# HG changeset patch
# User wenzelm
# Date 1159479752 -7200
# Node ID 9bc632ae588f3dd00a833a88bab056a51792a6e1
# Parent  9913d3bc3d1720c139f2476bc08ce03179244728
removed obsolete Real/document/root.tex;
removed obsolete Isar_examples/Cantor.ML;
renamed Real/Float.ML to Real/float.ML;

diff -r 9913d3bc3d17 -r 9bc632ae588f src/HOL/IsaMakefile
--- a/src/HOL/IsaMakefile	Thu Sep 28 23:42:30 2006 +0200
+++ b/src/HOL/IsaMakefile	Thu Sep 28 23:42:32 2006 +0200
@@ -162,11 +162,10 @@
 HOL-Complex: HOL $(OUT)/HOL-Complex
 
 $(OUT)/HOL-Complex: $(OUT)/HOL Complex/ROOT.ML Library/Zorn.thy			\
-  Real/ContNotDenum.thy Real/Ferrante_Rackoff.thy Real/Float.ML			\
+  Real/ContNotDenum.thy Real/Ferrante_Rackoff.thy Real/float.ML			\
   Real/Float.thy Real/Lubs.thy Real/PReal.thy Real/RComplete.thy		\
   Real/ROOT.ML Real/Rational.thy Real/Real.thy Real/RealDef.thy			\
-  Real/RealPow.thy Real/RealVector.thy Real/document/root.tex                   \
-  Real/ferrante_rackoff_proof.ML	                                        \
+  Real/RealPow.thy Real/RealVector.thy Real/ferrante_rackoff_proof.ML           \
   Real/ferrante_rackoff.ML Real/rat_arith.ML Real/real_arith.ML			\
   Hyperreal/StarDef.thy Hyperreal/StarClasses.thy				\
   Hyperreal/EvenOdd.thy Hyperreal/Fact.thy Hyperreal/HLog.thy			\
@@ -665,7 +664,7 @@
 HOL-Isar_examples: HOL $(LOG)/HOL-Isar_examples.gz
 
 $(LOG)/HOL-Isar_examples.gz: $(OUT)/HOL Isar_examples/BasicLogic.thy \
-  Isar_examples/Cantor.ML Isar_examples/Cantor.thy Isar_examples/Drinker.thy \
+  Isar_examples/Cantor.thy Isar_examples/Drinker.thy \
   Isar_examples/ExprCompiler.thy Isar_examples/Fibonacci.thy \
   Isar_examples/Group.thy Isar_examples/Hoare.thy Isar_examples/HoareEx.thy \
   Isar_examples/KnasterTarski.thy Isar_examples/MutilatedCheckerboard.thy \
diff -r 9913d3bc3d17 -r 9bc632ae588f src/HOL/Real/Float.ML
--- a/src/HOL/Real/Float.ML	Thu Sep 28 23:42:30 2006 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,510 +0,0 @@
-(*  Title: HOL/Real/Float.ML
-    ID:    $Id$
-    Author: Steven Obua
-*)
-
-structure ExactFloatingPoint :
-sig
-    exception Destruct_floatstr of string
-    val destruct_floatstr : (char -> bool) -> (char -> bool) -> string -> bool * string * string * bool * string
-
-    exception Floating_point of string
-
-    type floatrep = IntInf.int * IntInf.int
-    val approx_dec_by_bin : IntInf.int -> floatrep -> floatrep * floatrep
-    val approx_decstr_by_bin : int -> string -> floatrep * floatrep
-end 
-=
-struct
-
-exception Destruct_floatstr of string;
-
-fun destruct_floatstr isDigit isExp number = 
-    let
-	val numlist = filter (not o Char.isSpace) (String.explode number)
-	
-	fun countsigns ((#"+")::cs) = countsigns cs
-	  | countsigns ((#"-")::cs) = 
-	    let	
-		val (positive, rest) = countsigns cs 
-	    in
-		(not positive, rest)
-	    end
-	  | countsigns cs = (true, cs)
-
-	fun readdigits [] = ([], [])
-	  | readdigits (q as c::cs) = 
-	    if (isDigit c) then 
-		let
-		    val (digits, rest) = readdigits cs
-		in
-		    (c::digits, rest)
-		end
-	    else
-		([], q)		
-
-	fun readfromexp_helper cs =
-	    let
-		val (positive, rest) = countsigns cs
-		val (digits, rest') = readdigits rest
-	    in
-		case rest' of
-		    [] => (positive, digits)
-		  | _ => raise (Destruct_floatstr number)
-	    end	    
-
-	fun readfromexp [] = (true, [])
-	  | readfromexp (c::cs) = 
-	    if isExp c then
-		readfromexp_helper cs
-	    else 
-		raise (Destruct_floatstr number)		
-
-	fun readfromdot [] = ([], readfromexp [])
-	  | readfromdot ((#".")::cs) = 
-	    let		
-		val (digits, rest) = readdigits cs
-		val exp = readfromexp rest
-	    in
-		(digits, exp)
-	    end		
-	  | readfromdot cs = readfromdot ((#".")::cs)
-			    
-	val (positive, numlist) = countsigns numlist				 
