# HG changeset patch
# User huffman
# Date 1320835482 -3600
# Node ID 62bc9474d04b9a9e3a2c3d624cccab2cf931d600
# Parent  d660c4b9daa6c9bae57d73b2ebe21bc2c60f303a
use simproc_setup for some nat_numeral simprocs; add simproc tests

diff -r d660c4b9daa6 -r 62bc9474d04b src/HOL/Numeral_Simprocs.thy
--- a/src/HOL/Numeral_Simprocs.thy	Wed Nov 09 10:58:08 2011 +0100
+++ b/src/HOL/Numeral_Simprocs.thy	Wed Nov 09 11:44:42 2011 +0100
@@ -202,6 +202,30 @@
 
 use "Tools/nat_numeral_simprocs.ML"
 
+simproc_setup nateq_cancel_numerals
+  ("(l::nat) + m = n" | "(l::nat) = m + n" |
+   "(l::nat) * m = n" | "(l::nat) = m * n" |
+   "Suc m = n" | "m = Suc n") =
+  {* fn phi => Nat_Numeral_Simprocs.eq_cancel_numerals *}
+
+simproc_setup natless_cancel_numerals
+  ("(l::nat) + m < n" | "(l::nat) < m + n" |
+   "(l::nat) * m < n" | "(l::nat) < m * n" |
+   "Suc m < n" | "m < Suc n") =
+  {* fn phi => Nat_Numeral_Simprocs.less_cancel_numerals *}
+
+simproc_setup natle_cancel_numerals
+  ("(l::nat) + m \<le> n" | "(l::nat) \<le> m + n" |
+   "(l::nat) * m \<le> n" | "(l::nat) \<le> m * n" |
+   "Suc m \<le> n" | "m \<le> Suc n") =
+  {* fn phi => Nat_Numeral_Simprocs.le_cancel_numerals *}
+
+simproc_setup natdiff_cancel_numerals
+  ("((l::nat) + m) - n" | "(l::nat) - (m + n)" |
+   "(l::nat) * m - n" | "(l::nat) - m * n" |
+   "Suc m - n" | "m - Suc n") =
+  {* fn phi => Nat_Numeral_Simprocs.diff_cancel_numerals *}
+
 declaration {* 
   K (Lin_Arith.add_simps (@{thms neg_simps} @ [@{thm Suc_nat_number_of}, @{thm int_nat_number_of}])
   #> Lin_Arith.add_simps (@{thms ring_distribs} @ [@{thm Let_number_of}, @{thm Let_0}, @{thm Let_1},
@@ -222,7 +246,12 @@
        @{simproc inteq_cancel_numerals},
        @{simproc intless_cancel_numerals},
        @{simproc intle_cancel_numerals}]
-  #> Lin_Arith.add_simprocs (Nat_Numeral_Simprocs.combine_numerals :: Nat_Numeral_Simprocs.cancel_numerals))
+  #> Lin_Arith.add_simprocs
+      [Nat_Numeral_Simprocs.combine_numerals,
+       @{simproc nateq_cancel_numerals},
+       @{simproc natless_cancel_numerals},
+       @{simproc natle_cancel_numerals},
+       @{simproc natdiff_cancel_numerals}])
 *}
 
 end
diff -r d660c4b9daa6 -r 62bc9474d04b src/HOL/Tools/nat_numeral_simprocs.ML
--- a/src/HOL/Tools/nat_numeral_simprocs.ML	Wed Nov 09 10:58:08 2011 +0100
+++ b/src/HOL/Tools/nat_numeral_simprocs.ML	Wed Nov 09 11:44:42 2011 +0100
@@ -6,7 +6,10 @@
 signature NAT_NUMERAL_SIMPROCS =
 sig
   val combine_numerals: simproc
-  val cancel_numerals: simproc list
+  val eq_cancel_numerals: simpset -> cterm -> thm option
+  val less_cancel_numerals: simpset -> cterm -> thm option
+  val le_cancel_numerals: simpset -> cterm -> thm option
+  val diff_cancel_numerals: simpset -> cterm -> thm option
   val cancel_factors: simproc list
   val cancel_numeral_factors: simproc list
 end;
@@ -195,29 +198,10 @@
   val bal_add2 = @{thm nat_diff_add_eq2} RS trans
 );
 
