src/HOL/TPTP/CASC_Setup.thy

--- a/src/HOL/TPTP/CASC_Setup.thy	Wed Jul 13 22:16:19 2011 +0200
+++ b/src/HOL/TPTP/CASC_Setup.thy	Wed Jul 13 22:16:19 2011 +0200
@@ -1,4 +1,4 @@
-(*  Title:      HOL/ex/CASC_Setup.thy
+(*  Title:      HOL/TPTP/CASC_Setup.thy
     Author:     Jasmin Blanchette
     Copyright   2011
 
@@ -9,8 +9,85 @@
 
 theory CASC_Setup
 imports Complex_Main
-uses "sledgehammer_tactics.ML"
+uses "../ex/sledgehammer_tactics.ML"
+begin
+
+consts
+  is_int :: "'a \<Rightarrow> bool"
+  is_rat :: "'a \<Rightarrow> bool"
+
+overloading rat_is_int \<equiv> "is_int :: rat \<Rightarrow> bool"
+begin
+  definition "rat_is_int (q\<Colon>rat) \<longleftrightarrow> (\<exists>n\<Colon>int. q = of_int n)"
+end
+
+overloading real_is_int \<equiv> "is_int :: real \<Rightarrow> bool"
+begin
+  definition "real_is_int (x\<Colon>real) \<longleftrightarrow> x \<in> \<int>"
+end
+
+overloading real_is_rat \<equiv> "is_rat :: real \<Rightarrow> bool"
+begin
+  definition "real_is_rat (x\<Colon>real) \<longleftrightarrow> x \<in> \<rat>"
+end
+
+consts
+  to_int :: "'a \<Rightarrow> int"
+  to_rat :: "'a \<Rightarrow> rat"
+  to_real :: "'a \<Rightarrow> real"
+
+overloading rat_to_int \<equiv> "to_int :: rat \<Rightarrow> int"
+begin
+  definition "rat_to_int (q\<Colon>rat) = floor q"
+end
+
+overloading real_to_int \<equiv> "to_int :: real \<Rightarrow> int"
+begin
+  definition "real_to_int (x\<Colon>real) = floor x"
+end
+
+overloading int_to_rat \<equiv> "to_rat :: int \<Rightarrow> rat"
 begin
+  definition "int_to_rat (n\<Colon>int) = (of_int n\<Colon>rat)"
+end
+
+overloading real_to_rat \<equiv> "to_rat :: real \<Rightarrow> rat"
+begin
+  definition "real_to_rat (x\<Colon>real) = (inv real x\<Colon>rat)"
+end
+
+overloading int_to_real \<equiv> "to_real :: int \<Rightarrow> real"
+begin
+  definition "int_to_real (n\<Colon>int) = real n"
+end
+
+overloading rat_to_real \<equiv> "to_real :: rat \<Rightarrow> real"
+begin
+  definition "rat_to_real (x\<Colon>rat) = (of_rat x\<Colon>real)"
+end
+
+declare
+  rat_is_int_def [simp]
+  real_is_int_def [simp]
+  real_is_rat_def [simp]
+  rat_to_int_def [simp]
+  real_to_int_def [simp]
+  int_to_rat_def [simp]
+  real_to_rat_def [simp]
+  int_to_real_def [simp]
+  rat_to_real_def [simp]
+
+lemma to_rat_is_int [intro, simp]: "is_int (to_rat (n\<Colon>int))"
+by (metis int_to_rat_def rat_is_int_def)
+
+lemma to_real_is_int [intro, simp]: "is_int (to_real (n\<Colon>int))"
+by (metis Ints_real_of_int int_to_real_def real_is_int_def)
+
+lemma to_real_is_rat [intro, simp]: "is_rat (to_real (q\<Colon>rat))"
+by (metis Rats_of_rat rat_to_real_def real_is_rat_def)
+
+lemma inj_of_rat [intro, simp]: "inj (of_rat\<Colon>rat\<Rightarrow>real)"
+by (metis injI of_rat_eq_iff rat_to_real_def)
 
 declare mem_def [simp add]