joins-an-attribute-named-left-of-a-copy-in-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 whose every attribute is a copy of 'L_join' (#2024). Both sides
# bind 'ke' to an object with an attribute named 'left', as the 'if' of a bool
# in EO has a void named 'left'. The program asks the copy under 'ke' for
# 'left', which the copy names none of its own attributes, since those carry
# the 🌵 mark (#2027), so the copy fires 'L_join', whose entry joins the 'ke'
# of both sides, two objects that differ in a symbol alone, and the program
# takes the 'left' of what the join made.
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 ↦ ⟦ left ↦ ⟦ λ ⤍ 𝜎2 ⟧ ⟧ ⟧, b ↦ ⟦ ke ↦ ⟦ left ↦ ⟦ λ ⤍ 𝜎3 ⟧ ⟧ ⟧, λ ⤍ L_fork ⟧.ke.left ⟧'
result: '𝜎4:λ'
protocol: |
  𝕄(Φ.y):
    𝔼(L_fork):
      𝛿1·1 := 𝔻(𝜎1:λ)  # 𝔻(ξ.c)
      fabricated 𝑛·1·1 := ⟦ φ ↦ Φ.hx, ke ↦ 𝜎2:λ:left ⟧ and 𝜎3:λ:left:ke  # ⟦ left🌵 ↦ ⟦ φ ↦ Φ.hx, ke ↦ 𝜎2:λ:left ⟧, right🌵 ↦ 𝜎3:λ:left:ke, φ ↦ ⟦ λ ⤍ L_join, on🌵 ↦ 𝜎1:λ, left🌵 ↦ ρ.left🌵.φ, right🌵 ↦ ρ.right🌵.φ ⟧, ke ↦ ⟦ λ ⤍ L_join, on🌵 ↦ 𝜎1:λ, left🌵 ↦ ρ.left🌵.ke, right🌵 ↦ ρ.right🌵.ke ⟧ ⟧
    𝔼(L_join):
      joined 𝜎4 := ξ.on🌵 ? 𝜎2 : 𝜎3
      𝑛·2·1 := 𝜎4:λ:left  # 𝕄(ξ.left🌵), 𝕄(ξ.right🌵)