proof/: add StarForth_Q48_Words.thy (q48_words.c coverage)
17 of 23 words fully modelled (Q.+/-/*//, Q.ABS/NEG, Q.FROM-INT/TO-INT, Q.1/0/SCALE, Q.=/</>/0=, Q.MAX/MIN), reusing q48_add/q48_mul/q48_div/ q48_from_u64/q48_to_u64 already in StarForth_Q48_16.thy and cell_abs (Q.ABS's raw sign-bit test is bit-for-bit cell_abs's `n <s 0`). Added q48_sub there alongside, the one missing arithmetic primitive. Q.LOG/EXP/SQRT/SIN/COS deferred (same transcendental-approximation class already excluded from the sweep at q48_16_words.c). Q.PRINT deferred (stdout only). Finding: every word in this file pops/pushes via the VM_POP/VM_PUSH macros, which resolve to completely unchecked vm_pop_fast/vm_push_fast when STARFORTH_PERFORMANCE is defined -- a build-flag-gated stack-safety hazard distinct from (and broader than) the individual missing-guard instances found elsewhere in the sweep, since it silently disables every guard in the entire file at once. Modelled assuming the safe path. Suite now 52 theories, green.
This commit is contained in:
Robert Allan James
@@ -36,6 +36,7 @@ session "StarForth" = "HOL-Library" +
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StarForth_Lifecycle_Words_Hosted
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StarForth_Defer_Words
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StarForth_Log_Words
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StarForth_Q48_Words
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StarForth_Loop1_Heat
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StarForth_Loop2_Window
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StarForth_Loop3_Decay
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@@ -121,6 +121,29 @@ lemma q48_add_zero_right [simp]: "q48_add a 0 = a"
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lemma q48_add_zero_left [simp]: "q48_add 0 a = a"
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by (simp add: q48_add_def)
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(* q48_sub: pointwise subtraction, wrapping on underflow (matches C - on
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uint64_t). Added for src/word_source/q48_words.c's Q.- (StarForth_Q48_
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Words.thy).
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C: static inline q48_16_t q48_sub(q48_16_t a, q48_16_t b) { return a-b; } *)
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definition q48_sub :: "q48 \<Rightarrow> q48 \<Rightarrow> q48" where
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"q48_sub a b = a - b"
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lemma q48_sub_zero_right [simp]: "q48_sub a 0 = a"
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by (simp add: q48_sub_def)
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lemma q48_sub_self [simp]: "q48_sub a a = 0"
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by (simp add: q48_sub_def)
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lemma q48_add_sub_cancel [simp]: "q48_sub (q48_add a b) b = a"
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by (simp add: q48_sub_def q48_add_def)
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(* q48_abs: C compares the raw uint64 bit pattern against 0x8000...0 (the
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sign bit threshold) rather than using a signed comparison operator, but
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this is bit-for-bit the same test as `cell_abs`'s `n <s 0`
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(StarForth_Base.thy) -- both are exactly "is the sign bit set". q48_abs
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is therefore not modelled as a separate definition here: StarForth_Q48_
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Words.thy's Q.ABS uses `cell_abs` directly under the `q48` type synonym. *)
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(* q48_mul: (a * b) >> 16, wrapping.
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C: q48_16_t q48_mul(q48_16_t a, q48_16_t b) { return ((__uint128_t)a*b) >> 16; }
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⚠ HUMAN-REVIEW: The C implementation uses __uint128_t for the intermediate
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@@ -0,0 +1,321 @@
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theory StarForth_Q48_Words
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imports StarForth_Base StarForth_Q48_16
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begin
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(* =========================================================================
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Mirrors: src/word_source/q48_words.c
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Registers: Q.+ Q.- Q.* Q./ Q.ABS Q.NEG Q.LOG Q.EXP Q.SQRT Q.SIN Q.COS
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Q.FROM-INT Q.TO-INT Q.1 Q.0 Q.SCALE Q.= Q.< Q.> Q.0=
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Q.MAX Q.MIN Q.PRINT
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Thin FORTH stack wrappers around the q48_16.h math library. `q48_16_t`
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is the same 64-bit representation as `cell`/`q48` (StarForth_Base.thy/
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StarForth_Q48_16.thy) reinterpreted, so most of these words reduce
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directly to already-modelled q48 operations.