-
-val cancel_numerals =
-  map (Numeral_Simprocs.prep_simproc @{theory})
-   [("nateq_cancel_numerals",
-     ["(l::nat) + m = n", "(l::nat) = m + n",
-      "(l::nat) * m = n", "(l::nat) = m * n",
-      "Suc m = n", "m = Suc n"],
-     K EqCancelNumerals.proc),
-    ("natless_cancel_numerals",
-     ["(l::nat) + m < n", "(l::nat) < m + n",
-      "(l::nat) * m < n", "(l::nat) < m * n",
-      "Suc m < n", "m < Suc n"],
-     K LessCancelNumerals.proc),
-    ("natle_cancel_numerals",
-     ["(l::nat) + m <= n", "(l::nat) <= m + n",
-      "(l::nat) * m <= n", "(l::nat) <= m * n",
-      "Suc m <= n", "m <= Suc n"],
-     K LeCancelNumerals.proc),
-    ("natdiff_cancel_numerals",
-     ["((l::nat) + m) - n", "(l::nat) - (m + n)",
-      "(l::nat) * m - n", "(l::nat) - m * n",
-      "Suc m - n", "m - Suc n"],
-     K DiffCancelNumerals.proc)];
+fun eq_cancel_numerals ss ct = EqCancelNumerals.proc ss (term_of ct)
+fun less_cancel_numerals ss ct = LessCancelNumerals.proc ss (term_of ct)
+fun le_cancel_numerals ss ct = LeCancelNumerals.proc ss (term_of ct)
+fun diff_cancel_numerals ss ct = DiffCancelNumerals.proc ss (term_of ct)
 
 
 (*** Applying CombineNumeralsFun ***)
@@ -424,7 +408,6 @@
 end;
 
 
-Addsimprocs Nat_Numeral_Simprocs.cancel_numerals;
 Addsimprocs [Nat_Numeral_Simprocs.combine_numerals];
 Addsimprocs Nat_Numeral_Simprocs.cancel_numeral_factors;
 Addsimprocs Nat_Numeral_Simprocs.cancel_factor;
@@ -436,57 +419,6 @@
 set simp_trace;
 fun test s = (Goal s; by (Simp_tac 1));
 
