const("Numeral.number_of", _) $ w) = true |
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diff
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|
234 |
| is_numeral _ = false; |
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diff
changeset
|
235 |
|
0f16ad464c62
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diff
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|
236 |
fun prod_has_numeral t = exists is_numeral (dest_prod t); |
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|
237 |
|
0f16ad464c62
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diff
changeset
|
238 |
fun restricted_dest_Sucs_sum t = |
12196 | 239 |
if exists prod_has_numeral (dest_sum (ignore_Sucs t)) |
240 |
then dest_Sucs_sum t |
|
241 |
else raise TERM("Nat_Numeral_Simprocs.restricted_dest_Sucs_sum", [t]); |
|
11377
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changeset
|
242 |
|
0f16ad464c62
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parents:
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diff
changeset
|
243 |
|
10704 | 244 |
(*** Applying CancelNumeralsFun ***) |
10536 | 245 |
|
9436
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|
246 |
structure CancelNumeralsCommon = |
62bb04ab4b01
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|
247 |
struct |
62bb04ab4b01
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|
248 |
val mk_sum = mk_sum |
62bb04ab4b01
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|
249 |
val dest_sum = dest_Sucs_sum |
62bb04ab4b01
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diff
changeset
|
250 |
val mk_coeff = mk_coeff |
62bb04ab4b01
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diff
changeset
|
251 |
val dest_coeff = dest_coeff |
62bb04ab4b01
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|
252 |
val find_first_coeff = find_first_coeff [] |
62bb04ab4b01
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parents:
diff
changeset
|
253 |
val trans_tac = trans_tac |
62bb04ab4b01
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wenzelm
parents:
diff
changeset
|
254 |
val norm_tac = ALLGOALS |
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11704
diff
changeset
|
255 |
(simp_tac (HOL_ss addsimps numeral_syms@add_0s@mult_1s@ |
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11704
diff
changeset
|
256 |
[Suc_eq_add_numeral_1] @ add_ac)) |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
257 |
THEN ALLGOALS (simp_tac |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
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diff
changeset
|
258 |
(HOL_ss addsimps bin_simps@add_ac@mult_ac)) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
259 |
val numeral_simp_tac = ALLGOALS |
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
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diff
changeset
|
260 |
(simp_tac (HOL_ss addsimps add_0s@bin_simps)) |
9436
62bb04ab4b01
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parents:
diff
changeset
|
261 |
val simplify_meta_eq = simplify_meta_eq |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
262 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
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parents:
diff
changeset
|
263 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
264 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
265 |
structure EqCancelNumerals = CancelNumeralsFun |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
266 |
(open CancelNumeralsCommon |
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11704
diff
changeset
|
267 |
val prove_conv = Bin_Simprocs.prove_conv "nateq_cancel_numerals" |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
268 |
val mk_bal = HOLogic.mk_eq |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
269 |
val dest_bal = HOLogic.dest_bin "op =" HOLogic.natT |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
270 |
val bal_add1 = nat_eq_add_iff1 RS trans |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
271 |
val bal_add2 = nat_eq_add_iff2 RS trans |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
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parents:
diff
changeset
|
272 |
); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
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parents:
diff
changeset
|
273 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
274 |
structure LessCancelNumerals = CancelNumeralsFun |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
275 |
(open CancelNumeralsCommon |
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11704
diff
changeset
|
276 |
val prove_conv = Bin_Simprocs.prove_conv "natless_cancel_numerals" |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
277 |
val mk_bal = HOLogic.mk_binrel "op <" |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
278 |
val dest_bal = HOLogic.dest_bin "op <" HOLogic.natT |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
279 |
