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proof/: add StarForth_Defining_Words.thy (defining_words.c coverage)

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4 of 19 words fully modelled ([, ], STATE, IMMEDIATE), 2 guard-only
partial (:, ;), rest deferred behind three named model gaps: dictionary-
entry creation (never modelled anywhere in this suite before now),
data-field addressing (same class as the existing >BODY gap), and
mutable per-entry dispatch (word_table is a fixed global, can't express
DEFER/IS).

Finding: defining_words.c's [/]/STATE are registered after (and thus
permanently shadow) dictionary_manipulation_words.c's versions of the
same names -- that file's prior "dead cross-VM-shared static" finding
only ever applied to the shadowed, unreachable code. The live versions
correctly use vm->state_addr, a real per-VM field, now added to
vm_state.
This commit is contained in:
Robert Allan James
2026-08-14 14:33:29 -04:00
parent a34fba5c1c
commit 4d025ab0f4
3 changed files with 346 additions and 0 deletions
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proof/ROOT
+1
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@@ -12,6 +12,7 @@ session "StarForth" = "HOL-Library" +
StarForth_Memory_Words
StarForth_Dictionary_Words
StarForth_Dictionary_Manipulation_Words
StarForth_Defining_Words
StarForth_Control_Words
StarForth_String_Words
StarForth_Block_Words
proof/StarForth_Base.thy
+9
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@@ -531,6 +531,15 @@ record vm_state =
base_addr :: nat
hold_addr :: nat
hold_pos :: nat
(* ○ CODE-MUST-MATCH: C: vaddr_t state_addr (include/vm.h:452) -- VM
address of the cell holding STATE (0=interp, -1=compile). Distinct from
`state_var` (above), which is the host-side mirror cell_t field. Added
for StarForth_Defining_Words.thy's `[`/`]`/STATE -- these are the LIVE,
reachable implementations (defining_words.c registers over
dictionary_manipulation_words.c's `[`/`]`/STATE, which are dead code
once shadowed; see that file for the shadowed versions and this file
for the correction). *)
state_addr :: nat
(* ── Physics Loop #1: Execution heat tracking ───────────────────────── *)
(* ○ CODE-MUST-MATCH: heat_threshold_{25th,50th,75th} in C VM struct.
proof/StarForth_Defining_Words.thy
+336
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@@ -0,0 +1,336 @@
theory StarForth_Defining_Words
imports StarForth_Base StarForth_Memory_Words
begin
(* =========================================================================
Mirrors: src/word_source/defining_words.c
Registers: : ; CREATE VARIABLE CONSTANT IMMEDIATE STATE [ ] FORGET
COMPILE [COMPILE] LIT LITERAL does_rt DOES> DEFER IS DEFER@
── Duplicate-registration finding (corrects a StarForth_Dictionary_
Manipulation_Words.thy note) ────────────────────────────────────────
`src/word_registry.c` registers dictionary_manipulation_words.c's `[`,
`]`, `STATE` (Module 13, line 122) BEFORE defining_words.c's `[`, `]`,
`STATE` (Module 17, line 126). FORTH dictionary lookup finds the MOST
RECENT definition of a name first, so defining_words.c's versions are
the only ones ever reachable -- dictionary_manipulation_words.c's `[`/
`]`/`STATE`/`INTERPRET` are permanently shadowed, dead code from the
moment boot registration completes.
This also CORRECTS that file's finding, not just supersedes it: its
`[`/`]`/`STATE` write/read a dead file-scope `static cell_t
state_variable`, cross-VM-shared and never the real per-VM STATE. The
LIVE versions here (defining_word_left_bracket/right_bracket/state) use
`vm->state_addr` (include/vm.h:452) -- a genuine per-VM VM-memory
address, correctly written via `vm_store_cell`. The dead-static bug is
real IN THE SHADOWED CODE, but does not reach runtime: no VM instance's
`[`/`]`/`STATE` actually touches that static. Added `state_addr :: nat`
to vm_state (StarForth_Base.thy) to model this correctly.
── Scope of this file ──────────────────────────────────────────────────
Split three ways:
1. Mode/flag/address words ([, ], STATE, IMMEDIATE) -- fully modelled,
provable against `vm_mode`/`state_addr`/`memory`/`dictionary`/
`latest_id`.