-(*cancel_numerals*)
-test "l +( 2) + (2) + 2 + (l + 2) + (oo  + 2) = (uu::nat)";
-test "(2*length xs < 2*length xs + j)";
-test "(2*length xs < length xs * 2 + j)";
-test "2*u = (u::nat)";
-test "2*u = Suc (u)";
-test "(i + j + 12 + (k::nat)) - 15 = y";
-test "(i + j + 12 + (k::nat)) - 5 = y";
-test "Suc u - 2 = y";
-test "Suc (Suc (Suc u)) - 2 = y";
-test "(i + j + 2 + (k::nat)) - 1 = y";
-test "(i + j + 1 + (k::nat)) - 2 = y";
-
-test "(2*x + (u*v) + y) - v*3*u = (w::nat)";
-test "(2*x*u*v + 5 + (u*v)*4 + y) - v*u*4 = (w::nat)";
-test "(2*x*u*v + (u*v)*4 + y) - v*u = (w::nat)";
-test "Suc (Suc (2*x*u*v + u*4 + y)) - u = w";
-test "Suc ((u*v)*4) - v*3*u = w";
-test "Suc (Suc ((u*v)*3)) - v*3*u = w";
-
-test "(i + j + 12 + (k::nat)) = u + 15 + y";
-test "(i + j + 32 + (k::nat)) - (u + 15 + y) = zz";
-test "(i + j + 12 + (k::nat)) = u + 5 + y";
-(*Suc*)
-test "(i + j + 12 + k) = Suc (u + y)";
-test "Suc (Suc (Suc (Suc (Suc (u + y))))) <= ((i + j) + 41 + k)";
-test "(i + j + 5 + k) < Suc (Suc (Suc (Suc (Suc (u + y)))))";
-test "Suc (Suc (Suc (Suc (Suc (u + y))))) - 5 = v";
-test "(i + j + 5 + k) = Suc (Suc (Suc (Suc (Suc (Suc (Suc (u + y)))))))";
-test "2*y + 3*z + 2*u = Suc (u)";
-test "2*y + 3*z + 6*w + 2*y + 3*z + 2*u = Suc (u)";
-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)";
-test "6 + 2*y + 3*z + 4*u = Suc (vv + 2*u + z)";
-test "(2*n*m) < (3*(m*n)) + (u::nat)";
-
-test "(Suc (Suc (Suc (Suc (Suc (Suc (case length (f c) of 0 => 0 | Suc k => k)))))) <= Suc 0)";
- 
-test "Suc (Suc (Suc (Suc (Suc (Suc (length l1 + length l2)))))) <= length l1";
-
-test "( (Suc (Suc (Suc (Suc (Suc (length (compT P E A ST mxr e) + length l3)))))) <= length (compT P E A ST mxr e))";
-
-test "( (Suc (Suc (Suc (Suc (Suc (length (compT P E A ST mxr e) + length (compT P E (A Un \<A> e) ST mxr c))))))) <= length (compT P E A ST mxr e))";
-
-
-(*negative numerals: FAIL*)
-test "(i + j + -23 + (k::nat)) < u + 15 + y";
-test "(i + j + 3 + (k::nat)) < u + -15 + y";
-test "(i + j + -12 + (k::nat)) - 15 = y";
-test "(i + j + 12 + (k::nat)) - -15 = y";
-test "(i + j + -12 + (k::nat)) - -15 = y";
-
 (*combine_numerals*)
 test "k + 3*k = (u::nat)";
 test "Suc (i + 3) = u";
diff -r d660c4b9daa6 -r 62bc9474d04b src/HOL/ex/Simproc_Tests.thy
--- a/src/HOL/ex/Simproc_Tests.thy	Wed Nov 09 10:58:08 2011 +0100
+++ b/src/HOL/ex/Simproc_Tests.thy	Wed Nov 09 11:44:42 2011 +0100
@@ -380,4 +380,176 @@
 apply (tactic {* test [@{simproc field_combine_numerals}] *})?
 oops -- "FIXME: test fails"
 
