# HG changeset patch # User obua # Date 1121197778 -7200 # Node ID b214f21ae396ec1ae1b724103ec1189440020acc # Parent 6632354665629603da96e6b82c117cf6dc730bb0 - use TableFun instead of homebrew binary tree in am_interpreter.ML - add Floats to HOL/Real diff -r 663235466562 -r b214f21ae396 src/HOL/IsaMakefile --- a/src/HOL/IsaMakefile Tue Jul 12 19:29:52 2005 +0200 +++ b/src/HOL/IsaMakefile Tue Jul 12 21:49:38 2005 +0200 @@ -143,6 +143,7 @@ Real/Rational.thy Real/PReal.thy Real/RComplete.thy \ Real/ROOT.ML Real/Real.thy Real/real_arith.ML Real/RealDef.thy \ Real/RealPow.thy Real/document/root.tex \ + Real/Float.thy Real/Float.ML \ Hyperreal/EvenOdd.thy Hyperreal/Fact.thy Hyperreal/HLog.thy \ Hyperreal/Filter.thy Hyperreal/HSeries.thy \ Hyperreal/HTranscendental.thy Hyperreal/HyperArith.thy \ diff -r 663235466562 -r b214f21ae396 src/HOL/Real/Float.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Real/Float.ML Tue Jul 12 21:49:38 2005 +0200 @@ -0,0 +1,519 @@ +(* 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 + +fun fst (a,b) = a +fun snd (a,b) = b + +val filter = List.filter; + +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 ("op +", HOLogic.realT --> HOLogic.realT --> HOLogic.realT) +val float_diff_const = Const ("op -", HOLogic.realT --> HOLogic.realT --> HOLogic.realT) +val float_mult_const = Const ("op *", HOLogic.realT --> HOLogic.realT --> HOLogic.realT) +val float_uminus_const = Const ("uminus", HOLogic.realT --> HOLogic.realT) +val float_abs_const = Const ("HOL.abs", HOLogic.realT --> HOLogic.realT) +val float_le_const = Const ("op <=", 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 ("op <=", HOLogic.natT --> HOLogic.natT --> HOLogic.boolT) +val nat_less_const = Const ("op <", 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.false_const else HOLogic.true_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): doesn't work in SML 10.0.7, but in newer versions!!!*) + val q = IntInf.div (n, two) + val r = IntInf.mod (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 ("False", _) => FloatArith.izero + | Const ("True", _) => 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.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; \ No newline at end of file diff -r 663235466562 -r b214f21ae396 src/HOL/Real/Float.thy --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Real/Float.thy Tue Jul 12 21:49:38 2005 +0200 @@ -0,0 +1,525 @@ +(* Title: HOL/Real/Float.thy + ID: $Id$ + Author: Steven Obua +*) + +theory Float = Real: + +constdefs + pow2 :: "int \ real" + "pow2 a == if (0 <= a) then (2^(nat a)) else (inverse (2^(nat (-a))))" + float :: "int * int \ real" + "float x == (real (fst x)) * (pow2 (snd x))" + +lemma pow2_0[simp]: "pow2 0 = 1" +by (simp add: pow2_def) + +lemma pow2_1[simp]: "pow2 1 = 2" +by (simp add: pow2_def) + +lemma pow2_neg: "pow2 x = inverse (pow2 (-x))" +by (simp add: pow2_def) + +lemma pow2_add1: "pow2 (1 + a) = 2 * (pow2 a)" +proof - + have h: "! n. nat (2 + int n) - Suc 0 = nat (1 + int n)" by arith + have g: "! a b. a - -1 = a + (1::int)" by arith + have pos: "! n. pow2 (int n + 1) = 2 * pow2 (int n)" + apply (auto, induct_tac n) + apply (simp_all add: pow2_def) + apply (rule_tac m1="2" and n1="nat (2 + int na)" in ssubst[OF realpow_num_eq_if]) + apply (auto simp add: h) + apply arith + done + show ?thesis + proof (induct a) + case (1 