\DOC

\TYPE {WORD_SHIFT_ss : ssfrag}

\SYNOPSIS

Simplification fragment for words.

\KEYWORDS

simplification, words.

\DESCRIBE

The fragment {WORD_SHIFT_ss} does some basic simplifications for the
operations: {<<} (left shift), {>>} (arithmetic right shift), {>>>} (logical
right shift), {#>>} (rotate right) and {#<<} (rotate left).  More
simplification is possible when used in combination with {wordsLib.SIZES_ss}.

\EXAMPLE

{
- SIMP_CONV (std_ss++WORD_SHIFT_ss) [] ``a << 2 << 3 + a >> 3 >> 2 + a >>> 1 >>> 2 + a #<< 1 #<< 2``
<<HOL message: inventing new type variable names: 'a>>
> val it =
    |- a << 2 << 3 + a >> 3 >> 2 + a >>> 1 >>> 2 + a #<< 1 #<< 2 =
       a << 5 + a >> 5 + a >>> 3 + a #<< 3 : thm

- SIMP_CONV (std_ss++WORD_SHIFT_ss) [] ``a >> 0 + 0w << n + a #<< 2 #>> 2``
<<HOL message: inventing new type variable names: 'a>>
> val it = |- a >> 0 + 0w << n + a #<< 2 #>> 2 = a + 0w + a : thm
}

More simplification is possible when the word length is known.
{
- SIMP_CONV (std_ss++SIZES_ss++WORD_SHIFT_ss) [] ``a << 4 + (a #<< 6) : word4``
> val it = |- a << 4 = 0w + a #<< 2 : thm
}

\COMMENTS

When the word length is known the fragment {WORD_ss} simplifies {#<<} to {#>>}.

\SEEALSO

fcpLib.FCP_ss, wordsLib.BIT_ss, wordsLib.SIZES_ss, wordsLib.WORD_ARITH_ss,
wordsLib.WORD_LOGIC_ss, wordsLib.WORD_ARITH_EQ_ss, wordsLib.WORD_BIT_EQ_ss,
wordsLib.WORD_EXTRACT_ss, wordsLib.WORD_MUL_LSL_ss, wordsLib.WORD_ss

\ENDDOC