-	val (digits1, numlist) = readdigits numlist				 
- 	val (digits2, exp) = readfromdot numlist
-    in
-	(positive, String.implode digits1, String.implode digits2, fst exp, String.implode (snd exp))
-    end
-
-type floatrep = IntInf.int * IntInf.int
-
-exception Floating_point of string;
-
-val ln2_10 = (Math.ln 10.0)/(Math.ln 2.0)
-	
-fun intmul a b = IntInf.* (a,b)
-fun intsub a b = IntInf.- (a,b)	
-fun intadd a b = IntInf.+ (a,b) 		 
-fun intpow a b = IntInf.pow (a, IntInf.toInt b);
-fun intle a b = IntInf.<= (a, b);
-fun intless a b = IntInf.< (a, b);
-fun intneg a = IntInf.~ a;
-val zero = IntInf.fromInt 0;
-val one = IntInf.fromInt 1;
-val two = IntInf.fromInt 2;
-val ten = IntInf.fromInt 10;
-val five = IntInf.fromInt 5;
-
-fun find_most_significant q r = 
-    let 
-	fun int2real i = 
-	    case Real.fromString (IntInf.toString i) of 
-		SOME r => r 
-	      | NONE => raise (Floating_point "int2real")	
-	fun subtract (q, r) (q', r') = 
-	    if intle r r' then
-		(intsub q (intmul q' (intpow ten (intsub r' r))), r)
-	    else
-		(intsub (intmul q (intpow ten (intsub r r'))) q', r')
-	fun bin2dec d =
-	    if intle zero d then 
-		(intpow two d, zero)
-	    else
-		(intpow five (intneg d), d)				
-		
-	val L = IntInf.fromInt (Real.floor (int2real (IntInf.fromInt (IntInf.log2 q)) + (int2real r) * ln2_10))	
-	val L1 = intadd L one
-
-	val (q1, r1) = subtract (q, r) (bin2dec L1) 		
-    in
-	if intle zero q1 then 
-	    let
-		val (q2, r2) = subtract (q, r) (bin2dec (intadd L1 one))
-	    in
-		if intle zero q2 then 
-		    raise (Floating_point "find_most_significant")
-		else
-		    (L1, (q1, r1))
-	    end
-	else
-	    let
-		val (q0, r0) = subtract (q, r) (bin2dec L)
-	    in
-		if intle zero q0 then
-		    (L, (q0, r0))
-		else
-		    raise (Floating_point "find_most_significant")
-	    end		    
-    end
-
-fun approx_dec_by_bin n (q,r) =
-    let	
-	fun addseq acc d' [] = acc
-	  | addseq acc d' (d::ds) = addseq (intadd acc (intpow two (intsub d d'))) d' ds
-
-	fun seq2bin [] = (zero, zero)
-	  | seq2bin (d::ds) = (intadd (addseq zero d ds) one, d)
-
-	fun approx d_seq d0 precision (q,r) = 
-	    if q = zero then 
-		let val x = seq2bin d_seq in
-		    (x, x)
-		end
-	    else    
-		let 
-		    val (d, (q', r')) = find_most_significant q r
-		in	
-		    if intless precision (intsub d0 d) then 
-			let 
-			    val d' = intsub d0 precision
-			    val x1 = seq2bin (d_seq)
-			    val x2 = (intadd (intmul (fst x1) (intpow two (intsub (snd x1) d'))) one,  d') (* = seq2bin (d'::d_seq) *) 
-			in
-			    (x1, x2)
-			end
-		    else
-			approx (d::d_seq) d0 precision (q', r') 						    		
-		end		
-	
-	fun approx_start precision (q, r) =
-	    if q = zero then 
-		((zero, zero), (zero, zero))
-	    else
-		let 
-		    val (d, (q', r')) = find_most_significant q r
-		in	
-		    if intle precision zero then 
-			let
-			    val x1 = seq2bin [d]
-			in
-			    if q' = zero then 
-				(x1, x1)
-			    else
-				(x1, seq2bin [intadd d one])
-			end
-		    else
-			approx [d] d precision (q', r')
-		end		
-    in
-	if intle zero q then 
-	    approx_start n (q,r)
-	else
-	    let 
-		val ((a1,b1), (a2, b2)) = approx_start n (intneg q, r) 
-	    in
-		((intneg a2, b2), (intneg a1, b1))
-	    end					
-    end
-
-fun approx_decstr_by_bin n decstr =
-    let 
-	fun str2int s = case IntInf.fromString s of SOME x => x | NONE => zero 
-	fun signint p x = if p then x else intneg x
-
-	val (p, d1, d2, ep, e) = destruct_floatstr Char.isDigit (fn e => e = #"e" orelse e = #"E") decstr
-	val s = IntInf.fromInt (size d2)
-		
-	val q = signint p (intadd (intmul (str2int d1) (intpow ten s)) (str2int d2))
-	val r = intsub (signint ep (str2int e)) s
-    in
-	approx_dec_by_bin (IntInf.fromInt n) (q,r)
-    end
-
-end;
-
-structure FloatArith = 
