Covers word_source/mixed_arithmetic_words.c. Two genuine findings recorded
in comments rather than fixed:
- register_mixed_arithmetic_words registers MOD and /MOD a second time,
after arithmetic_words.c's own registrations; vm_create_word links new
entries at the head of vm->latest and FIND scans from vm->latest forward,
so arithmetic_words.c's MOD//MOD are permanently shadowed, unreachable
dead code once bootstrap completes (verified against
dictionary_management.c and the module order in word_registry.c).
- M*, M/MOD, and the "avoids intermediate overflow" claim on */ and */MOD
are false on 64-bit builds: cell_t and "long long" are the same width
there, so the long-long intermediate does not actually widen the
product -- it wraps mod 2^64 like plain cell multiplication before the
32-bit-style split/reconstruction runs. M*/M/MOD are left undefined
here (oops-equivalent: documented as not modelled, since formalizing
"the wrong thing, faithfully" adds no proof value) rather than fixed.
MOD//MOD/*//*/MOD reuse cell_sdiv/cell_smod from the arithmetic-words
migration; M+/M- transcribe the C's hand-rolled signed carry/borrow
detection literally, proving only stack-level plumbing (not double-
precision correctness, which needs an interpretation function this
suite doesn't build).
All 24 theory files verify with zero errors.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
cell_t is a 64-bit signed C long; the formal model previously used
unbounded HOL int, hiding wraparound and signed/unsigned distinctions
entirely. Switches cell to "64 word" throughout and fixes every proof
site that assumed int semantics:
- StarForth_Base.thy: cell_safe/cell_abs/cell_sdiv/cell_smod plus the
sint-bridging lemmas used across the suite
- StarForth_Loop1_Heat.thy, StarForth_Loop3_Decay.thy: heat tracking
converted to signed word comparisons (<s/\<le>s)
- StarForth_Stack_Words.thy: PICK/ROLL against real C ground truth
- StarForth_Arithmetic_Words.thy: ABS/MIN/MAX/div/mod rebuilt on signed
word semantics (cell_sdiv/cell_smod match C99 truncating division;
2/ uses signed_drop_bit to match "n >> 1"); documents a genuine
ABS(INT64_MIN) wraparound hazard mirroring the real C behavior
- StarForth_Memory_Words.thy: @/!/C@/C! address checks converted to
the signed order
All 23 theory files verify with zero errors, including
StarForth_Concurrent and StarForth_Correctness.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Covers the pure double-cell data-stack shuffle words from
src/word_source/double_words.c. Deliberately scoped to exclude:
- 2>R/2R>/2R@: branch on vm->ecw_nesting, a field vm_state doesn't track
at all -- needs a model extension first, not attempted here.
- S>D/D+/D-/DNEGATE/DABS/DMAX/DMIN/D</D=/D0=/D0</D2*/D2/: depend on
cell_t being a fixed-width (64-bit) wrapping integer (explicit
unsigned-long carry/borrow arithmetic, bitwise complement with
wraparound). StarForth_Base.thy's "cell = int" is unbounded, not
fixed-width, so this isn't expressible as currently modeled. Fixing it
means deciding whether cell becomes a 64-bit word type everywhere
(ripples into all 23 already-verified theories) -- a foundational
decision, flagged for later, not made as a side effect of this file.
24 theory files now verify with zero errors.
ROLL: forth_roll_def implemented a third, invented convention matching
neither the theory's own test lemma nor the real C stack_word_roll(). Traced
the actual C source (src/word_source/stack_words.c:287-320) and its passing
tests (stack_words_test.c roll_1/roll_2) to the real semantics -- ROLL is
1-indexed from the BOTTOM of the stack, not top-indexed as the old
definition assumed. Rewrote forth_roll_def to match, replaced the false
roll_one_nop/roll_two_is_rot with lemmas verified against the actual test
vectors.
PICK: forth_pick_def indexed into the pre-pop stack (still containing the
count n as its own head) instead of the post-pop stack, off by one position,
plus a bound check one too permissive. Fixed against src/word_source/
stack_words.c:265-282 and its pick_0/pick_1/pick_2 test vectors.
pm_wf: pm_record_hit_preserves_wf/pm_record_miss_preserves_wf were
oops-flagged as a genuine invariant gap. Fixed with the minimal added
hypothesis (pm_last_accuracy_den pm > 0), matching this session's established
discipline. Also documents a deeper finding: pm_last_accuracy_num/den don't
correspond to any field in the real PipelineGlobalMetrics C struct (which has
a single "double last_checked_accuracy", not a fraction) -- flagged for a
separate field-level audit, not attempted here.
All 23 theory files verify with zero errors.
Isabelle toolchain replaced (was genuinely 2011, 14+ years stale) and every
theory file fixed to actually compile -- most had apparently never been
checked under a working Isabelle at all. Fixed the vm_state self-reference
in StarForth_Base.thy properly (word_table is now a free-standing global
constant, not a circular record field), corrected the word_physics_transparent
axiom (was claiming full state equality from mere exec-equivalence, provably
too strong), and worked through 14 years of HOL-Library drift plus several
missing-hypothesis bugs across the physics-loop and ACL theories.
Two genuine (non-tactical) bugs found and left oops-flagged rather than
silently resolved: forth_roll's index arithmetic disagrees with both its own
test lemma and the real C ROLL implementation (three-way inconsistency), and
pm_wf isn't actually preserved by pm_record_hit/pm_record_miss. Both need a
decision, not a proof-script fix.
Full writeup in FABRIC-2.md item 5.2.