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── Build-flag stack-safety hazard, distinct from the rest of the sweep ──
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Every word here pops/pushes via the `VM_POP`/`VM_PUSH` MACROS (include/
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vm.h:706-719), not a direct `vm_pop`/`vm_push` call the way virtually
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every other file in this sweep does. Those macros resolve to
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`vm_pop_fast`/`vm_push_fast` (raw `vm->data_stack[vm->dsp--/++]`, NO
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bounds check at all) when `STARFORTH_PERFORMANCE` is defined, and to
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the safe, bounds-checked `vm_pop`/`vm_push` otherwise. This is a
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genuinely different hazard shape from anything else in the sweep: it
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isn't a missing guard in this file's own code (the missing-guard
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pattern from DECAY-RATE@ onward), it's that EVERY guard in this ENTIRE
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FILE is conditionally compiled away by a build flag most other word
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files never consult. Modelled below assuming the safe (non-
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`STARFORTH_PERFORMANCE`) path, consistent with this suite's general
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assumption that stack words check bounds; the fast-path variant is
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flagged, not modelled, since "no check at all" has no useful lemma to
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state beyond "anything can happen."
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── Q48 operations reused from StarForth_Q48_16.thy ─────────────────────
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q48_add/q48_sub/q48_mul/q48_div/q48_from_u64/q48_to_u64 were already
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modelled (q48_sub added there alongside this file, since it's a genuine
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Q48 arithmetic primitive, not FORTH-word-specific). Q.ABS uses
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`cell_abs` directly (StarForth_Base.thy) -- q48_abs's raw-bit sign-bit
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test is bit-for-bit identical to `cell_abs`'s `n <s 0` test, see
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StarForth_Q48_16.thy's note. Q.=/Q.</Q.>/Q.0=/Q.MAX/Q.MIN use PLAIN
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(unsigned) word comparison operators, matching the C's direct
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`uint64_t` `==`/`<`/`>` -- Q48.16 in this codebase is fundamentally an
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unsigned fixed-point format, unlike `cell`'s general signed
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two's-complement use elsewhere in this suite.
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── Scope ─────────────────────────────────────────────────────────────
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Fully modelled: Q.+, Q.-, Q.*, Q./, Q.ABS, Q.NEG, Q.FROM-INT, Q.TO-INT,
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Q.1, Q.0, Q.SCALE, Q.=, Q.<, Q.>, Q.0=, Q.MAX, Q.MIN (17 of 23 words).
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Not modelled: Q.LOG/Q.EXP/Q.SQRT/Q.SIN/Q.COS (the same transcendental
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approximation functions already excluded from this sweep entirely at
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q48_16_words.c -- Newton-Raphson/Taylor-series numerical algorithms
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needing error-bound proofs, a different kind of work than this sweep's
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plumbing-lemma style) and Q.PRINT (stdout formatting only, no vm_state
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write beyond its pop).
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======================================================================== *)
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(* ── Q.+ / Q.- / Q.* / Q./ ( q1 q2 -- q_result ) ──────────────────────── *)
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(* C pops b then a (b is TOS); data_stack list convention: b # a # xs. *)
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definition forth_q_add :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_add vm =
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(case data_stack vm of
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b # a # xs \<Rightarrow> vm\<lparr>data_stack := q48_add a b # xs\<rparr>
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| _ \<Rightarrow> set_error vm)"
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definition forth_q_sub :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_sub vm =
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(case data_stack vm of
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b # a # xs \<Rightarrow> vm\<lparr>data_stack := q48_sub a b # xs\<rparr>
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| _ \<Rightarrow> set_error vm)"
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definition forth_q_mul :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_mul vm =
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(case data_stack vm of
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b # a # xs \<Rightarrow> vm\<lparr>data_stack := q48_mul a b # xs\<rparr>
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| _ \<Rightarrow> set_error vm)"
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definition forth_q_div :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_div vm =
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(case data_stack vm of