val bal_add1 = nat_less_add_iff1 RS trans |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
280 |
val bal_add2 = nat_less_add_iff2 RS trans |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
281 |
); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
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parents:
diff
changeset
|
282 |
|
62bb04ab4b01
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283 |
structure LeCancelNumerals = CancelNumeralsFun |
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284 |
(open CancelNumeralsCommon |
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285 |
val prove_conv = Bin_Simprocs.prove_conv "natle_cancel_numerals" |
9436
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286 |
val mk_bal = HOLogic.mk_binrel "op <=" |
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val dest_bal = HOLogic.dest_bin "op <=" HOLogic.natT |
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val bal_add1 = nat_le_add_iff1 RS trans |
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289 |
val bal_add2 = nat_le_add_iff2 RS trans |
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290 |
); |
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291 |
|
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292 |
structure DiffCancelNumerals = CancelNumeralsFun |
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293 |
(open CancelNumeralsCommon |
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|
294 |
val prove_conv = Bin_Simprocs.prove_conv "natdiff_cancel_numerals" |
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val mk_bal = HOLogic.mk_binop "op -" |
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val dest_bal = HOLogic.dest_bin "op -" HOLogic.natT |
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val bal_add1 = nat_diff_add_eq1 RS trans |
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298 |
val bal_add2 = nat_diff_add_eq2 RS trans |
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299 |
); |
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300 |
|
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301 |
|
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val cancel_numerals = |
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|
303 |
map prep_simproc |
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[("nateq_cancel_numerals", |
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prep_pats ["(l::nat) + m = n", "(l::nat) = m + n", |
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306 |
"(l::nat) * m = n", "(l::nat) = m * n", |
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307 |
"Suc m = n", "m = Suc n"], |
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|
308 |
EqCancelNumerals.proc), |
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|
309 |
("natless_cancel_numerals", |
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|
310 |
prep_pats ["(l::nat) + m < n", "(l::nat) < m + n", |
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311 |
"(l::nat) * m < n", "(l::nat) < m * n", |
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"Suc m < n", "m < Suc n"], |
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|
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LessCancelNumerals.proc), |
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|
314 |
("natle_cancel_numerals", |
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|
315 |
prep_pats ["(l::nat) + m <= n", "(l::nat) <= m + n", |
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|
316 |
"(l::nat) * m <= n", "(l::nat) <= m * n", |
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|
317 |
"Suc m <= n", "m <= Suc n"], |
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|
318 |
LeCancelNumerals.proc), |
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|
319 |
("natdiff_cancel_numerals", |
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|
320 |
prep_pats ["((l::nat) + m) - n", "(l::nat) - (m + n)", |
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|
321 |
"(l::nat) * m - n", "(l::nat) - m * n", |
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|
322 |
"Suc m - n", "m - Suc n"], |
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|
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DiffCancelNumerals.proc)]; |
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324 |
|
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325 |
|
10704 | 326 |
(*** Applying CombineNumeralsFun ***) |
10536 | 327 |
|
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328 |
structure CombineNumeralsData = |
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|
329 |
struct |
9571 | 330 |
val add = op + : int*int -> int |
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changeset
|
331 |
val mk_sum = long_mk_sum (*to work for e.g. 2*x + 3*x *) |
11377
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|
332 |
val dest_sum = restricted_dest_Sucs_sum |