-struct
-
-type float = IntInf.int * IntInf.int 
-
-val izero = IntInf.fromInt 0
-val ione = IntInf.fromInt 1
-val imone = IntInf.fromInt ~1
-val itwo = IntInf.fromInt 2
-fun imul a b = IntInf.* (a,b)
-fun isub a b = IntInf.- (a,b)
-fun iadd a b = IntInf.+ (a,b)
-
-val floatzero = (izero, izero)
-
-fun positive_part (a,b) = 
-    (if IntInf.< (a,izero) then izero else a, b)
-
-fun negative_part (a,b) = 
-    (if IntInf.< (a,izero) then a else izero, b)
-
-fun is_negative (a,b) = 
-    if IntInf.< (a, izero) then true else false
-
-fun is_positive (a,b) = 
-    if IntInf.< (izero, a) then true else false
-
-fun is_zero (a,b) = 
-    if a = izero then true else false
-
-fun ipow2 a = IntInf.pow ((IntInf.fromInt 2), IntInf.toInt a)
-
-fun add (a1, b1) (a2, b2) = 
-    if IntInf.< (b1, b2) then
-	(iadd a1 (imul a2 (ipow2 (isub b2 b1))), b1)
-    else
-	(iadd (imul a1 (ipow2 (isub b1 b2))) a2, b2)
-
-fun sub (a1, b1) (a2, b2) = 
-    if IntInf.< (b1, b2) then
-	(isub a1 (imul a2 (ipow2 (isub b2 b1))), b1)
-    else
-	(isub (imul a1 (ipow2 (isub b1 b2))) a2, b2)
-
-fun neg (a, b) = (IntInf.~ a, b)
-
-fun is_equal a b = is_zero (sub a b)
-
-fun is_less a b = is_negative (sub a b)
-
-fun max a b = if is_less a b then b else a
-
-fun min a b = if is_less a b then a else b
-
-fun abs a = if is_negative a then neg a else a
-
-fun mul (a1, b1) (a2, b2) = (imul a1 a2, iadd b1 b2)
-
-end;
-
-
-structure Float:
-sig
-    type float = FloatArith.float
-    type floatfunc = float * float -> float * float
-
-    val mk_intinf : typ -> IntInf.int -> term
-    val mk_float : float -> term
-
-    exception Dest_intinf;
-    val dest_intinf : term -> IntInf.int
-    val dest_nat : term -> IntInf.int
-    
-    exception Dest_float;
-    val dest_float : term -> float
-
-    val float_const : term
-
-    val float_add_const : term
-    val float_diff_const : term
-    val float_uminus_const : term
-    val float_pprt_const : term
-    val float_nprt_const : term
-    val float_abs_const : term
-    val float_mult_const : term 
-    val float_le_const : term
-
-    val nat_le_const : term
-    val nat_less_const : term
-    val nat_eq_const : term
-
-    val approx_float : int -> floatfunc -> string -> term * term
-
-    val sign_term : term -> cterm
-
-(*    exception Float_op_oracle_data of term
-    exception Nat_op_oracle_data of term
-
-    val float_op_oracle : Sign.sg * exn -> term
-    val nat_op_oracle : Sign.sg * exn -> term
-
-    val invoke_float_op : term -> thm
-    val invoke_nat_op : term -> thm*)
-end 
-= 
-struct
-
-structure Inttab = TableFun(type key = int val ord = (rev_order o int_ord));
-
-type float = IntInf.int*IntInf.int
-type floatfunc = float*float -> float*float
-
-val th = theory "Float"
-val sg = sign_of th
-		
-val float_const = Const ("Float.float", HOLogic.mk_prodT (HOLogic.intT, HOLogic.intT) --> HOLogic.realT)
-
-val float_add_const = Const ("HOL.plus", HOLogic.realT --> HOLogic.realT --> HOLogic.realT)
-val float_diff_const = Const ("HOL.minus", HOLogic.realT --> HOLogic.realT --> HOLogic.realT)
-val float_mult_const = Const ("HOL.times", HOLogic.realT --> HOLogic.realT --> HOLogic.realT)
-val float_uminus_const = Const ("HOL.uminus", HOLogic.realT --> HOLogic.realT)
-val float_abs_const = Const ("HOL.abs", HOLogic.realT --> HOLogic.realT)
-val float_le_const = Const ("Orderings.less_eq", HOLogic.realT --> HOLogic.realT --> HOLogic.boolT)
-val float_pprt_const = Const ("OrderedGroup.pprt", HOLogic.realT --> HOLogic.realT)
-val float_nprt_const = Const ("OrderedGroup.nprt", HOLogic.realT --> HOLogic.realT)
-
-val nat_le_const = Const ("Orderings.less_eq", HOLogic.natT --> HOLogic.natT --> HOLogic.boolT)
-val nat_less_const = Const ("Orderings.less", HOLogic.natT --> HOLogic.natT --> HOLogic.boolT)