2. `:` / `;` -- guard conditions modelled; `:`'s STATE/mode-setting half
of `vm_enter_compile_mode` is modelled (identical shape to `]`), but
the dictionary-entry-creation half (`vm_create_word` -> a fresh
DictEntry with `vm->compiling_word` tracking it) is NOT modelled --
see the finding below. `;`'s entire effect beyond the guard
(`vm_exit_compile_mode`: find/compile EXIT, clear WORD_SMUDGED, set
WORD_COMPILED, evict hot-words cache) is NOT modelled for the same
reason plus dependence on the hot-words cache, itself never modelled
in this suite.
3. Everything else (CREATE, VARIABLE, CONSTANT, FORGET, COMPILE,
[COMPILE], LIT, LITERAL, does_rt, DOES>, DEFER, IS, DEFER@, and the
three defining-runtime functions CREATE/VARIABLE/CONSTANT install) --
NOT modelled. Each hits one or more of the same three model gaps,
named once here rather than repeated per word:
(a) DICTIONARY-ENTRY CREATION is not modelled anywhere in this proof
suite. `dictionary :: nat \<Rightarrow> dict_entry option` (StarForth_
Base.thy:498) is treated as a fixed, pre-populated table by every
theory so far -- FIND/TRAVERSE/etc. in StarForth_Dictionary_
Manipulation_Words.thy only READ it. This is the first file in
the sweep whose primary job IS insertion (`:`, CREATE, VARIABLE,
CONSTANT, DEFER all call `vm_create_word`). `vm_create_word`
itself parses no input (name arrives pre-parsed) but allocates a
new DictEntry, links it into `vm->latest`, and returns a raw
`DictEntry*` the caller mutates directly (`entry->flags |=
WORD_SMUDGED`, etc.) -- none of which has a counterpart in the
word_id-indexed abstract model with no live pointer aliasing.
This is a materially bigger gap than the raw-pointer-navigation
gap already flagged in dictionary_manipulation_words.c (which
only reads), and is the single largest finding of this file.
(b) DATA-FIELD (DF) ADDRESSING: `dict_entry` (StarForth_Base.thy:293)
has no field corresponding to a DictEntry's data-field cell (the
storage `vm_dictionary_get_data_field` returns a pointer into).
CREATE/VARIABLE/CONSTANT's runtimes, DODOES, and does_rt all
read or write this cell -- the exact gap already named for
`>BODY` in StarForth_Dictionary_Manipulation_Words.thy
(`to_body_not_modelled`). Same root cause, different words.
(c) MUTABLE PER-ENTRY DISPATCH: `word_table` (StarForth_Base.thy:626)
is a fixed, uninterpreted global constant -- by design (see that
section's comment), not a per-VM-instance mutable field. DEFER's
`IS` reassigns an entry's *effective* dispatch target at runtime
(stored in the DF cell and read by `defining_runtime_defer`); a
fixed `word_table` cannot express this at all, independent of
gap (b).
LIT additionally treats the top return-stack cell as a raw C
`cell_t*` threaded-code instruction pointer, advanced with C pointer
arithmetic (`rip++`) and dereferenced directly -- NOT as a VM address
resolved through `vm_ptr`/`vm_addr_ok` the way control_words.c's
return-stack-held IP values were (see StarForth_Control_Words.thy's
resume note: that gap turned out to already be covered by `mem_read`
on VM-address-valued return-stack entries). LIT's IP is a genuinely
different, raw-host-pointer usage of the same field; the list-based
`return_stack :: cell list` model has no way to hold or advance a
host pointer.