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333 |
val mk_coeff = mk_coeff |
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val dest_coeff = dest_coeff |
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|
335 |
val left_distrib = left_add_mult_distrib RS trans |
11868
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Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
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parents:
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diff
changeset
|
336 |
val prove_conv = Bin_Simprocs.prove_conv_nohyps "nat_combine_numerals" |
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val trans_tac = trans_tac |
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|
338 |
val norm_tac = ALLGOALS |
11868
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parents:
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diff
changeset
|
339 |
(simp_tac (HOL_ss addsimps numeral_syms@add_0s@mult_1s@ |
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|
340 |
[Suc_eq_add_numeral_1] @ add_ac)) |
9436
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|
341 |
THEN ALLGOALS (simp_tac |
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342 |
(HOL_ss addsimps bin_simps@add_ac@mult_ac)) |
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|
343 |
val numeral_simp_tac = ALLGOALS |
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|
344 |
(simp_tac (HOL_ss addsimps add_0s@bin_simps)) |
9436
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|
345 |
val simplify_meta_eq = simplify_meta_eq |
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346 |
end; |
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|
347 |
|
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348 |
structure CombineNumerals = CombineNumeralsFun(CombineNumeralsData); |
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349 |
|
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|
350 |
val combine_numerals = |
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|
351 |
prep_simproc ("nat_combine_numerals", |
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|
352 |
prep_pats ["(i::nat) + j", "Suc (i + j)"], |
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|
353 |
CombineNumerals.proc); |
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|
354 |
|
10536 | 355 |
|
10704 | 356 |
(*** Applying CancelNumeralFactorFun ***) |
10536 | 357 |
|
358 |
structure CancelNumeralFactorCommon = |
|
359 |
struct |
|
360 |
val mk_coeff = mk_coeff |
|
361 |
val dest_coeff = dest_coeff |
|
362 |
val trans_tac = trans_tac |
|
11868
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paulson
parents:
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diff
changeset
|
363 |
val norm_tac = ALLGOALS |
56db9f3a6b3e
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paulson
parents:
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diff
changeset
|
364 |
(simp_tac (HOL_ss addsimps [Suc_eq_add_numeral_1]@mult_1s)) |
10536 | 365 |
THEN ALLGOALS (simp_tac (HOL_ss addsimps bin_simps@mult_ac)) |
366 |
val numeral_simp_tac = ALLGOALS (simp_tac (HOL_ss addsimps bin_simps)) |
|
367 |
val simplify_meta_eq = simplify_meta_eq |
|
368 |
end |
|
369 |
||
370 |
structure DivCancelNumeralFactor = CancelNumeralFactorFun |
|
371 |
(open CancelNumeralFactorCommon |
|
11868
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paulson
parents:
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diff
changeset
|
372 |
val prove_conv = Bin_Simprocs.prove_conv "natdiv_cancel_numeral_factor" |
10536 | 373 |
val mk_bal = HOLogic.mk_binop "Divides.op div" |
374 |
val dest_bal = HOLogic.dest_bin "Divides.op div" HOLogic.natT |
|
375 |
val cancel = nat_mult_div_cancel1 RS trans |
|
376 |
val neg_exchanges = false |
|
377 |
) |
|
378 |
||
379 |
structure EqCancelNumeralFactor = CancelNumeralFactorFun |
|
380 |
(open CancelNumeralFactorCommon |
|
11868
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paulson
parents:
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diff
changeset
|
381 |
val prove_conv = Bin_Simprocs.prove_conv "nateq_cancel_numeral_factor" |
10536 | 382 |
val mk_bal = HOLogic.mk_eq |
383 |
val dest_bal = HOLogic.dest_bin "op =" HOLogic.natT |
|
384 |
val cancel = nat_mult_eq_cancel1 RS trans |
|
385 |
val neg_exchanges = false |
|
386 |
) |
|
387 |
||
388 |
structure LessCancelNumeralFactor = CancelNumeralFactorFun |
|
389 |
(open CancelNumeralFactorCommon |
|
11868
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Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11704
diff
changeset
|
390 |
val prove_conv = Bin_Simprocs.prove_conv "natless_cancel_numeral_factor" |
10536 | 391 |
val mk_bal = HOLogic.mk_binrel "op <" |
392 |
val dest_bal = HOLogic.dest_bin "op <" HOLogic.natT |
|
393 |
val cancel = nat_mult_less_cancel1 RS trans |
|
394 |
val neg_exchanges = true |
|
395 |
) |
|
396 |
||
397 |
structure LeCancelNumeralFactor = CancelNumeralFactorFun |