-val nat_eq_const = Const ("op =", HOLogic.natT --> HOLogic.natT --> HOLogic.boolT)
- 		  
-val zero = FloatArith.izero
-val minus_one = FloatArith.imone
-val two = FloatArith.itwo
-	  
-exception Dest_intinf;
-exception Dest_float;
-
-fun mk_intinf ty n =
-  let
-    fun mk_bit n = if n = zero then HOLogic.B0_const else HOLogic.B1_const
-    fun bin_of n = 
-      if n = zero then HOLogic.pls_const
-      else if n = minus_one then HOLogic.min_const
-      else let 
-        val (q,r) = IntInf.divMod (n, two)
-      in
-        HOLogic.bit_const $ bin_of q $ mk_bit r
-      end
-  in 
-    HOLogic.number_of_const ty $ (bin_of n)
-  end
-
-fun dest_intinf n = 
-    let
-	fun dest_bit n = 
-	    case n of 
-		Const ("Numeral.bit.B0", _) => FloatArith.izero
-	      | Const ("Numeral.bit.B1", _) => FloatArith.ione
-	      | _ => raise Dest_intinf
-			 
-	fun int_of n = 
-	    case n of
-		Const ("Numeral.Pls", _) => FloatArith.izero
-	      | Const ("Numeral.Min", _) => FloatArith.imone
-	      | Const ("Numeral.Bit", _) $ q $ r => FloatArith.iadd (FloatArith.imul (int_of q) FloatArith.itwo) (dest_bit r)
-	      | _ => raise Dest_intinf
-    in
-	case n of 
-	    Const ("Numeral.number_of", _) $ n' => int_of n'
-	  | Const ("Numeral0", _) => FloatArith.izero
-	  | Const ("Numeral1", _) => FloatArith.ione    
-	  | _ => raise Dest_intinf
-    end
-
-fun mk_float (a,b) = 
-    float_const $ (HOLogic.mk_prod ((mk_intinf HOLogic.intT a), (mk_intinf HOLogic.intT b)))
-
-fun dest_float f = 
-    case f of 
-	(Const ("Float.float", _) $ (Const ("Pair", _) $ a $ b)) => (dest_intinf a, dest_intinf b)
-      | Const ("Numeral.number_of",_) $ a => (dest_intinf f, 0)
-      | Const ("Numeral0", _) => (FloatArith.izero, FloatArith.izero)
-      | Const ("Numeral1", _) => (FloatArith.ione, FloatArith.izero)
-      | _ => raise Dest_float
-
-fun dest_nat n = 
-    let 
-	val v = dest_intinf n
-    in
-	if IntInf.< (v, FloatArith.izero) then
-	    FloatArith.izero
-	else
-	    v
-    end
-
-fun approx_float prec f value = 
-    let
-	val interval = ExactFloatingPoint.approx_decstr_by_bin prec value
-	val (flower, fupper) = f interval
-    in
-	(mk_float flower, mk_float fupper)
-    end
-
-fun sign_term t = cterm_of sg t
-
-(*exception Float_op_oracle_data of term;
-
-fun float_op_oracle (sg, exn as Float_op_oracle_data t) =
-    Logic.mk_equals (t,
-		     case t of 
-			 f $ a $ b => 
-			 let 
-			     val a' = dest_float a 
-			     val b' = dest_float b
-			 in
-			     if f = float_add_const then
-				 mk_float (FloatArith.add a' b')	
-			     else if f = float_diff_const then
-				 mk_float (FloatArith.sub a' b')
-			     else if f = float_mult_const then
-				 mk_float (FloatArith.mul a' b')		
-			     else if f = float_le_const then
-				 (if FloatArith.is_less b' a' then
-				     HOLogic.false_const
-				 else
-				     HOLogic.true_const)
-			     else raise exn	    		    	       
-			 end
-		       | f $ a => 
-			 let
-			     val a' = dest_float a
-			 in
-			     if f = float_uminus_const then
-				 mk_float (FloatArith.neg a')
-			     else if f = float_abs_const then
-				 mk_float (FloatArith.abs a')
-			     else if f = float_pprt_const then
-				 mk_float (FloatArith.positive_part a')
-			     else if f = float_nprt_const then
-				 mk_float (FloatArith.negative_part a')
-			     else
-				 raise exn
-			 end
-		       | _ => raise exn
-		    )
-val th = ref ([]: theory list)
-val sg = ref ([]: Sign.sg list)
-
-fun invoke_float_op c = 
-    let
-	val th = (if length(!th) = 0 then th := [theory "MatrixLP"] else (); hd (!th))
-	val sg = (if length(!sg) = 0 then sg := [sign_of th] else (); hd (!sg))
-    in
-	invoke_oracle th "float_op" (sg, Float_op_oracle_data c)
-    end
-
-exception Nat_op_oracle_data of term;
-
