phino-0.0.156: test-resources/evaluate-packs/joins-a-branch-it-unfolded-whose-phi-reads-its-own-object.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 'unfold' line takes the step the
# join used to hide (#1921): it morphs the φ of that branch, fires what it
# comes to through 𝔼, the way an 'evaluate' line does, and binds the answer,
# so the 'join' line pairs two bare symbols (#1885).
symbolic: |
  - λ: L_eq
    𝑛: ⟦ φ ↦ ⟦ λ ⤍ 𝜎 ⟧ ⟧
  - λ: L_fork
    morph:
      𝑛1: $.a
      𝑛2: $.b
    unfold:
      𝑛3: 𝑛1
    join:
      𝑛4: [𝑛3, 𝑛2]
    𝑛: 𝑛4
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)
      𝑛3·1 := 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)
      𝑛3·1 := 𝑛·2·2  # 𝔼(𝑛1)
      𝔻(𝜎3:λ) ∈ { 𝔻(𝜎2:λ), 𝔻(𝜎1:λ) }
      𝑛4·1 := 𝜎3:λ:φ  # [𝑛3, 𝑛2]
      𝑛·1·1 := 𝑛4·1  # 𝑛
      𝑛·1·2 := 𝑛4·1  # 𝕄(𝑛·1·1)