|
398 |
(open CancelNumeralFactorCommon |
|
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11704
diff
changeset
|
399 |
val prove_conv = Bin_Simprocs.prove_conv "natle_cancel_numeral_factor" |
10536 | 400 |
val mk_bal = HOLogic.mk_binrel "op <=" |
401 |
val dest_bal = HOLogic.dest_bin "op <=" HOLogic.natT |
|
402 |
val cancel = nat_mult_le_cancel1 RS trans |
|
403 |
val neg_exchanges = true |
|
404 |
) |
|
405 |
||
406 |
val cancel_numeral_factors = |
|
407 |
map prep_simproc |
|
408 |
[("nateq_cancel_numeral_factors", |
|
409 |
prep_pats ["(l::nat) * m = n", "(l::nat) = m * n"], |
|
410 |
EqCancelNumeralFactor.proc), |
|
411 |
("natless_cancel_numeral_factors", |
|
412 |
prep_pats ["(l::nat) * m < n", "(l::nat) < m * n"], |
|
413 |
LessCancelNumeralFactor.proc), |
|
414 |
("natle_cancel_numeral_factors", |
|
415 |
prep_pats ["(l::nat) * m <= n", "(l::nat) <= m * n"], |
|
416 |
LeCancelNumeralFactor.proc), |
|
417 |
("natdiv_cancel_numeral_factors", |
|
418 |
prep_pats ["((l::nat) * m) div n", "(l::nat) div (m * n)"], |
|
419 |
DivCancelNumeralFactor.proc)]; |
|
420 |
||
10704 | 421 |
|
422 |
||
423 |
(*** Applying ExtractCommonTermFun ***) |
|
424 |
||
425 |
(*this version ALWAYS includes a trailing one*) |
|
426 |
fun long_mk_prod [] = one |
|
427 |
| long_mk_prod (t :: ts) = mk_times (t, mk_prod ts); |
|
428 |
||
429 |
(*Find first term that matches u*) |
|
430 |
fun find_first past u [] = raise TERM("find_first", []) |
|
431 |
| find_first past u (t::terms) = |
|
432 |
if u aconv t then (rev past @ terms) |
|
433 |
else find_first (t::past) u terms |
|
434 |
handle TERM _ => find_first (t::past) u terms; |
|
435 |
||
436 |
(*Final simplification: cancel + and * *) |
|
437 |
fun cancel_simplify_meta_eq cancel_th th = |
|
438 |
Int_Numeral_Simprocs.simplify_meta_eq [zmult_1, zmult_1_right] |
|
439 |
(([th, cancel_th]) MRS trans); |
|
440 |
||
441 |
structure CancelFactorCommon = |
|
442 |
struct |
|
443 |
val mk_sum = long_mk_prod |
|
444 |
val dest_sum = dest_prod |
|
445 |
val mk_coeff = mk_coeff |
|
446 |
val dest_coeff = dest_coeff |
|
447 |
val find_first = find_first [] |
|
448 |
val trans_tac = trans_tac |
|
449 |
val norm_tac = ALLGOALS (simp_tac (HOL_ss addsimps mult_1s@mult_ac)) |
|
450 |
end; |
|
451 |
||
452 |
structure EqCancelFactor = ExtractCommonTermFun |
|
453 |
(open CancelFactorCommon |
|
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11704
diff
changeset
|
454 |
val prove_conv = Bin_Simprocs.prove_conv "nat_eq_cancel_factor" |
10704 | 455 |
val mk_bal = HOLogic.mk_eq |
456 |
val dest_bal = HOLogic.dest_bin "op =" HOLogic.natT |
|
457 |
val simplify_meta_eq = cancel_simplify_meta_eq nat_mult_eq_cancel_disj |
|
458 |
); |
|
459 |
||
460 |
structure LessCancelFactor = ExtractCommonTermFun |
|
461 |
(open CancelFactorCommon |
|
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11704
diff
changeset
|
462 |
val prove_conv = Bin_Simprocs.prove_conv "nat_less_cancel_factor" |
10704 | 463 |
val mk_bal = HOLogic.mk_binrel "op <" |
464 |
val dest_bal = HOLogic.dest_bin "op <" HOLogic.natT |
|
465 |
val simplify_meta_eq = cancel_simplify_meta_eq nat_mult_less_cancel_disj |
|
466 |
); |
|
467 |
||
468 |
structure LeCancelFactor = ExtractCommonTermFun |
|
469 |
(open CancelFactorCommon |
|
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11704
diff
changeset
|
470 |
val prove_conv = Bin_Simprocs.prove_conv "nat_leq_cancel_factor" |
10704 | 471 |
val mk_bal = HOLogic.mk_binrel "op <=" |
472 |
val dest_bal = HOLogic.dest_bin "op <=" HOLogic.natT |
|
473 |
val simplify_meta_eq = cancel_simplify_meta_eq nat_mult_le_cancel_disj |
|
474 |
); |
|
475 |
||
476 |
structure DivideCancelFactor = ExtractCommonTermFun |
|
477 |
(open CancelFactorCommon |
|
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11704
diff
changeset
|
478 |
val prove_conv = Bin_Simprocs.prove_conv "nat_divide_cancel_factor" |
10704 | 479 |
val mk_bal = HOLogic.mk_binop "Divides.op div" |
480 |
val dest_bal = HOLogic.dest_bin "Divides.op div" HOLogic.natT |
|
481 |
val simplify_meta_eq = cancel_simplify_meta_eq nat_mult_div_cancel_disj |
|
482 |
); |
|
483 |
||
484 |
val cancel_factor = |
|
485 |
map prep_simproc |
|
486 |
[("nat_eq_cancel_factor", |
|
487 |
prep_pats ["(l::nat) * m = n", "(l::nat) = m * n"], |
|
488 |
EqCancelFactor.proc), |
|
489 |
("nat_less_cancel_factor", |
|
490 |
prep_pats ["(l::nat) * m < n", "(l::nat) < m * n"], |
|
491 |
LessCancelFactor.proc), |
|
492 |
("nat_le_cancel_factor", |
|
493 |
prep_pats ["(l::nat) * m <= n", "(l::nat) <= m * n"], |
|
494 |
LeCancelFactor.proc), |
|
495 |
("nat_divide_cancel_factor", |
|
496 |
prep_pats ["((l::nat) * m) div n", "(l::nat) div (m * n)"], |
|
497 |
DivideCancelFactor.proc)]; |
|
498 |
||
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
499 |
end; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
500 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
501 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
