Improving naming of bit-vector signed division constants.

This renaming introduces incompatibilities:

• words$word_sdiv -> words$word_quot (this is proved to be related to int_quot for a non-zero divisor).
• words$word_srem -> words$word_rem (this is proved to be related to int_rem for a non-zero divisor).
• integer_word$word_sdiv (this is a new constant defined directly in terms of int_div).
• words$word_smod -> integer_word$word_smod (this is now defined directly in terms of int_mod).

Update for L3 examples.

Fixes a potential problem with the handling of word replicate.

Moves some shared code into stateLib (the register_combinations function).

Some other minor fixes.

Add BIT_SET syntax functions to wordsSyntax signature.

Move bit_count constants from examples/ARM/v7 to wordsTheory.

Add min and max operations to wordsTheory.

Overhaul to wordSyntax to make it less verbose. Added some missing constants (word_from_bin_list etc.) at the same time.

Add support for "word_abs" and "word_len" in wordsSyntax.

Add wordsSyntax.size_of.

Added new definitions and theorems for various bit-vector "saturation"
operations.

These operations return maximal or minimal values instead of, e.g.,
overflowing (wrapping). For example:

|- signed_saturate_add 100w 50w = 127w: thm

Also added a new configuration option for printing word literals as 2's
complement values. For example:

> set_trace "word pp as 2's comp" 1;
> ``253w:word8``;
val it = ``-3w``: term

Be warned that this term is actually ``n2w 253``, it's just being printed as
``word_2comp (n2w 3)``.

This printing mode is useful when checking the veracity of machine arithmetic.
For example:

> EVAL ``signed_saturate_sub 226w 100w : word8``;
val it = |- signed_saturate_sub -30w 100w = -128w: thm

Added new operations for shifting by a bit-vector value, namely:

LSL: <<~
LSR: >>>~
ASR: >>~
ROR: #>>~
ROL: #<<~

These are supported by the procedures in blastLib. For example, one can prove

w <+ 10w /\ s <+ 3w ==> w <<~ (s + 1w) <+ 73w : word16

The time-complexity is a pretty shocking but "simple" 32-bit problems seem to
be okay. NB. ROR and ROL only bit-blast with word sizes that are a power of
two.

Added a new conversion WORD_MOD_BITS_CONV for mapping applications of
``word_mod w (n2w n)`` into ``(h -- 0) w`` where n is a power of two.

Also added support for bit-blasting arbitrary multiplication, but the word-size
limit is set to 8 bits by default. Things seem to be just about feasible with
that limit (and become horrendously slow after that).

To improve performance, the conversion BBLAST_CONV does not have exactly the
same coverage as before. For backward compatibility, a conversion
EBLAST_CONV (which calls SAT at every bit position) is now available.

Add fcpSyntax and tidy up related code.

Added a function word_compare, along with the usual syntax operations.

Added functions word_s{rem,mod} (2's complement signed remainder), along with
their usual syntax operations.

Tuned.

Added the usual syntax operations for word_sdiv.

Make WORD_MUL_LSL_CONV more robust with respect to oversized word literals.
For example, we now have

> WORD_MUL_LSL_CONV ``130w * w : word4``;
val it = |- 130w * w = w ≪ 1 : thm

whereas previously it would fail.

Added a bit-blasting conversion: BBLAST_CONV. This goes beyond the
capabilities of WORD_BIT_EQ_CONV by expanding out additions / subtractions.
This allows the new conversion to automatically handle small but tricky bit
vector goals. For example:

``(x && 3w = 0w:word32) ==> ((x + 4w * y) && 3w = 0w)``

and

``!a:word8. a <+ 4w /\ b <+ a /\ c <=+ 5w ==> (b + c) <=+ 7w``

(These aren't provable with wordsLib.WORD_DECIDE.)

Obviously bit-blasting is a brute force approach, so the new conversion should
be used with care. It will only work well for smallish word sizes and when
there is only and handful of additions around. It is also "eager" -- additions
are expanded out even when not strictly necessary. For example, in

``(a + b) <+ c /\ c <+ d ==> (a + b) <+ d:word32``

the sum ``a + b`` is expanded. Users may be able to achieve speed-ups by first
introducing abbreviations and then proving general forms, e.g.

``x <+ c /\ c <+ d ==> x <+ d:word32``

The conversion handles most operators, however, the following are not covered /
interpreted:

-- Type variables for word lengths, i.e. terms of type ``:'a word``.

-- General multiplication, i.e. ``w1 * w2``. Multiplication by a literal is
okay, although this may introduce many additions.

-- Bit field selections with non-literal bounds, e.g. ``(exp1 -- exp2) w``.

-- Shifting by non-literal amounts, e.g. ``w << exp``.

-- ``n2w exp`` and ``w2n w``. Also w2s, s2w, w2l and l2w.

-- word_div, word_sdiv, word_mod and word_log2.

Further extend the bounds generation under WORD_DECIDE. For example, can now
prove:

wordsLib.WORD_DECIDE
``((4w * (3 >< 1) b + 10w) << 2) // 3w <+ 57w :word16``

Also added WORD_EXTRACT_ss to WORD_CONV. Unfortunately this can break proofs.

Added the usual syntax functions for word_mod.

Added the usual syntax functions for word_div.

Add dest_word_literal and uint_of_word to wordsSyntax.

Add notification for guessing the type of L2V - also added its definition to
the words compset.

Add syntax support for bit_field_insert.

Add syntax support for the new words operations.

Removed trailing whitespace from all .sml and .sig files.

This affects over 900 files and was done using emacs's delete-trailing-whitespace
function in batch mode. Building the system with Poly/ML and Moscow ML seems to
work, so I'm hoping these changes don't break anything. Please complain if
they do!

Free the name "index".

Extended the Unicode overloading.

Also minor changes in evaluation and two new functions:
mk_wordi and mk_wordii, which are ML integer versions of mk_word.

Added a number of tools for working with words.

The main additions are:

WORD_ss: Does some basic simplification, evaluation and AC rewriting
(over *, +, && and !!). For example, ``a * 3w + a`` -> ``4w * a`` and
``a && 3w !! a && 2w`` -> ``3w && a``.

BIT_ss: For example, ``BIT n 3`` -> ``n IN {0; 1}``.

WORD_MUL_LSL_ss: Converts multiplications to left-shifts e.g.
``2w * a`` -> ``a << 1``.

WORD_BIT_EQ_ss: Can be used to establish bit-wise (in)equality e.g.
``a && ~a = 0w`` -> ``T``. Does not work with *, + etc.

WORD_ARITH_EQ_ss: Can be used to establish arithmetic (in)equality e.g.
``~(b + 1w = b + 4294967295w:word32)`` -> ``T``.

WORD_EXTRACT_ss: Simplification for shifts and bit extraction.
"Simplifies" --, w2w, sw2sw, #>>, @@ etc. and expresses operations
using ><, << and !!.

WORD_DECIDE: A decision procedure. Will solve Boolean (bitwise) problems
and some problems over <, <+ etc.

Added a bunch of new theorems.

Changed the definition of word_rxx to something more sensible.

Changed the definition of word_concat so that it now applies a word-to-word
conversion. Thus, it is now possible to do:

- EVAL ``((0b1111w:word4) @@ (0b110011w:word6)):word10``;
> val it = |- 0b1111w @@ 0b110011w = 0b1111110011w : thm

The old definition (which produced something of type :word4+word6) has been
renamed to word_join. Apologies to anyone affected by this update.

Fixed some syntax operations to project out the dimension
types, instead of the bool ** dim types.

Fixed mistakes in signature.

Syntax support for words.