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b # a # xs \<Rightarrow> vm\<lparr>data_stack := q48_div a b # xs\<rparr>
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| _ \<Rightarrow> set_error vm)"
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lemma q_add_underflow_nil: "data_stack vm = [] \<Longrightarrow> vm_error (forth_q_add vm)"
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by (simp add: forth_q_add_def set_error_def)
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lemma q_add_underflow_one: "data_stack vm = [x] \<Longrightarrow> vm_error (forth_q_add vm)"
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by (simp add: forth_q_add_def set_error_def)
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lemma q_add_normal:
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assumes "data_stack vm = b # a # xs"
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shows "data_stack (forth_q_add vm) = q48_add a b # xs"
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by (simp add: forth_q_add_def assms)
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lemma q_sub_normal:
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assumes "data_stack vm = b # a # xs"
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shows "data_stack (forth_q_sub vm) = q48_sub a b # xs"
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by (simp add: forth_q_sub_def assms)
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lemma q_mul_normal:
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assumes "data_stack vm = b # a # xs"
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shows "data_stack (forth_q_mul vm) = q48_mul a b # xs"
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by (simp add: forth_q_mul_def assms)
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lemma q_div_normal:
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assumes "data_stack vm = b # a # xs"
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shows "data_stack (forth_q_div vm) = q48_div a b # xs"
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by (simp add: forth_q_div_def assms)
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lemma q_div_by_zero_is_zero:
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assumes "data_stack vm = 0 # a # xs"
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shows "data_stack (forth_q_div vm) = 0 # xs"
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using assms by (simp add: forth_q_div_def q48_div_def)
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(* ── Q.ABS / Q.NEG ( q -- q' ) ─────────────────────────────────────────── *)
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definition forth_q_abs :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_abs vm =
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(case data_stack vm of
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a # xs \<Rightarrow> vm\<lparr>data_stack := cell_abs a # xs\<rparr>
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| _ \<Rightarrow> set_error vm)"
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definition forth_q_neg :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_neg vm =
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(case data_stack vm of
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a # xs \<Rightarrow> vm\<lparr>data_stack := -a # xs\<rparr>
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| _ \<Rightarrow> set_error vm)"
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lemma q_abs_underflow: "data_stack vm = [] \<Longrightarrow> vm_error (forth_q_abs vm)"
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by (simp add: forth_q_abs_def set_error_def)
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lemma q_abs_normal:
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assumes "data_stack vm = a # xs"
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shows "data_stack (forth_q_abs vm) = cell_abs a # xs"
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by (simp add: forth_q_abs_def assms)
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lemma q_neg_underflow: "data_stack vm = [] \<Longrightarrow> vm_error (forth_q_neg vm)"
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by (simp add: forth_q_neg_def set_error_def)
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lemma q_neg_normal:
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assumes "data_stack vm = a # xs"
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shows "data_stack (forth_q_neg vm) = -a # xs"
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by (simp add: forth_q_neg_def assms)
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lemma q_neg_involutive:
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assumes "data_stack vm = a # xs"
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shows "data_stack (forth_q_neg (forth_q_neg vm)) = a # xs"
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by (simp add: forth_q_neg_def assms)
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(* ── Q.FROM-INT ( n -- q ) / Q.TO-INT ( q -- n ) ──────────────────────── *)
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(* C: Q.FROM-INT clamps negative n to 0 before q48_from_u64 (the C source
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pops via bare VM_POP, a signed cell_t, then treats negative as 0). *)
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definition forth_q_from_int :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_from_int vm =
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(case data_stack vm of
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n # xs \<Rightarrow> vm\<lparr>data_stack := q48_from_u64 (if n <s 0 then 0 else n) # xs\<rparr>
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| _ \<Rightarrow> set_error vm)"
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definition forth_q_to_int :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_to_int vm =
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(case data_stack vm of
