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Implements the cells-spec vision: a computation space that preserves auditability, correctness, interactivity. Phase 1 (Lean kernel + naga-IR Rust backend) is closed; foundation hypothesis stack (Selection H1+H2, Subobject H3, Trace H5, Obs.Ctx C2, Cubical.Trace) landed. Highlights: - Cubical-HoTT syntax + value/eval/readback in Lean - naga-IR pipeline (no GLSL string crosses FFI; 17/17 probes pass) - Honesty audit: every non-transport (sealed cells, vertex shader, Y-flip, presentation conventions) is documented as such - Polymorphic Trace α as free monoid; Cubical.Trace gives CTerm → Trace CTerm by structural fold (homomorphism = definition) - Selection as Huet zipper; Subobject as Boolean algebra over WCell - All theorems proven; the proof IS the implementation See STATUS.md for the resume guide. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
90 lines
4.1 KiB
Text
90 lines
4.1 KiB
Text
-- EML tree: S → 1 | eml(S, S)
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-- eml(x, y) = exp(x) − ln(y)
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--
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-- Single binary primitive that generates all elementary functions.
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-- (Odrzywolek 2026, arXiv:2603.21852)
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-- ── Core inductive ────────────────────────────────────────────────────────────
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inductive EMLExpr where
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| one : EMLExpr
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| var (name : String) : EMLExpr -- free variable resolved in the rendering env
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| eml (l r : EMLExpr) : EMLExpr
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-- ── Derived forms ─────────────────────────────────────────────────────────────
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-- exp(x) = eml(x, 1) since exp(x) − ln(1) = exp(x) − 0 = exp(x)
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def EMLExpr.expOf (x : EMLExpr) : EMLExpr := .eml x .one
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-- ln(x) = eml(1, eml(eml(1, x), 1))
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def EMLExpr.lnOf (x : EMLExpr) : EMLExpr :=
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.eml .one (.eml (.eml .one x) .one)
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-- ── Plot configuration ────────────────────────────────────────────────────────
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/-- A path config: an EML expression plus its distinguished path-dimension
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variable. `dimName` is the name that ranges over `{0, 1}` when the
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config is interpreted as an `EMLPath` (see `EML/Path.lean`'s
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`PlotConfig.toEMLPath`). When `dimName` does not occur in `expr`,
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the path is *constant* (its value is the same at both endpoints);
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when it does, the path is genuinely parametric. -/
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structure PlotConfig where
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expr : EMLExpr
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dimName : String := "t"
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-- ── Named demo expressions (probe test fixtures) ─────────────────────────────
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-- exp(x): depth-1 EML tree, one node.
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def plotExp : PlotConfig := {
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expr := EMLExpr.expOf (.var "px")
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}
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-- ln(x): depth-3 EML tree, three nodes.
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--
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-- Historical note: an earlier `plotLn` used the variable name
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-- `"max(px, 0.001)"` to clamp negative inputs on the GPU side. That
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-- made the GPU shader evaluate `max(px, 0.001)` as a GLSL expression
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-- but left Lean's `shaderVar` hitting the fallback `0.0` — the two
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-- sides disagreed on the semantic of the variable. The probe test
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-- surfaced the divergence; the fix is to use a real variable `px`
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-- and accept that `ln` of negative `px` produces `NaN` on both sides
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-- (the two sides agree, which is what `render_faithful` cares about).
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def plotLn : PlotConfig := {
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expr := EMLExpr.lnOf (.var "px")
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}
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-- ── Continuous-homotopy demo: a genuinely parametric path ────────────────────
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-- `exp(px) − t` translates the exponential curve down by `t`. At `t=0`
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-- the curve is `y = exp(x)`; at `t=1` it's `y = exp(x) − 1`; in between it
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-- smoothly slides. EML-expressible because `exp(px) - log(exp(t))` reduces
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-- (via `log ∘ exp = id`) to `exp(px) - t`; body is
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-- `eml(var "px", eml(var "t", one))`.
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def plotTransp : PlotConfig := {
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expr := .eml (.var "px") (.eml (.var "t") .one)
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dimName := "t"
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}
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-- ── Clean fibers in [0, 1] for greyscale demos ──────────────────────────────
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-- These bodies are picked specifically so their image lies in `[0, 1]`,
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-- matching the framebuffer's natural display range. Each is a 1-cell;
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-- their shape under different `pathParam` values shows the transport
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-- in action with no clamping artifacts.
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/-- The 1-cell whose body IS the dim variable: at `pathParam = c` every
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pixel evaluates to `c`. Different fibers display as solid-color
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panels with brightness equal to the fiber's parameter.
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`at0 = solid black`, `at1 = solid white`, `mid = solid 50% grey`. -/
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def plotT : PlotConfig := {
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expr := .var "t"
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dimName := "t"
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}
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/-- The 1-cell whose body is `px`: image is the horizontal coordinate
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itself, a black-to-white left-to-right gradient. Constant
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1-cell (no `t` dependence) — every fiber is the same gradient.
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Useful as a sanity check: fibers should NOT differ. -/
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def plotPx : PlotConfig := {
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expr := .var "px"
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dimName := "t"
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}
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