======================================================================== *)
definition WORD_IMMEDIATE :: nat where "WORD_IMMEDIATE = 0x80"
(* ── [ ( -- ) : interpret mode, LIVE version (see file header) ──────────── *)
(* C: vm_store_cell(vm, vm->state_addr, 0); vm->mode = MODE_INTERPRET. *)
definition forth_d_left_bracket :: "vm_state \<Rightarrow> vm_state" where
"forth_d_left_bracket vm =
vm\<lparr>memory := mem_write (memory vm) (state_addr vm) 0,
vm_mode := ModeInterpret\<rparr>"
lemma d_left_bracket_sets_interpret:
"vm_mode (forth_d_left_bracket vm) = ModeInterpret"
by (simp add: forth_d_left_bracket_def)
lemma d_left_bracket_writes_state_cell:
"mem_read (memory (forth_d_left_bracket vm)) (state_addr vm) = 0"
by (simp add: forth_d_left_bracket_def mem_read_def mem_write_def)
lemma d_left_bracket_data_stack_unchanged:
"data_stack (forth_d_left_bracket vm) = data_stack vm"
by (simp add: forth_d_left_bracket_def)
lemma d_left_bracket_never_errors:
"vm_error (forth_d_left_bracket vm) = vm_error vm"
by (simp add: forth_d_left_bracket_def)
(* ── ] ( -- ) : compile mode, LIVE version ───────────────────────────────── *)
(* C: vm_store_cell(vm, vm->state_addr, (cell_t)-1); vm->mode = MODE_COMPILE. *)
definition forth_d_right_bracket :: "vm_state \<Rightarrow> vm_state" where
"forth_d_right_bracket vm =
vm\<lparr>memory := mem_write (memory vm) (state_addr vm) (-1),
vm_mode := ModeCompile\<rparr>"
lemma d_right_bracket_sets_compile:
"vm_mode (forth_d_right_bracket vm) = ModeCompile"
by (simp add: forth_d_right_bracket_def)
lemma d_right_bracket_writes_state_cell:
"mem_read (memory (forth_d_right_bracket vm)) (state_addr vm) = -1"
by (simp add: forth_d_right_bracket_def mem_read_def mem_write_def)
lemma d_right_bracket_data_stack_unchanged:
"data_stack (forth_d_right_bracket vm) = data_stack vm"
by (simp add: forth_d_right_bracket_def)
lemma d_right_bracket_never_errors:
"vm_error (forth_d_right_bracket vm) = vm_error vm"
by (simp add: forth_d_right_bracket_def)
lemma d_bracket_right_then_left:
"vm_mode (forth_d_left_bracket (forth_d_right_bracket vm)) = ModeInterpret"
by (simp add: forth_d_left_bracket_def)
lemma d_bracket_left_then_right:
"vm_mode (forth_d_right_bracket (forth_d_left_bracket vm)) = ModeCompile"
by (simp add: forth_d_right_bracket_def)
(* ── STATE ( -- addr ) : LIVE version, pushes a real VM address ─────────── *)
(* C: vm_push(vm, (cell_t)vm->state_addr). Unlike the shadowed dictionary_
manipulation_words.c version (which pushed the address of a dead host
static, and was left unmodelled), this pushes `state_addr` -- a genuine
per-VM field, so this word IS modellable. *)
definition forth_d_state :: "vm_state \<Rightarrow> vm_state" where
"forth_d_state vm =
(if ds_full vm
then set_error vm
else vm\<lparr>data_stack := word_of_nat (state_addr vm) # data_stack vm\<rparr>)"
lemma d_state_normal:
assumes "\<not> ds_full vm"
shows "data_stack (forth_d_state vm) = word_of_nat (state_addr vm) # data_stack vm"
by (simp add: forth_d_state_def assms)
lemma d_state_overflow:
assumes "ds_full vm"
shows "vm_error (forth_d_state vm)"
by (simp add: forth_d_state_def set_error_def assms)
lemma d_state_preserves_state_addr:
"state_addr (forth_d_state vm) = state_addr vm"
by (simp add: forth_d_state_def set_error_def)
(* ── IMMEDIATE ( -- ) : mark latest word immediate, no mode guard ───────── *)
(* C: error if vm->latest is NULL; else vm->latest->flags |= WORD_IMMEDIATE.
