Skip to content

Commit 58aa8ce

Browse files
committed
docs(yhwh): show the lambda Y combinator explicitly as the foundation
Y was named in the model but never shown as the formal symbol it is. The Y combinator is the canonical operational name of self-reference; without it visible, the four-phase mnemonic loses the anchor that distinguishes mago-dbe from generic 'self-referential' branding. - README hero: Y = λf. (λx. f (x x)) (λx. f (x x)) and the fixed-point equation Y f = f (Y f), with one-paragraph commentary on how mago-dbe materialises this at the type-system level (typed primitive-recursive analogue of an otherwise ill-typed combinator in System F). - docs/YHWH.md §Y: same combinator and equation in a fenced block; explicit citation to Curry & Feys 1958; explicit correspondence Y f = f (Y f) ↔ G* = C[G*](M); explanation of why the typed, terminating, byte-stable variant differs from the untyped Y. Curry & Feys 1958 was already in the SELF-HOST-PROOF bibliography; this commit just makes the symbol visible at the front of the docs.
1 parent d4b3ace commit 58aa8ce

2 files changed

Lines changed: 16 additions & 0 deletions

File tree

README.md

Lines changed: 6 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -2,6 +2,12 @@
22

33
A self-referential build model: **Y · Hydrate · Weave · Hatch**.
44

5+
```
6+
Y = λf. (λx. f (x x)) (λx. f (x x)) Y f = f (Y f)
7+
```
8+
9+
The first letter is the **Y combinator** (Curry & Feys, *Combinatory Logic* I, 1958) — the canonical name of self-reference computed without an external base case. mago-dbe materialises this fixed-point equation at the type-system level: the compiler `C` is typed by `G`, and `G = C(M)` is the output of `C` — proved unique, byte-stable, and sandbox-replicable in [`docs/SELF-HOST-PROOF.md`](docs/SELF-HOST-PROOF.md) (Theorem 5.1).
10+
511
The repo implements a spec/workflow engine that takes authored markdown intent and produces validated, typed, byte-stable runtime artefacts. The model name `YHWH` is read as a four-phase sequence — `Y` (self-reference), `Hydrate` (intent into structure), `Weave` (structure into composition), `Hatch` (composition into runtime). The internal project id is `mago-dbe`. The architectural pattern is formally proven self-hosted and metacircular at `bootstrap-complete-source` (v0.5.0).
612

713
> **Honest floor.** The system does **not** learn, does **not** autonomously evolve, and does **not** synthesise new primitives. What it does is described and mapped to code in [`docs/YHWH.md`](docs/YHWH.md). What it provably does is in [`docs/SELF-HOST-PROOF.md`](docs/SELF-HOST-PROOF.md) (PhD-grade paper, 5 lemmas + theorem + physical-realisation argument).

docs/YHWH.md

Lines changed: 10 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -32,6 +32,16 @@ What the system *does* converge toward is **self-compilation through specs**: ev
3232

3333
> The Y combinator. The fixed point. The system emerging from its own definitional core.
3434
35+
```
36+
Y = λf. (λx. f (x x)) (λx. f (x x))
37+
38+
Y f = f (Y f) -- the fixed-point equation
39+
```
40+
41+
The first letter of the model is **the Y combinator** — Curry's untyped fixed-point operator (Curry & Feys, *Combinatory Logic* I, 1958). Given any function `f`, `Y f` produces an `x` such that `x = f x`. It is the canonical formal name of *self-reference computed without an external base case*; the regress is closed by structural duplication (`x x`) at the lambda level.
42+
43+
mago-dbe materialises this combinator at the *type-system level*, not the value level. The compiler `C` is typed by `G`; `G` is the output of `C`; the equation `G = C(M, G)` holds at every iteration with `G* := C(M)` as its unique fixed point. The full formal correspondence — `Y f = f (Y f)``G* = C[G*](M)` — is proved as Theorem 5.1 in [`SELF-HOST-PROOF.md`](SELF-HOST-PROOF.md). One-step convergence (Lemma 4.5) and acyclic primitive recursion (Lemma 4.4) replace the untyped recursion-via-self-application that makes `Y` ill-typed in System F: ours is a *typed*, *terminating*, *byte-stable* analogue of `Y`, restricted to a primitive-recursive transducer.
44+
3545
The `Y` phase is the meta-circular fixed point: the compiler whose runtime types are produced by the compiler itself, given canonical source `M`. This is not a future feature; it is provably implemented and empirically verified across two physical sandboxes by SHA-256 equality across four independent measurements.
3646

3747
| Concern | Implementation |

0 commit comments

Comments
 (0)