-fun nat_op_oracle (sg, exn as Nat_op_oracle_data t) =
-    Logic.mk_equals (t,
-		     case t of 
-			 f $ a $ b => 
-			 let 
-			     val a' = dest_nat a 
-			     val b' = dest_nat b
-			 in
-			     if f = nat_le_const then
-				 (if IntInf.<= (a', b') then
-				     HOLogic.true_const
-				 else
-				     HOLogic.false_const)
-			     else if f = nat_eq_const then
-				 (if a' = b' then 
-				      HOLogic.true_const
-				  else
-				      HOLogic.false_const)
-			     else if f = nat_less_const then
-				 (if IntInf.< (a', b') then
-				      HOLogic.true_const
-				  else
-				      HOLogic.false_const)
-			     else 
-				 raise exn	    	
-			 end
-		       | _ => raise exn)
-
-fun invoke_nat_op c = 
-    let
-	val th = (if length (!th) = 0 then th := [theory "MatrixLP"] else (); hd (!th))
-	val sg = (if length (!sg) = 0 then sg := [sign_of th] else (); hd (!sg))
-    in
-	invoke_oracle th "nat_op" (sg, Nat_op_oracle_data c)
-    end
-*)
-end;
diff -r 9913d3bc3d17 -r 9bc632ae588f src/HOL/Real/float.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Real/float.ML	Thu Sep 28 23:42:32 2006 +0200
@@ -0,0 +1,503 @@
+(*  Title: HOL/Real/Float.ML
+    ID:    $Id$
+    Author: Steven Obua
+*)
+
+structure ExactFloatingPoint :
+sig
+    exception Destruct_floatstr of string
+    val destruct_floatstr : (char -> bool) -> (char -> bool) -> string -> bool * string * string * bool * string
+
+    exception Floating_point of string
+
+    type floatrep = IntInf.int * IntInf.int
+    val approx_dec_by_bin : IntInf.int -> floatrep -> floatrep * floatrep
+    val approx_decstr_by_bin : int -> string -> floatrep * floatrep
+end 
+=
+struct
+
+exception Destruct_floatstr of string;
+
+fun destruct_floatstr isDigit isExp number = 
+    let
+	val numlist = filter (not o Char.isSpace) (String.explode number)
+	
+	fun countsigns ((#"+")::cs) = countsigns cs
+	  | countsigns ((#"-")::cs) = 
+	    let	
+		val (positive, rest) = countsigns cs 
+	    in
+		(not positive, rest)
+	    end
+	  | countsigns cs = (true, cs)
+
+	fun readdigits [] = ([], [])
+	  | readdigits (q as c::cs) = 
+	    if (isDigit c) then 
+		let
+		    val (digits, rest) = readdigits cs
+		in
+		    (c::digits, rest)
+		end
+	    else
+		([], q)		
+
+	fun readfromexp_helper cs =
+	    let
+		val (positive, rest) = countsigns cs
+		val (digits, rest') = readdigits rest
+	    in
+		case rest' of
+		    [] => (positive, digits)
+		  | _ => raise (Destruct_floatstr number)
+	    end	    
+
+	fun readfromexp [] = (true, [])
+	  | readfromexp (c::cs) = 
+	    if isExp c then
+		readfromexp_helper cs
+	    else 
+		raise (Destruct_floatstr number)		
+
+	fun readfromdot [] = ([], readfromexp [])
+	  | readfromdot ((#".")::cs) = 
+	    let		
+		val (digits, rest) = readdigits cs
+		val exp = readfromexp rest
+	    in
+		(digits, exp)
+	    end		
+	  | readfromdot cs = readfromdot ((#".")::cs)
+			    
+	val (positive, numlist) = countsigns numlist				 
+	val (digits1, numlist) = readdigits numlist				 
+ 	val (digits2, exp) = readfromdot numlist
+    in
+	(positive, String.implode digits1, String.implode digits2, fst exp, String.implode (snd exp))
+    end
+
+type floatrep = IntInf.int * IntInf.int
+
+exception Floating_point of string;
+
+val ln2_10 = (Math.ln 10.0)/(Math.ln 2.0)
+	
+fun intmul a b = IntInf.* (a,b)
+fun intsub a b = IntInf.- (a,b)	
+fun intadd a b = IntInf.+ (a,b) 		 
+fun intpow a b = IntInf.pow (a, IntInf.toInt b);
+fun intle a b = IntInf.<= (a, b);
+fun intless a b = IntInf.< (a, b);
+fun intneg a = IntInf.~ a;
+val zero = IntInf.fromInt 0;
+val one = IntInf.fromInt 1;
+val two = IntInf.fromInt 2;
+val ten = IntInf.fromInt 10;
+val five = IntInf.fromInt 5;
+
+fun find_most_significant q r = 
+    let 
+	fun int2real i = 
+	    case Real.fromString (IntInf.toString i) of 
