hands-a-positional-argument-to-both-sides-of-an-attribute-of-a-fabricated-formation.yaml

# SPDX-FileCopyrightText: Copyright (c) 2025 Objectionary.com
# SPDX-License-Identifier: MIT
---
# yamllint disable rule:line-length
# The two sides of 'L_fork' differ in shape, so the firing fabricates a
# formation (#2024). Both sides bind 'ke' to a formation leaving 'x' void, so
# the copy of 'L_join' under 'ke' leaves 'x' void too, as the first void it
# holds, and asks each side for 'ke' applied to 'x' (#2031). The program hands
# 'x' over by position and asks the answer for 'k': the copy takes 'x', both
# sides read it, and the join meets two sides that are the same.
symbolic: |
  - λ: L_fork
    dataize:
      𝛿1: $.c
    join:
      on: 𝛿1
      left: $.a
      right: $.b
      otherwise: L_join
  - λ: L_join
    join:
      on: $.on🌵
      left: $.left🌵
      right: $.right🌵
      otherwise: L_join
location: 'Q.y'
input: '⟦ y ↦ ⟦ c ↦ ⟦ λ ⤍ 𝜎1 ⟧, a ↦ ⟦ φ ↦ Φ.hx, ke ↦ ⟦ x ↦ ∅, k ↦ ξ.x ⟧ ⟧, b ↦ ⟦ ke ↦ ⟦ x ↦ ∅, k ↦ ξ.x ⟧ ⟧, λ ⤍ L_fork ⟧.ke( ⟦ λ ⤍ 𝜎2 ⟧ ).k ⟧'
result: '𝜎2:λ'
protocol: |
  𝕄(Φ.y):
    𝔼(L_fork):
      𝔻(ξ.c):
        𝛿·1·1 := 𝔻(𝜎1:λ)
      𝛿1·1 := 𝛿·1·1  # 𝔻(ξ.c)
      𝕄(ξ.a):
        morphed 𝑛·1·1 := ⟦ φ ↦ Φ.hx, ke(x) ↦ x:k ⟧
      𝕄(ξ.b):
        morphed 𝑛·1·2 := ⟦ ke(x) ↦ x:k ⟧
      fabricated 𝑛·1·3 := 𝑛·1·1 and 𝑛·1·2  # ⟦ left🌵 ↦ 𝑛·1·1, right🌵 ↦ 𝑛·1·2, φ ↦ ⟦ λ ⤍ L_join, on🌵 ↦ 𝜎1:λ, left🌵 ↦ ρ.left🌵.φ, right🌵 ↦ ρ.right🌵.φ ⟧, ke(x) ↦ ⟦ λ ⤍ L_join, on🌵 ↦ 𝜎1:λ, left🌵 ↦ ρ.left🌵.ke( x ↦ x ), right🌵 ↦ ρ.right🌵.ke( x ↦ x ) ⟧ ⟧
    𝑛·0·1 := ⟦ λ ⤍ L_join, x ↦ ∅, on🌵 ↦ 𝜎1:λ, left🌵 ↦ ρ.left🌵.ke( x ↦ x ), right🌵 ↦ ρ.right🌵.ke( x ↦ x ) ⟧( x ↦ 𝜎2:λ )
    𝔼(L_join):
      𝑛·2·1 := ⟦ x ↦ ∅, k ↦ x ⟧( x ↦ 𝜎2:λ )  # 𝕄(ξ.left🌵)
      𝕄(ξ.left🌵):
        morphed 𝑛·2·2 := 𝑛·2·1
      𝑛·2·3 := ⟦ x ↦ ∅, k ↦ x ⟧( x ↦ 𝜎2:λ )  # 𝕄(ξ.right🌵)
      𝕄(ξ.right🌵):
        morphed 𝑛·2·4 := 𝑛·2·3
      𝑛·2·5 := 𝑛·2·4  # 𝕄(ξ.left🌵), 𝕄(ξ.right🌵)
    morphed 𝑛·0·2 := 𝜎2:λ