502 |
Addsimprocs Nat_Numeral_Simprocs.cancel_numerals; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
503 |
Addsimprocs [Nat_Numeral_Simprocs.combine_numerals]; |
10536 | 504 |
Addsimprocs Nat_Numeral_Simprocs.cancel_numeral_factors; |
10704 | 505 |
Addsimprocs Nat_Numeral_Simprocs.cancel_factor; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
506 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
507 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
508 |
(*examples: |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
509 |
print_depth 22; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
510 |
set timing; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
511 |
set trace_simp; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
512 |
fun test s = (Goal s; by (Simp_tac 1)); |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
513 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
514 |
(*cancel_numerals*) |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
515 |
test "l +( 2) + (2) + 2 + (l + 2) + (oo + 2) = (uu::nat)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
516 |
test "(2*length xs < 2*length xs + j)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
517 |
test "(2*length xs < length xs * 2 + j)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
518 |
test "2*u = (u::nat)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
519 |
test "2*u = Suc (u)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
520 |
test "(i + j + 12 + (k::nat)) - 15 = y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
521 |
test "(i + j + 12 + (k::nat)) - 5 = y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
522 |
test "Suc u - 2 = y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
523 |
test "Suc (Suc (Suc u)) - 2 = y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
524 |
test "(i + j + 2 + (k::nat)) - 1 = y"; |
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11704
diff
changeset
|
525 |
test "(i + j + 1 + (k::nat)) - 2 = y"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
526 |
|
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
527 |
test "(2*x + (u*v) + y) - v*3*u = (w::nat)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
528 |
test "(2*x*u*v + 5 + (u*v)*4 + y) - v*u*4 = (w::nat)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
529 |
test "(2*x*u*v + (u*v)*4 + y) - v*u = (w::nat)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
530 |
test "Suc (Suc (2*x*u*v + u*4 + y)) - u = w"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
531 |
test "Suc ((u*v)*4) - v*3*u = w"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
532 |
test "Suc (Suc ((u*v)*3)) - v*3*u = w"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
533 |
|
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
534 |
test "(i + j + 12 + (k::nat)) = u + 15 + y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
535 |
test "(i + j + 32 + (k::nat)) - (u + 15 + y) = zz"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
536 |
test "(i + j + 12 + (k::nat)) = u + 5 + y"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
537 |
(*Suc*) |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
538 |
test "(i + j + 12 + k) = Suc (u + y)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
539 |
test "Suc (Suc (Suc (Suc (Suc (u + y))))) <= ((i + j) + 41 + k)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
540 |
test "(i + j + 5 + k) < Suc (Suc (Suc (Suc (Suc (u + y)))))"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
541 |
test "Suc (Suc (Suc (Suc (Suc (u + y))))) - 5 = v"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
542 |
test "(i + j + 5 + k) = Suc (Suc (Suc (Suc (Suc (Suc (Suc (u + y)))))))"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
543 |
test "2*y + 3*z + 2*u = Suc (u)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
544 |
test "2*y + 3*z + 6*w + 2*y + 3*z + 2*u = Suc (u)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
545 |
test "2*y + 3*z + 6*w + 2*y + 3*z + 2*u = 2*y' + 3*z' + 6*w' + 2*y' + 3*z' + u + (vv::nat)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
546 |
test "6 + 2*y + 3*z + 4*u = Suc (vv + 2*u + z)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
547 |
test "(2*n*m) < (3*(m*n)) + (u::nat)"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
548 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
549 |
(*negative numerals: FAIL*) |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
550 |
test "(i + j + -23 + (k::nat)) < u + 15 + y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
551 |
test "(i + j + 3 + (k::nat)) < u + -15 + y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
552 |
test "(i + j + -12 + (k::nat)) - 15 = y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
553 |
test "(i + j + 12 + (k::nat)) - -15 = y"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
554 |
test "(i + j + -12 + (k::nat)) - -15 = y"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