+		SOME r => r 
+	      | NONE => raise (Floating_point "int2real")	
+	fun subtract (q, r) (q', r') = 
+	    if intle r r' then
+		(intsub q (intmul q' (intpow ten (intsub r' r))), r)
+	    else
+		(intsub (intmul q (intpow ten (intsub r r'))) q', r')
+	fun bin2dec d =
+	    if intle zero d then 
+		(intpow two d, zero)
+	    else
+		(intpow five (intneg d), d)				
+		
+	val L = IntInf.fromInt (Real.floor (int2real (IntInf.fromInt (IntInf.log2 q)) + (int2real r) * ln2_10))	
+	val L1 = intadd L one
+
+	val (q1, r1) = subtract (q, r) (bin2dec L1) 		
+    in
+	if intle zero q1 then 
+	    let
+		val (q2, r2) = subtract (q, r) (bin2dec (intadd L1 one))
+	    in
+		if intle zero q2 then 
+		    raise (Floating_point "find_most_significant")
+		else
+		    (L1, (q1, r1))
+	    end
+	else
+	    let
+		val (q0, r0) = subtract (q, r) (bin2dec L)
+	    in
+		if intle zero q0 then
+		    (L, (q0, r0))
+		else
+		    raise (Floating_point "find_most_significant")
+	    end		    
+    end
+
+fun approx_dec_by_bin n (q,r) =
+    let	
+	fun addseq acc d' [] = acc
+	  | addseq acc d' (d::ds) = addseq (intadd acc (intpow two (intsub d d'))) d' ds
+
+	fun seq2bin [] = (zero, zero)
+	  | seq2bin (d::ds) = (intadd (addseq zero d ds) one, d)
+
+	fun approx d_seq d0 precision (q,r) = 
+	    if q = zero then 
+		let val x = seq2bin d_seq in
+		    (x, x)
+		end
+	    else    
+		let 
+		    val (d, (q', r')) = find_most_significant q r
+		in	
+		    if intless precision (intsub d0 d) then 
+			let 
+			    val d' = intsub d0 precision
+			    val x1 = seq2bin (d_seq)
+			    val x2 = (intadd (intmul (fst x1) (intpow two (intsub (snd x1) d'))) one,  d') (* = seq2bin (d'::d_seq) *) 
+			in
+			    (x1, x2)
+			end
+		    else
+			approx (d::d_seq) d0 precision (q', r') 						    		
+		end		
+	
+	fun approx_start precision (q, r) =
+	    if q = zero then 
+		((zero, zero), (zero, zero))
+	    else
+		let 
+		    val (d, (q', r')) = find_most_significant q r
+		in	
+		    if intle precision zero then 
+			let
+			    val x1 = seq2bin [d]
+			in
+			    if q' = zero then 
+				(x1, x1)
+			    else
+				(x1, seq2bin [intadd d one])
+			end
+		    else
+			approx [d] d precision (q', r')
+		end		
+    in
+	if intle zero q then 
+	    approx_start n (q,r)
+	else
+	    let 
+		val ((a1,b1), (a2, b2)) = approx_start n (intneg q, r) 
+	    in
+		((intneg a2, b2), (intneg a1, b1))
+	    end					
+    end
+
+fun approx_decstr_by_bin n decstr =
+    let 
+	fun str2int s = case IntInf.fromString s of SOME x => x | NONE => zero 
+	fun signint p x = if p then x else intneg x
+
+	val (p, d1, d2, ep, e) = destruct_floatstr Char.isDigit (fn e => e = #"e" orelse e = #"E") decstr
+	val s = IntInf.fromInt (size d2)
+		
+	val q = signint p (intadd (intmul (str2int d1) (intpow ten s)) (str2int d2))
+	val r = intsub (signint ep (str2int e)) s
+    in
+	approx_dec_by_bin (IntInf.fromInt n) (q,r)
+    end
+
+end;
+
+structure FloatArith = 
+struct
+
+type float = IntInf.int * IntInf.int 
+
+val izero = IntInf.fromInt 0
+val ione = IntInf.fromInt 1
+val imone = IntInf.fromInt ~1
+val itwo = IntInf.fromInt 2
+fun imul a b = IntInf.* (a,b)
+fun isub a b = IntInf.- (a,b)
+fun iadd a b = IntInf.+ (a,b)
+
+val floatzero = (izero, izero)
+
+fun positive_part (a,b) = 
+    (if IntInf.< (a,izero) then izero else a, b)
+
+fun negative_part (a,b) = 
+    (if IntInf.< (a,izero) then a else izero, b)
+
+fun is_negative (a,b) = 
+    if IntInf.< (a, izero) then true else false
+
+fun is_positive (a,b) = 
+    if IntInf.< (izero, a) then true else false
+
+fun is_zero (a,b) = 
+    if a = izero then true else false
+
+fun ipow2 a = IntInf.pow ((IntInf.fromInt 2), IntInf.toInt a)
+
+fun add (a1, b1) (a2, b2) = 
+    if IntInf.< (b1, b2) then
+	(iadd a1 (imul a2 (ipow2 (isub b2 b1))), b1)