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q # xs \<Rightarrow> vm\<lparr>data_stack := q48_to_u64 q # xs\<rparr>
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| _ \<Rightarrow> set_error vm)"
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lemma q_from_int_underflow: "data_stack vm = [] \<Longrightarrow> vm_error (forth_q_from_int vm)"
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by (simp add: forth_q_from_int_def set_error_def)
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lemma q_from_int_negative_clamped:
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assumes "data_stack vm = n # xs" "n <s 0"
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shows "data_stack (forth_q_from_int vm) = 0 # xs"
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using assms by (simp add: forth_q_from_int_def)
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lemma q_from_int_nonneg:
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assumes "data_stack vm = n # xs" "\<not> n <s 0"
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shows "data_stack (forth_q_from_int vm) = q48_from_u64 n # xs"
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using assms by (simp add: forth_q_from_int_def)
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lemma q_to_int_underflow: "data_stack vm = [] \<Longrightarrow> vm_error (forth_q_to_int vm)"
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by (simp add: forth_q_to_int_def set_error_def)
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lemma q_to_int_normal:
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assumes "data_stack vm = q # xs"
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shows "data_stack (forth_q_to_int vm) = q48_to_u64 q # xs"
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by (simp add: forth_q_to_int_def assms)
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(* ── Q.1 / Q.0 / Q.SCALE ( -- q ) : constants, no capacity guard ─────────── *)
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(* Like DECAY-RATE@/LOG-ERROR etc, these push with no ds_full check --
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another instance of the recurring missing-overflow-guard pattern. *)
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definition forth_q_one :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_one vm = vm\<lparr>data_stack := Q48_ONE # data_stack vm\<rparr>"
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definition forth_q_zero :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_zero vm = vm\<lparr>data_stack := 0 # data_stack vm\<rparr>"
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definition forth_q_scale :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_scale vm = vm\<lparr>data_stack := Q48_SCALE # data_stack vm\<rparr>"
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lemma q_one_pushes: "data_stack (forth_q_one vm) = 65536 # data_stack vm"
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by (simp add: forth_q_one_def Q48_ONE_def Q48_SCALE_def)
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lemma q_zero_pushes: "data_stack (forth_q_zero vm) = 0 # data_stack vm"
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by (simp add: forth_q_zero_def)
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lemma q_scale_pushes: "data_stack (forth_q_scale vm) = 65536 # data_stack vm"
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by (simp add: forth_q_scale_def Q48_SCALE_def)
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lemma q_one_scale_agree: "forth_q_one vm = forth_q_scale vm"
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by (simp add: forth_q_one_def forth_q_scale_def Q48_ONE_def Q48_SCALE_def)
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(* ── Q.= / Q.< / Q.> / Q.0= ( q1 q2 -- flag ) : unsigned comparison ───────── *)
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definition forth_q_eq :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_eq vm =
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(case data_stack vm of
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b # a # xs \<Rightarrow> vm\<lparr>data_stack := to_forth_bool (a = b) # xs\<rparr>
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| _ \<Rightarrow> set_error vm)"
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definition forth_q_lt :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_lt vm =
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(case data_stack vm of
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b # a # xs \<Rightarrow> vm\<lparr>data_stack := to_forth_bool (a < b) # xs\<rparr>
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| _ \<Rightarrow> set_error vm)"
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definition forth_q_gt :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_gt vm =
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(case data_stack vm of
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b # a # xs \<Rightarrow> vm\<lparr>data_stack := to_forth_bool (b < a) # xs\<rparr>
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| _ \<Rightarrow> set_error vm)"
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definition forth_q_zero_eq :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_zero_eq vm =
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(case data_stack vm of
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a # xs \<Rightarrow> vm\<lparr>data_stack := to_forth_bool (a = 0) # xs\<rparr>
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| _ \<Rightarrow> set_error vm)"
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lemma q_eq_normal:
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assumes "data_stack vm = b # a # xs"
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shows "data_stack (forth_q_eq vm) = to_forth_bool (a = b) # xs"
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by (simp add: forth_q_eq_def assms)
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lemma q_lt_normal:
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assumes "data_stack vm = b # a # xs"