Unlike HIDDEN (dictionary_manipulation_words.c), there is no compile-mode
guard at all. *)
definition forth_immediate :: "vm_state \<Rightarrow> vm_state" where
"forth_immediate vm =
(case latest_id vm of
None \<Rightarrow> set_error vm
| Some wid \<Rightarrow>
(case dictionary vm wid of
None \<Rightarrow> set_error vm
| Some e \<Rightarrow>
vm\<lparr>dictionary := (dictionary vm)
(wid := Some (e\<lparr>de_flags := de_flags e OR WORD_IMMEDIATE\<rparr>))\<rparr>))"
lemma immediate_requires_latest:
assumes "latest_id vm = None"
shows "vm_error (forth_immediate vm)"
by (simp add: forth_immediate_def set_error_def assms)
lemma immediate_requires_latest_present_in_dict:
assumes "latest_id vm = Some wid"
assumes "dictionary vm wid = None"
shows "vm_error (forth_immediate vm)"
by (simp add: forth_immediate_def set_error_def assms)
lemma immediate_sets_flag:
assumes "latest_id vm = Some wid"
assumes "dictionary vm wid = Some e"
shows "\<exists>e'. dictionary (forth_immediate vm) wid = Some e' \<and>
de_flags e' = de_flags e OR WORD_IMMEDIATE"
using assms by (simp add: forth_immediate_def)
lemma immediate_data_stack_unchanged:
"data_stack (forth_immediate vm) = data_stack vm"
by (auto simp: forth_immediate_def set_error_def split: option.split)
lemma immediate_no_mode_guard:
\<comment> \<open>Unlike HIDDEN, IMMEDIATE has no `vm_mode vm \<noteq> ModeCompile` check at
all -- when the latest-word guards above are satisfied, its error
status is exactly whatever it was on entry (no NEW error is raised by
a compile-mode check, since there is none). Stated explicitly since
every other flag-setting word in this sweep (SMUDGE, HIDDEN) DOES gate
on compile mode.\<close>
assumes "latest_id vm = Some wid" "dictionary vm wid = Some e"
shows "vm_error (forth_immediate vm) = vm_error vm"
using assms by (simp add: forth_immediate_def)
(* ── : ( "name" -- ) : nested-guard + mode/STATE half only ──────────────── *)
(* C (defining_word_colon + vm_enter_compile_mode): error if already in
MODE_COMPILE (nested ':' is illegal per FORTH-79); else vm->mode =
MODE_COMPILE, vm->state_var = -1, vm_store_cell(vm, vm->state_addr, -1),
THEN vm_create_word(...) -- the entry-creation half, see file header
finding (a), is NOT modelled. Modelled here: guard + the mode/state_var/
state_addr-cell effect, which is state-only and has the identical shape
to `]` plus the extra `state_var` write `]` itself does not do. *)
definition forth_colon_guard :: "vm_state \<Rightarrow> vm_state" where
"forth_colon_guard vm =
(if vm_mode vm = ModeCompile
then set_error vm
else vm\<lparr>vm_mode := ModeCompile,
state_var := -1,
memory := mem_write (memory vm) (state_addr vm) (-1)\<rparr>)"
lemma colon_nested_errors:
assumes "vm_mode vm = ModeCompile"
shows "vm_error (forth_colon_guard vm)"
by (simp add: forth_colon_guard_def set_error_def assms)
lemma colon_sets_compile_mode:
assumes "vm_mode vm \<noteq> ModeCompile"
shows "vm_mode (forth_colon_guard vm) = ModeCompile"
by (simp add: forth_colon_guard_def assms)
lemma colon_sets_state_var:
assumes "vm_mode vm \<noteq> ModeCompile"
shows "state_var (forth_colon_guard vm) = -1"
by (simp add: forth_colon_guard_def assms)
lemma colon_writes_state_cell:
assumes "vm_mode vm \<noteq> ModeCompile"
shows "mem_read (memory (forth_colon_guard vm)) (state_addr vm) = -1"
by (simp add: forth_colon_guard_def mem_read_def mem_write_def assms)
lemma colon_guard_not_full_colon: True
\<comment> \<open>forth_colon_guard is NOT a full model of `:` -- it omits the
dictionary-entry-creation half (`vm_create_word`, `vm->compiling_word`,
WORD_SMUDGED, the DF write of the threaded-body start address). See
file header finding (a)/(b). Named so the omission is greppable.\<close>
by simp
(* ── ; ( -- ) : compile-mode guard only ──────────────────────────────────── *)
(* C: error unless vm->mode == MODE_COMPILE; else calls vm_exit_compile_mode,
entirely unmodelled (finds/compiles EXIT, flips WORD_SMUDGED/WORD_COMPILED,
evicts hot-words cache -- none modelled in this suite). *)
definition forth_semicolon_guard :: "vm_state \<Rightarrow> vm_state" where
"forth_semicolon_guard vm = (if vm_mode vm \<noteq> ModeCompile then set_error vm else vm)"