+    else
+	(iadd (imul a1 (ipow2 (isub b1 b2))) a2, b2)
+
+fun sub (a1, b1) (a2, b2) = 
+    if IntInf.< (b1, b2) then
+	(isub a1 (imul a2 (ipow2 (isub b2 b1))), b1)
+    else
+	(isub (imul a1 (ipow2 (isub b1 b2))) a2, b2)
+
+fun neg (a, b) = (IntInf.~ a, b)
+
+fun is_equal a b = is_zero (sub a b)
+
+fun is_less a b = is_negative (sub a b)
+
+fun max a b = if is_less a b then b else a
+
+fun min a b = if is_less a b then a else b
+
+fun abs a = if is_negative a then neg a else a
+
+fun mul (a1, b1) (a2, b2) = (imul a1 a2, iadd b1 b2)
+
+end;
+
+
+structure Float:
+sig
+    type float = FloatArith.float
+    type floatfunc = float * float -> float * float
+
+    val mk_intinf : typ -> IntInf.int -> term
+    val mk_float : float -> term
+
+    exception Dest_intinf;
+    val dest_intinf : term -> IntInf.int
+    val dest_nat : term -> IntInf.int
+    
+    exception Dest_float;
+    val dest_float : term -> float
+
+    val float_const : term
+
+    val float_add_const : term
+    val float_diff_const : term
+    val float_uminus_const : term
+    val float_pprt_const : term
+    val float_nprt_const : term
+    val float_abs_const : term
+    val float_mult_const : term 
+    val float_le_const : term
+
+    val nat_le_const : term
+    val nat_less_const : term
+    val nat_eq_const : term
+
+    val approx_float : int -> floatfunc -> string -> term * term
+
+(*    exception Float_op_oracle_data of term
+    exception Nat_op_oracle_data of term
+
+    val float_op_oracle : Sign.sg * exn -> term
+    val nat_op_oracle : Sign.sg * exn -> term
+
+    val invoke_float_op : term -> thm
+    val invoke_nat_op : term -> thm*)
+end 
+= 
+struct
+
+structure Inttab = TableFun(type key = int val ord = (rev_order o int_ord));
+
+type float = IntInf.int*IntInf.int
+type floatfunc = float*float -> float*float
+
+val float_const = Const ("Float.float", HOLogic.mk_prodT (HOLogic.intT, HOLogic.intT) --> HOLogic.realT)
+
+val float_add_const = Const ("HOL.plus", HOLogic.realT --> HOLogic.realT --> HOLogic.realT)
+val float_diff_const = Const ("HOL.minus", HOLogic.realT --> HOLogic.realT --> HOLogic.realT)
+val float_mult_const = Const ("HOL.times", HOLogic.realT --> HOLogic.realT --> HOLogic.realT)
+val float_uminus_const = Const ("HOL.uminus", HOLogic.realT --> HOLogic.realT)
+val float_abs_const = Const ("HOL.abs", HOLogic.realT --> HOLogic.realT)
+val float_le_const = Const ("Orderings.less_eq", HOLogic.realT --> HOLogic.realT --> HOLogic.boolT)
+val float_pprt_const = Const ("OrderedGroup.pprt", HOLogic.realT --> HOLogic.realT)
+val float_nprt_const = Const ("OrderedGroup.nprt", HOLogic.realT --> HOLogic.realT)
+
+val nat_le_const = Const ("Orderings.less_eq", HOLogic.natT --> HOLogic.natT --> HOLogic.boolT)
+val nat_less_const = Const ("Orderings.less", HOLogic.natT --> HOLogic.natT --> HOLogic.boolT)
+val nat_eq_const = Const ("op =", HOLogic.natT --> HOLogic.natT --> HOLogic.boolT)
+ 		  
+val zero = FloatArith.izero
+val minus_one = FloatArith.imone
+val two = FloatArith.itwo
+	  
+exception Dest_intinf;
+exception Dest_float;
+
+fun mk_intinf ty n =
+  let
+    fun mk_bit n = if n = zero then HOLogic.B0_const else HOLogic.B1_const
+    fun bin_of n = 
+      if n = zero then HOLogic.pls_const
+      else if n = minus_one then HOLogic.min_const
+      else let 
+        val (q,r) = IntInf.divMod (n, two)
+      in
+        HOLogic.bit_const $ bin_of q $ mk_bit r
+      end
+  in 
+    HOLogic.number_of_const ty $ (bin_of n)
+  end
+
+fun dest_intinf n = 
+    let
+	fun dest_bit n = 
+	    case n of 
+		Const ("Numeral.bit.B0", _) => FloatArith.izero
+	      | Const ("Numeral.bit.B1", _) => FloatArith.ione
+	      | _ => raise Dest_intinf
+			 
+	fun int_of n = 
+	    case n of
+		Const ("Numeral.Pls", _) => FloatArith.izero