n) + from pos show ?case by (simp add: ring_eq_simps) + next + case (2 n) + show ?case + apply (auto) + apply (subst pow2_neg[of "- int n"]) + apply (subst pow2_neg[of "-1 - int n"]) + apply (auto simp add: g pos) + done + qed +qed + +lemma pow2_add: "pow2 (a+b) = (pow2 a) * (pow2 b)" +proof (induct b) + case (1 n) + show ?case + proof (induct n) + case 0 + show ?case by simp + next + case (Suc m) + show ?case by (auto simp add: ring_eq_simps pow2_add1 prems) + qed +next + case (2 n) + show ?case + proof (induct n) + case 0 + show ?case + apply (auto) + apply (subst pow2_neg[of "a + -1"]) + apply (subst pow2_neg[of "-1"]) + apply (simp) + apply (insert pow2_add1[of "-a"]) + apply (simp add: ring_eq_simps) + apply (subst pow2_neg[of "-a"]) + apply (simp) + done + case (Suc m) + have a: "int m - (a + -2) = 1 + (int m - a + 1)" by arith + have b: "int m - -2 = 1 + (int m + 1)" by arith + show ?case + apply (auto) + apply (subst pow2_neg[of "a + (-2 - int m)"]) + apply (subst pow2_neg[of "-2 - int m"]) + apply (auto simp add: ring_eq_simps) + apply (subst a) + apply (subst b) + apply (simp only: pow2_add1) + apply (subst pow2_neg[of "int m - a + 1"]) + apply (subst pow2_neg[of "int m + 1"]) + apply auto + apply (insert prems) + apply (auto simp add: ring_eq_simps) + done + qed +qed + +lemma "float (a, e) + float (b, e) = float (a + b, e)" +by (simp add: float_def ring_eq_simps) + +constdefs + int_of_real :: "real \ int" + "int_of_real x == SOME y. real y = x" + real_is_int :: "real \ bool" + "real_is_int x == ? (u::int). x = real u" + +lemma real_is_int_def2: "real_is_int x = (x = real (int_of_real x))" +by (auto simp add: real_is_int_def int_of_real_def) + +lemma float_transfer: "real_is_int ((real a)*(pow2 c)) \ float (a, b) = float (int_of_real ((real a)*(pow2 c)), b - c)" +by (simp add: float_def real_is_int_def2 pow2_add[symmetric]) + +lemma pow2_int: "pow2 (int c) = (2::real)^c" +by (simp add: pow2_def) + +lemma float_transfer_nat: "float (a, b) = float (a * 2^c, b - int c)" +by (simp add: float_def pow2_int[symmetric] pow2_add[symmetric]) + +lemma real_is_int_real[simp]: "real_is_int (real (x::int))" +by (auto simp add: real_is_int_def int_of_real_def) + +lemma int_of_real_real[simp]: "int_of_real (real x) = x" +by (simp add: int_of_real_def) + +lemma real_int_of_real[simp]: "real_is_int x \ real (int_of_real x) = x" +by (auto simp add: int_of_real_def real_is_int_def) + +lemma real_is_int_add_int_of_real: "real_is_int a \ real_is_int b \ (int_of_real (a+b)) = (int_of_real a) + (int_of_real b)" +by (auto simp add: int_of_real_def real_is_int_def) + +lemma real_is_int_add[simp]: "real_is_int a \ real_is_int b \ real_is_int (a+b)" +apply (subst real_is_int_def2) +apply (simp add: real_is_int_add_int_of_real real_int_of_real) +done + +lemma int_of_real_sub: "real_is_int a \ real_is_int b \ (int_of_real (a-b)) = (int_of_real a) - (int_of_real b)" +by (auto simp add: int_of_real_def real_is_int_def) + +lemma real_is_int_sub[simp]: "real_is_int a \ real_is_int b \ real_is_int (a-b)" +apply (subst real_is_int_def2) +apply (simp add: int_of_real_sub real_int_of_real) +done + +lemma real_is_int_rep: "real_is_int x \ ?! (a::int). real a = x" +by (auto simp add: real_is_int_def) + +lemma int_of_real_mult: + assumes "real_is_int a" "real_is_int b" + shows "(int_of_real (a*b)) = (int_of_real a) * (int_of_real