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shows "data_stack (forth_q_lt vm) = to_forth_bool (a < b) # xs"
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by (simp add: forth_q_lt_def assms)
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lemma q_gt_normal:
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assumes "data_stack vm = b # a # xs"
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shows "data_stack (forth_q_gt vm) = to_forth_bool (b < a) # xs"
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by (simp add: forth_q_gt_def assms)
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lemma q_zero_eq_normal:
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assumes "data_stack vm = a # xs"
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shows "data_stack (forth_q_zero_eq vm) = to_forth_bool (a = 0) # xs"
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by (simp add: forth_q_zero_eq_def assms)
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lemma q_lt_gt_antisymmetric:
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assumes "data_stack vm1 = b # a # xs" "data_stack vm2 = a # b # xs"
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shows "data_stack (forth_q_lt vm1) = data_stack (forth_q_gt vm2)"
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using assms by (simp add: forth_q_lt_def forth_q_gt_def)
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(* ── Q.MAX / Q.MIN ( q1 q2 -- q_result ) : unsigned comparison ──────────── *)
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definition forth_q_max :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_max vm =
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(case data_stack vm of
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b # a # xs \<Rightarrow> vm\<lparr>data_stack := (if b \<le> a then a else b) # xs\<rparr>
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| _ \<Rightarrow> set_error vm)"
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definition forth_q_min :: "vm_state \<Rightarrow> vm_state" where
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"forth_q_min vm =
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(case data_stack vm of
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b # a # xs \<Rightarrow> vm\<lparr>data_stack := (if a \<le> b then a else b) # xs\<rparr>
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| _ \<Rightarrow> set_error vm)"
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lemma q_max_normal:
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assumes "data_stack vm = b # a # xs"
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shows "data_stack (forth_q_max vm) = (if b \<le> a then a else b) # xs"
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by (simp add: forth_q_max_def assms)
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lemma q_min_normal:
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assumes "data_stack vm = b # a # xs"
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shows "data_stack (forth_q_min vm) = (if a \<le> b then a else b) # xs"
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by (simp add: forth_q_min_def assms)
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lemma q_max_ge_both:
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assumes "data_stack vm = b # a # xs"
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shows "a \<le> hd (data_stack (forth_q_max vm))" "b \<le> hd (data_stack (forth_q_max vm))"
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using assms by (auto simp add: forth_q_max_def)
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lemma q_min_le_both:
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assumes "data_stack vm = b # a # xs"
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shows "hd (data_stack (forth_q_min vm)) \<le> a" "hd (data_stack (forth_q_min vm)) \<le> b"
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using assms by (auto simp add: forth_q_min_def)
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(* ── Q.LOG / Q.EXP / Q.SQRT / Q.SIN / Q.COS -- NOT MODELLED ──────────────── *)
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|
||||
lemma q_log_not_modelled: True \<comment> \<open>q48_log_approx: Newton-Raphson, same excluded class as q48_16_words.c's transcendentals (see that file's sweep-skip note).\<close>
|
||||
by simp
|
||||
lemma q_exp_not_modelled: True \<comment> \<open>q48_exp_approx: Taylor series.\<close>
|
||||
by simp
|
||||
lemma q_sqrt_not_modelled: True \<comment> \<open>q48_sqrt_approx: Newton-Raphson.\<close>
|
||||
by simp
|
||||
lemma q_sin_not_modelled: True \<comment> \<open>q48_sin_approx: Taylor series.\<close>
|
||||
by simp
|
||||
lemma q_cos_not_modelled: True \<comment> \<open>q48_cos_approx: Taylor series.\<close>
|
||||
by simp
|
||||
|
||||
(* ── Q.PRINT ( q -- ) : pop + stdout, no further vm_state effect ────────── *)
|
||||
|
||||
definition forth_q_print :: "vm_state \<Rightarrow> vm_state" where
|
||||
"forth_q_print vm =
|
||||
(case data_stack vm of
|
||||
q # xs \<Rightarrow> vm\<lparr>data_stack := xs\<rparr>
|
||||
| _ \<Rightarrow> set_error vm)"
|
||||
|
||||
lemma q_print_underflow: "data_stack vm = [] \<Longrightarrow> vm_error (forth_q_print vm)"
|
||||
by (simp add: forth_q_print_def set_error_def)
|
||||
lemma q_print_pops_one:
|
||||
assumes "data_stack vm = q # xs"
|
||||
shows "data_stack (forth_q_print vm) = xs"
|
||||
by (simp add: forth_q_print_def assms)
|
||||
|
||||
(* ── Fast-path (STARFORTH_PERFORMANCE) variant -- NOT MODELLED ───────────── *)
|
||||
|
||||
lemma fast_path_variant_not_modelled: True
|
||||
\<comment> \<open>See file header -- when STARFORTH_PERFORMANCE is defined, every word
|
||||
above uses vm_pop_fast/vm_push_fast with NO bounds check at all, so
|
||||
none of the underflow lemmas above apply; there is no meaningful
|
||||
positive statement to make about that build configuration beyond
|
||||
"unchecked".\<close>
|
||||
by simp
|
||||
|
||||
end
|
||||
Reference in New Issue
Block a user