src/HOL/Real/float.ML

     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 
+end
 =
 struct
 
 exception Destruct_floatstr of string;
 
-fun destruct_floatstr isDigit isExp number = 
+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 
+	  | 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 
+	  | readdigits (q as c::cs) =
+	    if (isDigit c) then
 		let
 		    val (digits, rest) = readdigits cs
 		in
 		    (c::digits, rest)
 		end
 	    else
-		([], q)		
+		([], 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	    
+	    end
 
 	fun readfromexp [] = (true, [])
-	  | readfromexp (c::cs) = 
+	  | readfromexp (c::cs) =
 	    if isExp c then
 		readfromexp_helper cs
-	    else 
-		raise (Destruct_floatstr number)		
+	    else
+		raise (Destruct_floatstr number)
 
 	fun readfromdot [] = ([], readfromexp [])
-	  | readfromdot ((#".")::cs) = 
-	    let		
+	  | readfromdot ((#".")::cs) =
+	    let
 		val (digits, rest) = readdigits cs
 		val exp = readfromexp rest
 	    in
 		(digits, exp)
-	    end		
+	    end
 	  | readfromdot cs = readfromdot ((#".")::cs)
-			    
-	val (positive, numlist) = countsigns numlist				 
-	val (digits1, numlist) = readdigits numlist				 
+
+	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 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') = 
+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 
+	    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))	
+		(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 
+	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 
+		if intle zero q2 then
 		    raise (Floating_point "find_most_significant")
 		else
 		    (L1, (q1, r1))
 	    end
 	else

 	    in
 		if intle zero q0 then
 		    (L, (q0, r0))
 		else
 		    raise (Floating_point "find_most_significant")
-	    end		    
+	    end
     end
 
 fun approx_dec_by_bin n (q,r) =
-    let	
+    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 
+	fun approx d_seq d0 precision (q,r) =
+	    if q = zero then
 		let val x = seq2bin d_seq in
 		    (x, x)
 		end
-	    else    
-		let 
+	    else
+		let
 		    val (d, (q', r')) = find_most_significant q r
-		in	
-		    if intless precision (intsub d0 d) then 
-			let 
+		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) *) 
+			    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		
-	
+			approx (d::d_seq) d0 precision (q', r') 						    
+		end
+
 	fun approx_start precision (q, r) =
-	    if q = zero then 
+	    if q = zero then
 		((zero, zero), (zero, zero))
 	    else
-		let 
+		let
 		    val (d, (q', r')) = find_most_significant q r
-		in	
-		    if intle precision zero then 
+		in
+		    if intle precision zero then
 			let
 			    val x1 = seq2bin [d]
 			in
-			    if q' = zero then 
+			    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 
+		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) 
+	    let
+		val ((a1,b1), (a2, b2)) = approx_start n (intneg q, r)
 	    in
 		((intneg a2, b2), (intneg a1, b1))
-	    end					
+	    end
     end
 
 fun approx_decstr_by_bin n decstr =
-    let 
-	fun str2int s = case IntInf.fromString s of SOME x => x | NONE => zero 
+    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 = 
+structure FloatArith =
 struct
 
-type float = IntInf.int * IntInf.int 
+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 isub a b = IntInf.- (a,b)
 fun iadd a b = IntInf.+ (a,b)
 
 val floatzero = (izero, izero)
 
-fun positive_part (a,b) = 
+fun positive_part (a,b) =
     (if IntInf.< (a,izero) then izero else a, b)
 
-fun negative_part (a,b) = 
+fun negative_part (a,b) =
     (if IntInf.< (a,izero) then a else izero, b)
 
-fun is_negative (a,b) = 
+fun is_negative (a,b) =
     if IntInf.< (a, izero) then true else false
 
-fun is_positive (a,b) = 
+fun is_positive (a,b) =
     if IntInf.< (izero, a) then true else false
 
-fun is_zero (a,b) = 
+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) = 
+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) = 
+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)
 

     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_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_mult_const : term
     val float_le_const : term
 
     val nat_le_const : term
     val nat_less_const : term
     val nat_eq_const : 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 
-= 
+end
+=
 struct
 
 structure Inttab = TableFun(type key = int val ord = (rev_order o int_ord));
 
 type float = IntInf.int*IntInf.int

 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) = 
+fun mk_intinf ty n = HOLogic.number_of_const ty $ HOLogic.mk_numeral n;
+
+val dest_intinf = snd o HOLogic.dest_number
+
+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 
+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 
+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 = 
+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)

 
 (*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 
+		     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')	
+				 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')		
+				 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	    		    	       
+			     else raise exn	    		    
 			 end
-		       | f $ a => 
+		       | f $ a =>
 			 let
 			     val a' = dest_float a
 			 in
 			     if f = float_uminus_const then
 				 mk_float (FloatArith.neg a')

 		       | _ => raise exn
 		    )
 val th = ref ([]: theory list)
 val sg = ref ([]: Sign.sg list)
 
-fun invoke_float_op c = 
+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)

 
 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 
+		     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 
+				 (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	    	
+			     else
+				 raise exn
+
 			 end
 		       | _ => raise exn)
 
-fun invoke_nat_op c = 
+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)