b)" +proof - + from prems have a: "?! (a'::int). real a' = a" by (rule_tac real_is_int_rep, auto) + from prems have b: "?! (b'::int). real b' = b" by (rule_tac real_is_int_rep, auto) + from a obtain a'::int where a':"a = real a'" by auto + from b obtain b'::int where b':"b = real b'" by auto + have r: "real a' * real b' = real (a' * b')" by auto + show ?thesis + apply (simp add: a' b') + apply (subst r) + apply (simp only: int_of_real_real) + done +qed + +lemma real_is_int_mult[simp]: "real_is_int a \ real_is_int b \ real_is_int (a*b)" +apply (subst real_is_int_def2) +apply (simp add: int_of_real_mult) +done + +lemma real_is_int_0[simp]: "real_is_int (0::real)" +by (simp add: real_is_int_def int_of_real_def) + +lemma real_is_int_1[simp]: "real_is_int (1::real)" +proof - + have "real_is_int (1::real) = real_is_int(real (1::int))" by auto + also have "\ = True" by (simp only: real_is_int_real) + ultimately show ?thesis by auto +qed + +lemma real_is_int_n1: "real_is_int (-1::real)" +proof - + have "real_is_int (-1::real) = real_is_int(real (-1::int))" by auto + also have "\ = True" by (simp only: real_is_int_real) + ultimately show ?thesis by auto +qed + +lemma real_is_int_number_of[simp]: "real_is_int ((number_of::bin\real) x)" +proof - + have neg1: "real_is_int (-1::real)" + proof - + have "real_is_int (-1::real) = real_is_int(real (-1::int))" by auto + also have "\ = True" by (simp only: real_is_int_real) + ultimately show ?thesis by auto + qed + + { + fix x::int + have "!! y. real_is_int ((number_of::bin\real) (Abs_Bin x))" + apply (simp add: number_of_eq) + apply (subst Abs_Bin_inverse) + apply (simp add: Bin_def) + apply (induct x) + apply (induct_tac n) + apply (simp) + apply (simp) + apply (induct_tac n) + apply (simp add: neg1) + proof - + fix n :: nat + assume rn: "(real_is_int (of_int (- (int (Suc n)))))" + have s: "-(int (Suc (Suc n))) = -1 + - (int (Suc n))" by simp + show "real_is_int (of_int (- (int (Suc (Suc n)))))" + apply (simp only: s of_int_add) + apply (rule real_is_int_add) + apply (simp add: neg1) + apply (simp only: rn) + done + qed + } + note Abs_Bin = this + { + fix x :: bin + have "? u. x = Abs_Bin u" + apply (rule exI[where x = "Rep_Bin x"]) + apply (simp add: Rep_Bin_inverse) + done + } + then obtain u::int where "x = Abs_Bin u" by auto + with Abs_Bin show ?thesis by auto +qed + +lemma int_of_real_0[simp]: "int_of_real (0::real) = (0::int)" +by (simp add: int_of_real_def) + +lemma int_of_real_1[simp]: "int_of_real (1::real) = (1::int)" +proof - + have 1: "(1::real) = real (1::int)" by auto + show ?thesis by (simp only: 1 int_of_real_real) +qed + +lemma int_of_real_number_of[simp]: "int_of_real (number_of b) = number_of b" +proof - + have "real_is_int (number_of b)" by simp + then have uu: "?! u::int. number_of b = real u" by (auto simp add: real_is_int_rep) + then obtain u::int where u:"number_of b = real u" by auto + have "number_of b = real ((number_of b)::int)" + by (simp add: number_of_eq real_of_int_def) + have ub: "number_of b = real ((number_of b)::int)" + by (simp add: number_of_eq real_of_int_def) + from uu u ub have unb: "u = number_of b" + by blast + have "int_of_real (number_of b) = u" by (simp add: u) + with unb show ?thesis by simp +qed + +lemma float_transfer_even: "even a \ float (a, b) = float (a div 2, b+1)" + apply (subst float_transfer[where