removed obsolete Real/document/root.tex;
removed obsolete Isar_examples/Cantor.ML;
renamed Real/Float.ML to Real/float.ML;
--- 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 \
--- 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;
--- /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;