lemma semicolon_requires_compile_mode:
assumes "vm_mode vm \<noteq> ModeCompile"
shows "vm_error (forth_semicolon_guard vm)"
by (simp add: forth_semicolon_guard_def set_error_def assms)
lemma semicolon_guard_not_full_semicolon: True
\<comment> \<open>forth_semicolon_guard covers only the guard raised directly in
defining_word_semicolon. vm_exit_compile_mode's own effects (EXIT
lookup+compile, WORD_SMUDGED/WORD_COMPILED flag flip, hot-words cache
eviction) are entirely unmodelled -- none of EXIT-lookup, per-entry
mutable flags via a live pointer, or the hot-words cache have any
counterpart in this suite's abstract model.\<close>
by simp
(* ── Everything else in this file -- NOT MODELLED ─────────────────────────
See file header findings (a) dictionary-entry creation, (b) data-field
addressing, (c) mutable per-entry dispatch. One sentinel lemma per word/
helper, matching the StarForth_Dictionary_Manipulation_Words.thy
convention. *)
lemma create_not_modelled: True \<comment> \<open>CREATE: vm_create_word (gap a) + DF write of captured DFA (gap b).\<close>
by simp
lemma variable_not_modelled: True \<comment> \<open>VARIABLE: vm_allot + vm_create_word (gap a) + DF write of the cell's address (gap b).\<close>
by simp
lemma constant_not_modelled: True \<comment> \<open>CONSTANT: vm_create_word (gap a) + DF write of the popped value (gap b).\<close>
by simp
lemma create_runtime_not_modelled: True \<comment> \<open>defining_runtime_create: reads current_executing_entry's DF cell (gap b).\<close>
by simp
lemma variable_runtime_not_modelled: True \<comment> \<open>defining_runtime_variable: reads current_executing_entry's DF cell (gap b).\<close>
by simp
lemma constant_runtime_not_modelled: True \<comment> \<open>defining_runtime_constant: reads current_executing_entry's DF cell (gap b).\<close>
by simp
lemma lit_not_modelled: True \<comment> \<open>LIT: reads/advances the return-stack top as a raw C cell_t* threaded-code IP -- see file header, distinct from control_words.c's already-resolved IP-as-vaddr usage.\<close>
by simp
lemma literal_not_modelled: True \<comment> \<open>LITERAL: compiles a literal into threaded code via vm_compile_literal -- depends on the same unmodelled compile-target machinery as `:`/COMPILE.\<close>
by simp
lemma dodoes_not_modelled: True \<comment> \<open>defining_runtime_dodoes: DF/PFA layout (gap b) + runs a raw threaded-code interpreter loop over cell_t* IPs (gap c-adjacent, distinct mechanism from vm_ip).\<close>
by simp
lemma does_rt_not_modelled: True \<comment> \<open>defining_runtime_does_rt: patches vm->latest's DF (gap b) and reassigns its func pointer to defining_runtime_dodoes (gap c).\<close>
by simp
lemma does_greater_not_modelled: True \<comment> \<open>DOES>: compiles does_rt + EXIT into the defining word's body -- same unmodelled compile-target machinery as `:`.\<close>
by simp
lemma compile_not_modelled: True \<comment> \<open>COMPILE: vm_find_word (parse+lookup, same class as FIND, already flagged not-modelled) + vm_compile_word.\<close>
by simp
lemma bracket_compile_not_modelled: True \<comment> \<open>[COMPILE]: identical body to COMPILE (defining_word_bracket_compile IS defining_word_compile).\<close>
by simp
lemma forget_not_modelled: True \<comment> \<open>FORGET: walks vm->latest's raw linked chain by name, frees C structs, and rewinds `here` from a DF read (gap a/b combined) -- categorically the same class of gap as `block_words.c`'s cache-subsystem deferrals: a whole-subsystem project, not a one-word extension.\<close>
by simp
lemma defer_not_modelled: True \<comment> \<open>DEFER: vm_create_word (gap a) with a zeroed DF slot (gap b).\<close>
by simp
lemma defer_runtime_not_modelled: True \<comment> \<open>defining_runtime_defer: reads a DictEntry* out of the DF cell (gap b) and calls through it (gap c).\<close>
by simp
lemma is_not_modelled: True \<comment> \<open>IS: vm_find_word (parse+lookup) + writes an XT into the target's DF cell (gap b) -- the mutable-dispatch mechanism of gap (c).\<close>
by simp
lemma defer_fetch_not_modelled: True \<comment> \<open>DEFER@: vm_find_word + reads the DF cell (gap b).\<close>
by simp
end