+subsection {* @{text nateq_cancel_numerals} *}
+
+notepad begin
+  fix i j k l oo u uu vv w y z w' y' z' :: "nat"
+  {
+    assume "Suc 0 * u = 0" have "2*u = (u::nat)"
+      by (tactic {* test [@{simproc nateq_cancel_numerals}] *}) fact
+  next
+    assume "Suc 0 * u = Suc 0" have "2*u = Suc (u)"
+      by (tactic {* test [@{simproc nateq_cancel_numerals}] *}) fact
+  next
+    assume "i + (j + k) = 3 * Suc 0 + (u + y)"
+    have "(i + j + 12 + k) = u + 15 + y"
+      by (tactic {* test [@{simproc nateq_cancel_numerals}] *}) fact
+  next
+    assume "7 * Suc 0 + (i + (j + k)) = u + y"
+    have "(i + j + 12 + k) = u + 5 + y"
+      by (tactic {* test [@{simproc nateq_cancel_numerals}] *}) fact
+  next
+    assume "11 * Suc 0 + (i + (j + k)) = u + y"
+    have "(i + j + 12 + k) = Suc (u + y)"
+      by (tactic {* test [@{simproc nateq_cancel_numerals}] *}) fact
+  next
+    assume "i + (j + k) = 2 * Suc 0 + (u + y)"
+    have "(i + j + 5 + k) = Suc (Suc (Suc (Suc (Suc (Suc (Suc (u + y)))))))"
+      by (tactic {* test [@{simproc nateq_cancel_numerals}] *}) fact
+  next
+    assume "Suc 0 * u + (2 * y + 3 * z) = Suc 0"
+    have "2*y + 3*z + 2*u = Suc (u)"
+      by (tactic {* test [@{simproc nateq_cancel_numerals}] *}) fact
+  next
+    assume "Suc 0 * u + (2 * y + (3 * z + (6 * w + (2 * y + 3 * z)))) = Suc 0"
+    have "2*y + 3*z + 6*w + 2*y + 3*z + 2*u = Suc (u)"
+      by (tactic {* test [@{simproc nateq_cancel_numerals}] *}) fact
+  next
+    assume "Suc 0 * u + (2 * y + (3 * z + (6 * w + (2 * y + 3 * z)))) =
+      2 * y' + (3 * z' + (6 * w' + (2 * y' + (3 * z' + vv))))"
+    have "2*y + 3*z + 6*w + 2*y + 3*z + 2*u =
+      2*y' + 3*z' + 6*w' + 2*y' + 3*z' + u + vv"
+      by (tactic {* test [@{simproc nateq_cancel_numerals}] *}) fact
+  next
+    assume "2 * u + (2 * z + (5 * Suc 0 + 2 * y)) = vv"
+    have "6 + 2*y + 3*z + 4*u = Suc (vv + 2*u + z)"
+      by (tactic {* test [@{simproc nateq_cancel_numerals}] *}) fact
+  }
 end
+
+subsection {* @{text natless_cancel_numerals} *}
+
+notepad begin
+  fix length :: "'a \<Rightarrow> nat" and l1 l2 xs :: "'a" and f :: "nat \<Rightarrow> 'a"
+  fix c i j k l oo u uu vv w y z w' y' z' :: "nat"
+  {
+    assume "0 < j" have "(2*length xs < 2*length xs + j)"
+      by (tactic {* test [@{simproc natless_cancel_numerals}] *}) fact
+  next
+    assume "0 < j" have "(2*length xs < length xs * 2 + j)"
+      by (tactic {* test [@{simproc natless_cancel_numerals}] *}) fact
+  next
+    assume "i + (j + k) < u + y"
+    have "(i + j + 5 + k) < Suc (Suc (Suc (Suc (Suc (u + y)))))"
+      by (tactic {* test [@{simproc natless_cancel_numerals}] *}) fact
+  next
+    assume "0 < Suc 0 * (m * n) + u" have "(2*n*m) < (3*(m*n)) + u"
+      by (tactic {* test [@{simproc natless_cancel_numerals}] *}) fact
+  next
+    (* FIXME: negative numerals fail
+    have "(i + j + -23 + (k::nat)) < u + 15 + y"
+      apply (tactic {* test [@{simproc natless_cancel_numerals}] *})?
+      sorry
+    have "(i + j + 3 + (k::nat)) < u + -15 + y"
+      apply (tactic {* test [@{simproc natless_cancel_numerals}] *})?
+      sorry*)
+  }
+end
+
+subsection {* @{text natle_cancel_numerals} *}
+
+notepad begin
+  fix length :: "'a \<Rightarrow> nat" and l2 l3 :: "'a" and f :: "nat \<Rightarrow> 'a"
+  fix c e i j k l oo u uu vv w y z w' y' z' :: "nat"
+  {
+    assume "u + y \<le> 36 * Suc 0 + (i + (j + k))"
+    have "Suc (Suc (Suc (Suc (Suc (u + y))))) \<le> ((i + j) + 41 + k)"
+      by (tactic {* test [@{simproc natle_cancel_numerals}] *}) fact
+  next
+    assume "5 * Suc 0 + (case length (f c) of 0 \<Rightarrow> 0 | Suc k \<Rightarrow> k) = 0"
+    have "(Suc (Suc (Suc (Suc (Suc (Suc (case length (f c) of 0 => 0 | Suc k => k)))))) \<le> Suc 0)"
