--- a/src/ZF/Tools/twos_compl.ML Thu Aug 21 13:59:45 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,124 +0,0 @@
-(* Title: ZF/Tools/twos_compl.ML
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1993 University of Cambridge
-
-ML code for Arithmetic on binary integers; the model for theory Bin
-
- The sign Pls stands for an infinite string of leading 0s.
- The sign Min stands for an infinite string of leading 1s.
-
-See int_of_binary for the numerical interpretation. A number can have
-multiple representations, namely leading 0s with sign Pls and leading 1s with
-sign Min. A number is in NORMAL FORM if it has no such extra bits.
-
-The representation expects that (m mod 2) is 0 or 1, even if m is negative;
-For instance, ~5 div 2 = ~3 and ~5 mod 2 = 1; thus ~5 = (~3)*2 + 1
-
-Still needs division!
-*)
-
-infix 5 $$ $$$
-
-(*Recursive datatype of binary integers*)
-datatype bin = Pls | Min | $$ of bin * int;
-
-(** Conversions between bin and int **)
-
-fun int_of_binary Pls = 0
- | int_of_binary Min = ~1
- | int_of_binary (w$$b) = 2 * int_of_binary w + b;
-
-fun binary_of_int 0 = Pls
- | binary_of_int ~1 = Min
- | binary_of_int n = binary_of_int (n div 2) $$ (n mod 2);
-
-(*** Addition ***)
-
-(*Attach a bit while preserving the normal form. Cases left as default
- are Pls$$$1 and Min$$$0. *)
-fun Pls $$$ 0 = Pls
- | Min $$$ 1 = Min
- | v $$$ x = v$$x;
-
-(*Successor of an integer, assumed to be in normal form.
- If w$$1 is normal then w is not Min, so bin_succ(w) $$ 0 is normal.
- But Min$$0 is normal while Min$$1 is not.*)
-fun bin_succ Pls = Pls$$1
- | bin_succ Min = Pls
- | bin_succ (w$$1) = bin_succ(w) $$ 0
- | bin_succ (w$$0) = w $$$ 1;
-
-(*Predecessor of an integer, assumed to be in normal form.
- If w$$0 is normal then w is not Pls, so bin_pred(w) $$ 1 is normal.
- But Pls$$1 is normal while Pls$$0 is not.*)
-fun bin_pred Pls = Min
- | bin_pred Min = Min$$0
- | bin_pred (w$$1) = w $$$ 0
- | bin_pred (w$$0) = bin_pred(w) $$ 1;
-
-(*Sum of two binary integers in normal form.
- Ensure last $$ preserves normal form! *)
-fun bin_add (Pls, w) = w
- | bin_add (Min, w) = bin_pred w
- | bin_add (v$$x, Pls) = v$$x
- | bin_add (v$$x, Min) = bin_pred (v$$x)
- | bin_add (v$$x, w$$y) =
- bin_add(v, if x+y=2 then bin_succ w else w) $$$ ((x+y) mod 2);
-
-(*** Subtraction ***)
-
-(*Unary minus*)
-fun bin_minus Pls = Pls
- | bin_minus Min = Pls$$1
- | bin_minus (w$$1) = bin_pred (bin_minus(w) $$$ 0)
- | bin_minus (w$$0) = bin_minus(w) $$ 0;
-
-(*** Multiplication ***)
-
-(*product of two bins; a factor of 0 might cause leading 0s in result*)
-fun bin_mult (Pls, _) = Pls
- | bin_mult (Min, v) = bin_minus v
- | bin_mult (w$$1, v) = bin_add(bin_mult(w,v) $$$ 0, v)
- | bin_mult (w$$0, v) = bin_mult(w,v) $$$ 0;
-
-(*** Testing ***)
-
-(*tests addition*)
-fun checksum m n =
- let val wm = binary_of_int m
- and wn = binary_of_int n
- val wsum = bin_add(wm,wn)
- in if m+n = int_of_binary wsum then (wm, wn, wsum, m+n)
- else raise Match
- end;
-
-fun bfact n = if n=0 then Pls$$1
- else bin_mult(binary_of_int n, bfact(n-1));
-
-(*Examples...
-bfact 5;
-int_of_binary it;
-bfact 69;
-int_of_binary it;
-
-(*For {HOL,ZF}/ex/BinEx.ML*)
-bin_add(binary_of_int 13, binary_of_int 19);
-bin_add(binary_of_int 1234, binary_of_int 5678);
-bin_add(binary_of_int 1359, binary_of_int ~2468);
-bin_add(binary_of_int 93746, binary_of_int ~46375);
-bin_minus(binary_of_int 65745);
-bin_minus(binary_of_int ~54321);
-bin_mult(binary_of_int 13, binary_of_int 19);
-bin_mult(binary_of_int ~84, binary_of_int 51);
-bin_mult(binary_of_int 255, binary_of_int 255);
-bin_mult(binary_of_int 1359, binary_of_int ~2468);
-
-
-(*leading zeros??*)
-bin_add(binary_of_int 1234, binary_of_int ~1234);
-bin_mult(binary_of_int 1234, Pls);
-
-(*leading ones??*)
-bin_add(binary_of_int 1, binary_of_int ~2);
-bin_add(binary_of_int 1234, binary_of_int ~1235);
-*)