555 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
556 |
(*combine_numerals*) |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
557 |
test "k + 3*k = (u::nat)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
558 |
test "Suc (i + 3) = u"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
559 |
test "Suc (i + j + 3 + k) = u"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
560 |
test "k + j + 3*k + j = (u::nat)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
561 |
test "Suc (j*i + i + k + 5 + 3*k + i*j*4) = (u::nat)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
562 |
test "(2*n*m) + (3*(m*n)) = (u::nat)"; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
563 |
(*negative numerals: FAIL*) |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
564 |
test "Suc (i + j + -3 + k) = u"; |
10536 | 565 |
|
10704 | 566 |
(*cancel_numeral_factors*) |
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
567 |
test "9*x = 12 * (y::nat)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
568 |
test "(9*x) div (12 * (y::nat)) = z"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
569 |
test "9*x < 12 * (y::nat)"; |
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
|
570 |
test "9*x <= 12 * (y::nat)"; |
10704 | 571 |
|
572 |
(*cancel_factor*) |
|
573 |
test "x*k = k*(y::nat)"; |
|
574 |
test "k = k*(y::nat)"; |
|
575 |
test "a*(b*c) = (b::nat)"; |
|
576 |
test "a*(b*c) = d*(b::nat)*(x*a)"; |
|
577 |
||
578 |
test "x*k < k*(y::nat)"; |
|
579 |
test "k < k*(y::nat)"; |
|
580 |
test "a*(b*c) < (b::nat)"; |
|
581 |
test "a*(b*c) < d*(b::nat)*(x*a)"; |
|
582 |
||
583 |
test "x*k <= k*(y::nat)"; |
|
584 |
test "k <= k*(y::nat)"; |
|
585 |
test "a*(b*c) <= (b::nat)"; |
|
586 |
test "a*(b*c) <= d*(b::nat)*(x*a)"; |
|
587 |
||
588 |
test "(x*k) div (k*(y::nat)) = (uu::nat)"; |
|
589 |
test "(k) div (k*(y::nat)) = (uu::nat)"; |
|
590 |
test "(a*(b*c)) div ((b::nat)) = (uu::nat)"; |
|
591 |
test "(a*(b*c)) div (d*(b::nat)*(x*a)) = (uu::nat)"; |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
592 |
*) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
593 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
594 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
595 |
(*** Prepare linear arithmetic for nat numerals ***) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
596 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
597 |
local |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
598 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
599 |
(* reduce contradictory <= to False *) |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
600 |
val add_rules = |
11868
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11704
diff
changeset
|
601 |
[thm "Let_number_of", thm "Let_0", thm "Let_1", nat_0, nat_1, |
56db9f3a6b3e
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
paulson
parents:
11704
diff
changeset
|
602 |
add_nat_number_of, diff_nat_number_of, mult_nat_number_of, |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
603 |
eq_nat_number_of, less_nat_number_of, le_nat_number_of_eq_not_less, |
11296 | 604 |
le_Suc_number_of,le_number_of_Suc, |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
605 |
less_Suc_number_of,less_number_of_Suc, |
11296 | 606 |
Suc_eq_number_of,eq_number_of_Suc, |
11334
a16eaf2a1edd
Allow Suc-numerals as coefficients in lin-arith formulae
nipkow
parents:
11297
diff
changeset
|
607 |
mult_0, mult_0_right, mult_Suc, mult_Suc_right, |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
608 |
eq_number_of_0, eq_0_number_of, less_0_number_of, |
11701
3d51fbf81c17
sane numerals (stage 1): added generic 1, removed 1' and 2 on nat,
wenzelm
parents:
11377
diff
changeset
|
609 |
nat_number_of, thm "Let_number_of", if_True, if_False]; |
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
610 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
611 |
val simprocs = [Nat_Times_Assoc.conv, |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
612 |
Nat_Numeral_Simprocs.combine_numerals]@ |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
613 |
Nat_Numeral_Simprocs.cancel_numerals; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
614 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
615 |
in |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
616 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
617 |
val nat_simprocs_setup = |
10693 | 618 |
[Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, simpset} => |
619 |
{add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, |
|
620 |
inj_thms = inj_thms, lessD = lessD, |
|
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
621 |
simpset = simpset addsimps add_rules |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
622 |
addsimprocs simprocs})]; |
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
623 |
|
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset
|
624 |
end; |