+      by (tactic {* test [@{simproc natle_cancel_numerals}] *}) fact
+  next
+    assume "6 + length l2 = 0" have "Suc (Suc (Suc (Suc (Suc (Suc (length l1 + length l2)))))) \<le> length l1"
+      by (tactic {* test [@{simproc natle_cancel_numerals}] *}) fact
+  next
+    assume "5 + length l3 = 0"
+    have "( (Suc (Suc (Suc (Suc (Suc (length (compT P E A ST mxr e) + length l3)))))) \<le> length (compT P E A ST mxr e))"
+      by (tactic {* test [@{simproc natle_cancel_numerals}] *}) fact
+  next
+    assume "5 + length (compT P E (A \<union> A' e) ST mxr c) = 0"
+    have "( (Suc (Suc (Suc (Suc (Suc (length (compT P E A ST mxr e) + length (compT P E (A Un A' e) ST mxr c))))))) \<le> length (compT P E A ST mxr e))"
+      by (tactic {* test [@{simproc natle_cancel_numerals}] *}) fact
+  }
+end
+
+subsection {* @{text natdiff_cancel_numerals} *}
+
+notepad begin
+  fix length :: "'a \<Rightarrow> nat" and l2 l3 :: "'a" and f :: "nat \<Rightarrow> 'a"
+  fix c e i j k l oo u uu vv v w x y z zz w' y' z' :: "nat"
+  {
+    assume "i + (j + k) - 3 * Suc 0 = y" have "(i + j + 12 + k) - 15 = y"
+      by (tactic {* test [@{simproc natdiff_cancel_numerals}] *}) fact
+  next
+    assume "7 * Suc 0 + (i + (j + k)) - 0 = y" have "(i + j + 12 + k) - 5 = y"
+      by (tactic {* test [@{simproc natdiff_cancel_numerals}] *}) fact
+  next
+    assume "u - Suc 0 * Suc 0 = y" have "Suc u - 2 = y"
+      by (tactic {* test [@{simproc natdiff_cancel_numerals}] *}) fact
+  next
+    assume "Suc 0 * Suc 0 + u - 0 = y" have "Suc (Suc (Suc u)) - 2 = y"
+      by (tactic {* test [@{simproc natdiff_cancel_numerals}] *}) fact
+  next
+    assume "Suc 0 * Suc 0 + (i + (j + k)) - 0 = y"
+    have "(i + j + 2 + k) - 1 = y"
+      by (tactic {* test [@{simproc natdiff_cancel_numerals}] *}) fact
+  next
+    assume "i + (j + k) - Suc 0 * Suc 0 = y"
+    have "(i + j + 1 + k) - 2 = y"
+      by (tactic {* test [@{simproc natdiff_cancel_numerals}] *}) fact
+  next
+    assume "2 * x + y - 2 * (u * v) = w"
+    have "(2*x + (u*v) + y) - v*3*u = w"
+      by (tactic {* test [@{simproc natdiff_cancel_numerals}] *}) fact
+  next
+    assume "2 * x * u * v + (5 + y) - 0 = w"
+    have "(2*x*u*v + 5 + (u*v)*4 + y) - v*u*4 = w"
+      by (tactic {* test [@{simproc natdiff_cancel_numerals}] *}) fact
+  next
+    assume "3 * (u * v) + (2 * x * u * v + y) - 0 = w"
+    have "(2*x*u*v + (u*v)*4 + y) - v*u = w"
+      by (tactic {* test [@{simproc natdiff_cancel_numerals}] *}) fact
+  next
+    assume "3 * u + (2 + (2 * x * u * v + y)) - 0 = w"
+    have "Suc (Suc (2*x*u*v + u*4 + y)) - u = w"
+      by (tactic {* test [@{simproc natdiff_cancel_numerals}] *}) fact
+  next
+    assume "Suc (Suc 0 * (u * v)) - 0 = w"
+    have "Suc ((u*v)*4) - v*3*u = w"
+      by (tactic {* test [@{simproc natdiff_cancel_numerals}] *}) fact
+  next
+    assume "2 - 0 = w" have "Suc (Suc ((u*v)*3)) - v*3*u = w"
+      by (tactic {* test [@{simproc natdiff_cancel_numerals}] *}) fact
+  next
+    assume "17 * Suc 0 + (i + (j + k)) - (u + y) = zz"
+    have "(i + j + 32 + k) - (u + 15 + y) = zz"
+      by (tactic {* test [@{simproc natdiff_cancel_numerals}] *}) fact
+  next
+    assume "u + y - 0 = v" have "Suc (Suc (Suc (Suc (Suc (u + y))))) - 5 = v"
+      by (tactic {* test [@{simproc natdiff_cancel_numerals}] *}) fact
+  next
+    (* FIXME: negative numerals fail
+    have "(i + j + -12 + k) - 15 = y"
+      apply (tactic {* test [@{simproc natdiff_cancel_numerals}] *})?
+      sorry
+    have "(i + j + 12 + k) - -15 = y"
+      apply (tactic {* test [@{simproc natdiff_cancel_numerals}] *})?
+      sorry
+    have "(i + j + -12 + k) - -15 = y"
+      apply (tactic {* test [@{simproc natdiff_cancel_numerals}] *})?
+      sorry*)
+  }
+end
+
+end