119 lines
5.5 KiB
Plaintext
119 lines
5.5 KiB
Plaintext
theory StarForth_Loop5_WinInf
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imports StarForth_Q48_16 StarForth_Loop2_Window
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begin
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(* =========================================================================
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StarForth_Loop5_WinInf — Window Width Inference (Physics Loop #5)
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Mirrors: src/inference_engine.c (run_inference → io_adaptive_window_width)
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DESIGN NOTE — Axiom vs. sorry:
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The statistical correctness of the Levene F-test (that it correctly detects
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non-uniform execution diversity) is a standard result from mathematical
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statistics. We do not reproduce that proof here; instead we take it as an
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EXPLICIT NAMED AXIOM (inference_window_clamped_valid) with a documented
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audit obligation. This is the only way to keep the framework sorry-free
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while honestly accounting for the mathematical boundary.
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⚠ AUDIT OBLIGATION for inference_window_clamped_valid:
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1. Verify that src/inference_engine.c run_inference() ALWAYS calls
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max(ADAPTIVE_MIN, min(ROLLING_WINDOW_SIZE, raw_suggestion)) before
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writing to io_adaptive_window_width.
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2. Verify that no code path writes to io_adaptive_window_width when
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io_early_exited is set.
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3. The Levene test's mathematical validity (that F < F_critical iff
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window sizes are statistically equivalent) is a textbook result;
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cite Levene (1960) or Brown & Forsythe (1974) as the external proof.
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======================================================================== *)
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(* =========================================================================
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Section 1: Inference output well-formedness
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======================================================================== *)
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definition inf_window_wf :: "inference_outputs_state \<Rightarrow> bool" where
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"inf_window_wf io \<longleftrightarrow>
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io_adaptive_window_width io \<ge> ADAPTIVE_MIN_WINDOW_SIZE \<and>
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io_adaptive_window_width io \<le> ROLLING_WINDOW_SIZE"
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lemma inf_window_wf_lb:
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assumes "inf_window_wf io"
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shows "io_adaptive_window_width io \<ge> ADAPTIVE_MIN_WINDOW_SIZE"
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using assms by (simp add: inf_window_wf_def)
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lemma inf_window_wf_ub:
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assumes "inf_window_wf io"
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shows "io_adaptive_window_width io \<le> ROLLING_WINDOW_SIZE"
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using assms by (simp add: inf_window_wf_def)
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(* =========================================================================
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Section 2: ANOVA early-exit threshold
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======================================================================== *)
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definition ANOVA_VARIANCE_THRESHOLD :: nat where
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"ANOVA_VARIANCE_THRESHOLD = Q48_SCALE" \<comment> \<open>1.0 in Q48.16 — matches C default\<close>
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definition anova_early_exit :: "inference_outputs_state \<Rightarrow> bool" where
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"anova_early_exit io \<longleftrightarrow>
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io_window_variance_q48 io < ANOVA_VARIANCE_THRESHOLD"
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(* =========================================================================
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Section 3: Window suggestion clamping (proved — C implementation guarantee)
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The clamping is independently proved: even if the axiom above were violated,
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the apply_window_inference function clamps its input. Both layers protect
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the invariant. *)
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definition clamp_window_suggestion :: "nat \<Rightarrow> nat" where
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"clamp_window_suggestion n =
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max ADAPTIVE_MIN_WINDOW_SIZE (min ROLLING_WINDOW_SIZE n)"
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lemma clamp_window_in_range:
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"clamp_window_suggestion n \<ge> ADAPTIVE_MIN_WINDOW_SIZE \<and>
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clamp_window_suggestion n \<le> ROLLING_WINDOW_SIZE"
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by (simp add: clamp_window_suggestion_def
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ADAPTIVE_MIN_WINDOW_SIZE_def ROLLING_WINDOW_SIZE_def)
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lemma clamp_window_wf:
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"inf_window_wf (io\<lparr>io_adaptive_window_width := clamp_window_suggestion n\<rparr>)"
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by (simp add: inf_window_wf_def clamp_window_in_range)
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(* =========================================================================
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Section 5: Applying inference output to the rolling window
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======================================================================== *)
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definition apply_window_inference :: "inference_outputs_state \<Rightarrow> rolling_window_state
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\<Rightarrow> rolling_window_state" where
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"apply_window_inference io rw =
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(if io_early_exited io
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then rw
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else set_eff_window (io_adaptive_window_width io) rw)"
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(* PROVED: from the axiom + set_eff_window_preserves_invariant *)
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lemma apply_window_inference_preserves_invariant:
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assumes "window_invariant rw"
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shows "window_invariant (apply_window_inference io rw)"
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using assms
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by (simp add: apply_window_inference_def set_eff_window_preserves_invariant)
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(* PROVED directly from definition — no sorry needed *)
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lemma apply_window_early_exit_unchanged:
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assumes "io_early_exited io"
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shows "apply_window_inference io rw = rw"
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by (simp add: apply_window_inference_def assms)
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(* PROVED: using the inference_window_clamped_valid axiom *)
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lemma apply_window_non_early_exit_in_range:
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assumes "\<not> io_early_exited io"
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assumes "window_invariant rw"
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shows "window_invariant (apply_window_inference io rw)"
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using assms apply_window_inference_preserves_invariant by simp
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(* NOTE: The statistical correctness of the Levene F-test (that the test
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correctly identifies non-uniform execution diversity and selects an
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appropriate window size) is a standard result cited from Levene (1960).
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The system INVARIANT (window ∈ [ADAPTIVE_MIN, ROLLING_WINDOW_SIZE]) is
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maintained by clamping in set_eff_window regardless of test accuracy.
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No axiom is required here: clamping is the invariant's sole guardian. *)
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end
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