a="a" and b="b" and c="-1", simplified]) + apply (simp_all add: pow2_def even_def real_is_int_def ring_eq_simps) + apply (auto) +proof - + fix q::int + have a:"b - (-1\int) = (1\int) + b" by arith + show "(float (q, (b - (-1\int)))) = (float (q, ((1\int) + b)))" + by (simp add: a) +qed + +consts + norm_float :: "int*int \ int*int" + +lemma int_div_zdiv: "int (a div b) = (int a) div (int b)" +apply (subst split_div, auto) +apply (subst split_zdiv, auto) +apply (rule_tac a="int (b * i) + int j" and b="int b" and r="int j" and r'=ja in IntDiv.unique_quotient) +apply (auto simp add: IntDiv.quorem_def int_eq_of_nat) +done + +lemma int_mod_zmod: "int (a mod b) = (int a) mod (int b)" +apply (subst split_mod, auto) +apply (subst split_zmod, auto) +apply (rule_tac a="int (b * i) + int j" and b="int b" and q="int i" and q'=ia in IntDiv.unique_remainder) +apply (auto simp add: IntDiv.quorem_def int_eq_of_nat) +done + +lemma abs_div_2_less: "a \ 0 \ a \ -1 \ abs((a::int) div 2) < abs a" +by arith + +lemma terminating_norm_float: "\a. (a::int) \ 0 \ even a \ a \ 0 \ \a div 2\ < \a\" +apply (auto) +apply (rule abs_div_2_less) +apply (auto) +done + +ML {* simp_depth_limit := 2 *} +recdef norm_float "measure (% (a,b). nat (abs a))" + "norm_float (a,b) = (if (a \ 0) & (even a) then norm_float (a div 2, b+1) else (if a=0 then (0,0) else (a,b)))" +(hints simp: terminating_norm_float) +ML {* simp_depth_limit := 1000 *} + +lemma norm_float: "float x = float (norm_float x)" +proof - + { + fix a b :: int + have norm_float_pair: "float (a,b) = float (norm_float (a,b))" + proof (induct a b rule: norm_float.induct) + case (1 u v) + show ?case + proof cases + assume u: "u \ 0 \ even u" + with prems have ind: "float (u div 2, v + 1) = float (norm_float (u div 2, v + 1))" by auto + with u have "float (u,v) = float (u div 2, v+1)" by (simp add: float_transfer_even) + then show ?thesis + apply (subst norm_float.simps) + apply (simp add: ind) + done + next + assume "~(u \ 0 \ even u)" + then show ?thesis + by (simp add: prems float_def) + qed + qed + } + note helper = this + have "? a b. x = (a,b)" by auto + then obtain a b where "x = (a, b)" by blast + then show ?thesis by (simp only: helper) +qed + +lemma pow2_int: "pow2 (int n) = 2^n" + by (simp add: pow2_def) + +lemma float_add: + "float (a1, e1) + float (a2, e2) = + (if e1<=e2 then float (a1+a2*2^(nat(e2-e1)), e1) + else float (a1*2^(nat (e1-e2))+a2, e2))" + apply (simp add: float_def ring_eq_simps) + apply (auto simp add: pow2_int[symmetric] pow2_add[symmetric]) + done + +lemma float_mult: + "float (a1, e1) * float (a2, e2) = + (float (a1 * a2, e1 + e2))" + by (simp add: float_def pow2_add) + +lemma float_minus: + "- (float (a,b)) = float (-a, b)" + by (simp add: float_def) + +lemma zero_less_pow2: + "0 < pow2 x" +proof - + { + fix y + have "0 <= y \ 0 < pow2 y" + by (induct y, induct_tac n, simp_all add: pow2_add) + } + note helper=this + show ?thesis + apply (case_tac "0 <= x") + apply (simp add: helper) + apply (subst pow2_neg) + apply (simp add: helper) + done +qed + +lemma zero_le_float: + "(0 <= float (a,b)) = (0 <= a)" + apply (auto simp add: float_def) + apply (auto simp add: zero_le_mult_iff zero_less_pow2) + apply (insert zero_less_pow2[of b]) + apply (simp_all) + done + +lemma float_le_zero: + "(float (a,b) <= 0) = (a <= 0)" + apply (auto simp add: float_def) + apply (auto simp add: mult_le_0_iff) + apply (insert zero_less_pow2[of b]) + apply auto + done + +lemma float_abs: + "abs (float (a,b)) = (if 0 <= a then (float (a,b)) else (float (-a,b)))" + apply (auto simp add: abs_if) + apply (simp_all add: zero_le_float[symmetric, of a b] float_minus) + done + +lemma float_zero: + "float (0, b) = 0" + by (simp add: float_def) + +lemma float_pprt: + "pprt (float (a, b)) = (if 0 <= a then (float (a,b)) else (float (0, b)))" + by (auto simp add: zero_le_float float_le_zero float_zero) + +lemma float_nprt: + "nprt (float (a, b)) = (if 0 <= a then (float (0,b)) else (float (a, b)))" + by (auto simp add: zero_le_float float_le_zero float_zero) + +lemma norm_0_1: "(0::_::number_ring) = Numeral0 & (1::_::number_ring) = Numeral1" + by auto + +lemma add_left_zero: "0 + a = (a::'a::comm_monoid_add)" + by simp + +lemma add_right_zero: "a + 0 = (a::'a::comm_monoid_add)" + by simp + +lemma mult_left_one: "1 * a = (a::'a::semiring_1)" + by simp + +lemma mult_right_one: "a * 1 = (a::'a::semiring_1)" + by simp + +lemma int_pow_0: "(a::int)^(Numeral0) = 1" + by simp + +lemma int_pow_1: "(a::int)^(Numeral1) = a" + by simp + +lemma zero_eq_Numeral0_nring: "(0::'a::number_ring) = Numeral0" + by simp + +lemma one_eq_Numeral1_nring: "(1::'a::number_ring) = Numeral1" + by simp + +lemma zero_eq_Numeral0_nat: "(0::nat) = Numeral0" + by simp + +lemma one_eq_Numeral1_nat: "(1::nat) = Numeral1" + by simp + +lemma zpower_Pls: "(z::int)^Numeral0 = Numeral1" + by simp + +lemma zpower_Min: "(z::int)^((-1)::nat) = Numeral1" +proof - + have 1:"((-1)::nat) = 0" + by simp + show ?thesis by (simp add: 1) +qed + +lemma fst_cong: "a=a' \ fst (a,b) = fst (a',b)" + by simp + +lemma snd_cong: "b=b' \ snd (a,b) = snd (a,b')" + by simp + +lemma lift_bool: "x \ x=True" + by simp + +lemma nlift_bool: "~x \ x=False" + by simp + +lemma not_false_eq_true: "(~ False) = True" by simp + +lemma not_true_eq_false: "(~ True) = False" by simp + + +lemmas binarith = + Pls_0_eq Min_1_eq + bin_pred_Pls bin_pred_Min bin_pred_1 bin_pred_0 + bin_succ_Pls bin_succ_Min bin_succ_1 bin_succ_0 + bin_add_Pls bin_add_Min bin_add_BIT_0 bin_add_BIT_10 + bin_add_BIT_11 bin_minus_Pls bin_minus_Min bin_minus_1 + bin_minus_0 bin_mult_Pls bin_mult_Min bin_mult_1 bin_mult_0 + bin_add_Pls_right bin_add_Min_right + +lemma int_eq_number_of_eq: "(((number_of v)::int)=(number_of w)) = iszero ((number_of (bin_add v (bin_minus w)))::int)" + by simp + +lemma int_iszero_number_of_Pls: "iszero (Numeral0::int)" + by (simp only: iszero_number_of_Pls) + +lemma int_nonzero_number_of_Min: "~(iszero ((-1)::int))" + by simp + +lemma int_iszero_number_of_0: "iszero ((number_of (w BIT bit.B0))::int) = iszero ((number_of w)::int)" + by simp + +lemma int_iszero_number_of_1: "\ iszero ((number_of (w BIT bit.B1))::int)" + by simp + +lemma int_less_number_of_eq_neg: "(((number_of x)::int) < number_of y) = neg ((number_of (bin_add x (bin_minus y)))::int)" + by simp + +lemma int_not_neg_number_of_Pls: "\ (neg (Numeral0::int))" + by simp + +lemma int_neg_number_of_Min: "neg (-1::int)" + by simp + +lemma int_neg_number_of_BIT: "neg ((number_of (w BIT x))::int) = neg ((number_of w)::int)" + by simp + +lemma int_le_number_of_eq: "(((number_of x)::int) \ number_of y) = (\ neg ((number_of (bin_add y (bin_minus x)))::int))" + by simp + +lemmas intarithrel = + int_eq_number_of_eq + lift_bool[OF int_iszero_number_of_Pls] nlift_bool[OF int_nonzero_number_of_Min] int_iszero_number_of_0 + lift_bool[OF int_iszero_number_of_1] int_less_number_of_eq_neg nlift_bool[OF int_not_neg_number_of_Pls] lift_bool[OF int_neg_number_of_Min] + int_neg_number_of_BIT int_le_number_of_eq + +lemma int_number_of_add_sym: "((number_of v)::int) + number_of w = number_of (bin_add v w)" + by simp + +lemma int_number_of_diff_sym: "((number_of v)::int) - number_of w = number_of (bin_add v (bin_minus w))" + by simp + +lemma int_number_of_mult_sym: "((number_of v)::int) * number_of w = number_of (bin_mult v w)" + by simp + +lemma int_number_of_minus_sym: "- ((number_of v)::int) = number_of (bin_minus v)" + by simp + +lemmas intarith = int_number_of_add_sym int_number_of_minus_sym int_number_of_diff_sym int_number_of_mult_sym + +lemmas natarith = add_nat_number_of diff_nat_number_of mult_nat_number_of eq_nat_number_of less_nat_number_of + +lemmas powerarith = nat_number_of zpower_number_of_even + zpower_number_of_odd[simplified zero_eq_Numeral0_nring one_eq_Numeral1_nring] + zpower_Pls zpower_Min + +lemmas floatarith[simplified norm_0_1] = float_add float_mult float_minus float_abs zero_le_float float_pprt float_nprt + +(* for use with the compute oracle *) +lemmas arith = binarith intarith intarithrel natarith powerarith floatarith not_false_eq_true not_true_eq_false + +end + diff -r 663235466562 -r b214f21ae396 src/HOL/Real/ROOT.ML --- a/src/HOL/Real/ROOT.ML Tue Jul 12 19:29:52 2005 +0200 +++ b/src/HOL/Real/ROOT.ML Tue Jul 12 21:49:38 2005 +0200 @@ -8,3 +8,4 @@ *) time_use_thy "Real"; +use_thy "Float"; \ No newline at end of file diff -r 663235466562 -r b214f21ae396 src/Pure/Tools/am_compiler.ML --- a/src/Pure/Tools/am_compiler.ML Tue Jul 12 19:29:52 2005 +0200 +++ b/src/Pure/Tools/am_compiler.ML Tue Jul 12 21:49:38 2005 +0200 @@ -11,10 +11,15 @@ | CApp of closure * closure | CAbs of closure | Closure of (closure list) * closure val set_compiled_rewriter : (term -> closure) -> unit + val list_nth : 'a list * int -> 'a + val list_map : ('a -> 'b) -> 'a list -> 'b list end structure AM_Compiler :> COMPILING_AM = struct +val list_nth = List.nth; +val list_map = map; + datatype term = Var of int | Const of int | App of term * term | Abs of term datatype pattern = PVar | PConst of int * (pattern list) @@ -133,7 +138,7 @@ "and weak stack (Closure (e, App (a, b))) = weak (SAppL (Closure (e, b), stack)) (Closure (e, a))", " | weak (SAppL (b, stack)) (Closure (e, Abs m)) = weak stack (Closure (b::e, m))", " | weak stack (clos as Closure (_, Abs _)) = weak_last stack clos", - " | weak stack (Closure (e, Var n)) = weak stack (List.nth (e, n) handle Subscript => (Var (n-(length e))))", + " | weak stack (Closure (e, Var n)) = weak stack ("^sname^".list_nth (e, n) handle _ => (Var (n-(length e))))", " | weak stack (Closure (e, c)) = weak stack c", " | weak stack clos = lookup stack clos", "and weak_last (SAppR (a, stack)) b = weak stack (App(a, b))", @@ -177,7 +182,7 @@ " | exportTerm (Const c) = "^sname^".CConst c", " | exportTerm (App (a,b)) = "^sname^".CApp (exportTerm a, exportTerm b)", " | exportTerm (Abs m) = "^sname^".CAbs (exportTerm m)", - " | exportTerm (Closure (closlist, clos)) = "^sname^".Closure (map exportTerm closlist, exportTerm clos)"] + " | exportTerm (Closure (closlist, clos)) = "^sname^".Closure ("^sname^".list_map exportTerm closlist, exportTerm clos)"] val _ = writelist (map ec constants) val _ = writelist [ @@ -199,9 +204,9 @@ val _ = let - val fout = TextIO.openOut "gen_code.ML" + (*val fout = TextIO.openOut "gen_code.ML" val _ = TextIO.output (fout, !buffer) - val _ = TextIO.closeOut fout + val _ = TextIO.closeOut fout*) in () end diff -r 663235466562 -r b214f21ae396 src/Pure/Tools/am_interpreter.ML --- a/src/Pure/Tools/am_interpreter.ML Tue Jul 12 19:29:52 2005 +0200 +++ b/src/Pure/Tools/am_interpreter.ML Tue Jul 12 21:49:38 2005 +0200 @@ -18,66 +18,6 @@ end -signature BIN_TREE_KEY = -sig - type key - val less : key * key -> bool - val eq : key * key -> bool -end - -signature BIN_TREE = -sig - type key - type 'a t - val tree_of_list : (key * 'a list -> 'b) -> (key * 'a) list -> 'b t - val lookup : 'a t -> key -> 'a Option.option - val empty : 'a t -end - -functor BinTreeFun(Key: BIN_TREE_KEY) : BIN_TREE = -struct - -type key = Key.key - -datatype 'a t = Empty | Node of key * 'a * 'a t * 'a t - -val empty = Empty - -fun insert (k, a) [] = [(k, a)] - | insert (k, a) ((l,b)::x') = - if Key.less (k, l) then (k, a)::(l,b)::x' - else if Key.eq (k, l) then (k, a@b)::x' - else (l,b)::(insert (k, a) x') - -fun sort ((k, a)::x) = insert (k, a) (sort x) - | sort [] = [] - -fun tree_of_sorted_list [] = Empty - | tree_of_sorted_list l = - let - val len = length l - val leftlen = (len - 1) div 2 - val left = tree_of_sorted_list (List.take (l, leftlen)) - val rightl = List.drop (l, leftlen) - val (k, x) = hd rightl - in - Node (k, x, left, tree_of_sorted_list (tl rightl)) - end - -fun tree_of_list f l = tree_of_sorted_list (map (fn (k, a) => (k, f (k,a))) (sort (map (fn (k, a) => (k, [a])) l))) - -fun lookup Empty key = NONE - | lookup (Node (k, x, left, right)) key = - if Key.less (key, k) then - lookup left key - else if Key.less (k, key) then - lookup right key - else - SOME x -end; - -structure IntBinTree = BinTreeFun (type key = int val less = (op <) val eq = (op = : int * int -> bool)); - structure AM_Interpreter :> ABSTRACT_MACHINE = struct datatype term = Var of int | Const of int | App of term * term | Abs of term @@ -88,16 +28,9 @@ | CApp of closure * closure | CAbs of closure | Closure of (closure list) * closure -structure IntPairKey = -struct -type key = int * int -fun less ((x1, y1), (x2, y2)) = x1 < x2 orelse (x1 = x2 andalso y1 < y2) -fun eq (k1, k2) = (k1 = k2) -end +structure prog_struct = TableFun(type key = int*int val ord = prod_ord int_ord int_ord); -structure prog_struct = BinTreeFun (IntPairKey) - -type program = ((pattern * closure) list) prog_struct.t +type program = ((pattern * closure) list) prog_struct.table datatype stack = SEmpty | SAppL of closure * stack | SAppR of closure * stack | SAbs of stack @@ -160,7 +93,7 @@ val eqs = map (fn (p, r) => (check_freevars (count_patternvars p) r; (pattern_key p, (p, clos_of_term r)))) eqs in - prog_struct.tree_of_list (fn (key, rules) => rules) eqs + prog_struct.make (map (fn (k, a) => (k, [a])) eqs) end fun match_rules n [] clos = NONE @@ -172,7 +105,7 @@ fun match_closure prog clos = case len_head_of_closure 0 clos of (len, CConst c) => - (case prog_struct.lookup prog (c, len) of + (case prog_struct.lookup (prog, (c, len)) of NONE => NONE | SOME rules => match_rules 0 rules clos) | _ => NONE