+	      | Const ("Numeral.Min", _) => FloatArith.imone
+	      | Const ("Numeral.Bit", _) $ q $ r => FloatArith.iadd (FloatArith.imul (int_of q) FloatArith.itwo) (dest_bit r)
+	      | _ => raise Dest_intinf
+    in
+	case n of 
+	    Const ("Numeral.number_of", _) $ n' => int_of n'
+	  | Const ("Numeral0", _) => FloatArith.izero
+	  | Const ("Numeral1", _) => FloatArith.ione    
+	  | _ => raise Dest_intinf
+    end
+
+fun mk_float (a,b) = 
+    float_const $ (HOLogic.mk_prod ((mk_intinf HOLogic.intT a), (mk_intinf HOLogic.intT b)))
+
+fun dest_float f = 
+    case f of 
+	(Const ("Float.float", _) $ (Const ("Pair", _) $ a $ b)) => (dest_intinf a, dest_intinf b)
+      | Const ("Numeral.number_of",_) $ a => (dest_intinf f, 0)
+      | Const ("Numeral0", _) => (FloatArith.izero, FloatArith.izero)
+      | Const ("Numeral1", _) => (FloatArith.ione, FloatArith.izero)
+      | _ => raise Dest_float
+
+fun dest_nat n = 
+    let 
+	val v = dest_intinf n
+    in
+	if IntInf.< (v, FloatArith.izero) then
+	    FloatArith.izero
+	else
+	    v
+    end
+
+fun approx_float prec f value = 
+    let
+	val interval = ExactFloatingPoint.approx_decstr_by_bin prec value
+	val (flower, fupper) = f interval
+    in
+	(mk_float flower, mk_float fupper)
+    end
+
+(*exception Float_op_oracle_data of term;
+
+fun float_op_oracle (sg, exn as Float_op_oracle_data t) =
+    Logic.mk_equals (t,
+		     case t of 
+			 f $ a $ b => 
+			 let 
+			     val a' = dest_float a 
+			     val b' = dest_float b
+			 in
+			     if f = float_add_const then
+				 mk_float (FloatArith.add a' b')	
+			     else if f = float_diff_const then
+				 mk_float (FloatArith.sub a' b')
+			     else if f = float_mult_const then
+				 mk_float (FloatArith.mul a' b')		
+			     else if f = float_le_const then
+				 (if FloatArith.is_less b' a' then
+				     HOLogic.false_const
+				 else
+				     HOLogic.true_const)
+			     else raise exn	    		    	       
+			 end
+		       | f $ a => 
+			 let
+			     val a' = dest_float a
+			 in
+			     if f = float_uminus_const then
+				 mk_float (FloatArith.neg a')
+			     else if f = float_abs_const then
+				 mk_float (FloatArith.abs a')
+			     else if f = float_pprt_const then
+				 mk_float (FloatArith.positive_part a')
+			     else if f = float_nprt_const then
+				 mk_float (FloatArith.negative_part a')
+			     else
+				 raise exn
+			 end
+		       | _ => raise exn
+		    )
+val th = ref ([]: theory list)
+val sg = ref ([]: Sign.sg list)
+
+fun invoke_float_op c = 
+    let
+	val th = (if length(!th) = 0 then th := [theory "MatrixLP"] else (); hd (!th))
+	val sg = (if length(!sg) = 0 then sg := [sign_of th] else (); hd (!sg))
+    in
+	invoke_oracle th "float_op" (sg, Float_op_oracle_data c)
+    end
+
+exception Nat_op_oracle_data of term;
+
+fun nat_op_oracle (sg, exn as Nat_op_oracle_data t) =
+    Logic.mk_equals (t,
+		     case t of 
+			 f $ a $ b => 
+			 let 
+			     val a' = dest_nat a 
+			     val b' = dest_nat b
+			 in
+			     if f = nat_le_const then
+				 (if IntInf.<= (a', b') then
+				     HOLogic.true_const
+				 else
+				     HOLogic.false_const)
+			     else if f = nat_eq_const then
+				 (if a' = b' then 
+				      HOLogic.true_const
+				  else
+				      HOLogic.false_const)
+			     else if f = nat_less_const then
+				 (if IntInf.< (a', b') then
+				      HOLogic.true_const
+				  else
+				      HOLogic.false_const)
+			     else 
+				 raise exn	    	
+			 end
+		       | _ => raise exn)
+
+fun invoke_nat_op c = 
+    let
+	val th = (if length (!th) = 0 then th := [theory "MatrixLP"] else (); hd (!th))
+	val sg = (if length (!sg) = 0 then sg := [sign_of th] else (); hd (!sg))
+    in
+	invoke_oracle th "nat_op" (sg, Nat_op_oracle_data c)
+    end
+*)
+end;