joins-a-branch-whose-phi-reads-its-own-object-when-lenient.yaml

# SPDX-FileCopyrightText: Copyright (c) 2025 Objectionary.com
# SPDX-License-Identifier: MIT
---
# yamllint disable rule:line-length
# A fork whose one branch is an ordinary object: a formation with no λ, whose
# value sits in a φ that reads an attribute of the object itself. 𝕄 stops at
# that formation, so the branch and a bare symbol differ in shape and depth,
# and the join alone cannot pair them. An entry that says 'lenient: true'
# takes one more step before it gets stuck: it morphs the φ of that branch,
# fires what it comes to through 𝔼, the way 'morph' and 'evaluate' lines do,
# and joins once more, now two bare symbols (#1885).
symbolic: |
  - λ: L_eq
    𝑛: ⟦ φ ↦ ⟦ λ ⤍ 𝜎 ⟧ ⟧
  - λ: L_fork
    morph:
      𝑛1: $.a
      𝑛2: $.b
    join:
      𝑛3: [𝑛1, 𝑛2]
    lenient: true
    𝑛: 𝑛3
location: 'Q.y'
input: '⟦ y ↦ ⟦ a ↦ ⟦ φ ↦ ξ.eq, eq ↦ ⟦ λ ⤍ L_eq ⟧ ⟧, b ↦ ⟦ φ ↦ ⟦ λ ⤍ 𝜎1 ⟧ ⟧, λ ⤍ L_fork ⟧.φ ⟧'
result: '𝜎3:λ'
protocol: |
  𝕄(Φ.y):
    𝔼(L_fork):
      𝑛1·1 := ⟦ φ ↦ eq, eq ↦ L_eq:λ ⟧  # 𝕄(ξ.a)
      𝑛2·1 := 𝜎1:λ:φ  # 𝕄(ξ.b)
      𝑛1·1 := L_eq:λ  # 𝕄(𝑛1.φ)
      𝔼(L_eq):  # 𝔼(𝑛1)
        𝑛·2·1 := 𝜎2:λ:φ  # 𝑛
        𝑛·2·2 := 𝜎2:λ:φ  # 𝕄(𝑛·2·1)
      𝑛1·1 := 𝑛·2·2  # 𝔼(𝑛1)
      𝔻(𝜎3:λ) ∈ { 𝔻(𝜎2:λ), 𝔻(𝜎1:λ) }
      𝑛3·1 := 𝜎3:λ:φ  # [𝑛1, 𝑛2]
      𝑛·1·1 := 𝑛3·1  # 𝑛
      𝑛·1·2 := 𝑛3·1  # 𝕄(𝑛·1·1)