takes-the-one-term-both-sides-of-a-join-come-to.yaml

# SPDX-FileCopyrightText: Copyright (c) 2025 Objectionary.com
# SPDX-License-Identifier: MIT
---
# yamllint disable rule:line-length
# A join whose two sides come to the same normal form through 𝕄 has
# nothing to join (#1954): it mints no symbol and answers that one term,
# commented with both sides it came from.
symbolic: |
  - λ: L_number_gt
    dataize:
      𝛿1: $.ρ
      𝛿2: $.x
    𝑛: Φ.bool( φ ↦ ⟦ λ ⤍ 𝜎 ⟧ )
  - λ: L_number_plus
    dataize:
      𝛿1: $.ρ
      𝛿2: $.x
    𝑛: Φ.number( φ ↦ ⟦ λ ⤍ 𝜎 ⟧ )
  - λ: L_fork
    dataize:
      𝛿1: $.ρ
    join:
      on: 𝛿1
      left: $.then
      right: $.else
location: 'Q.@'
input: >
  ⟦ bytes(φ) ↦ ⟦⟧,
    bool(φ) ↦ ⟦ if ↦ ⟦ ρ ↦ ∅, then ↦ ∅, else ↦ ∅, λ ⤍ L_fork ⟧ ⟧,
    number(φ) ↦ ⟦
      gt(ρ, x) ↦ ⟦ λ ⤍ L_number_gt ⟧,
      plus(ρ, x) ↦ ⟦ λ ⤍ L_number_plus ⟧ ⟧,
    φ ↦ 5.gt( 0 ).if( 1.plus( 2 ), 1.plus( 2 ) ).φ ⟧
result: '𝜎2:λ'
protocol: |
  𝕄(Φ.φ):
    𝑛·0·1 := 5
    𝑛·0·2 := 𝑛·0·1.gt( x ↦ 0 )
    𝔼(L_number_gt):
      𝔻(Φ.a🌵0):
        𝕄(Φ.a🌵0):
          𝑛·1·1 := 5
          𝑛·1·2 := Φ.bytes( φ ↦ 40-14-00-00-00-00-00-00:Δ )
        𝛿·1·1 := 40-14-00-00-00-00-00-00  # 5.0
      𝛿1·1 := 𝛿·1·1  # 𝔻(ξ.ρ)
      𝔻(Φ.a🌵1):
        𝕄(Φ.a🌵1):
          𝑛·1·3 := 0
          𝑛·1·4 := Φ.bytes( φ ↦ 00-00-00-00-00-00-00-00:Δ )
        𝛿·1·2 := 00-00-00-00-00-00-00-00  # 0.0
      𝛿2·1 := 𝛿·1·2  # 𝔻(ξ.x)
      𝑛·1·5 := Φ.bool( φ ↦ 𝜎1:λ )  # 𝑛
      𝕄(𝑛·1·5):
        𝑛·1·6 := Φ.bool( φ ↦ 𝜎1:λ )
      𝑛·1·7 := 𝑛·1·6  # 𝕄(𝑛·1·5)
    𝑛·0·3 := 𝑛·1·6.if( then ↦ 1.plus( 2 ) )
    𝑛·0·4 := 𝑛·0·3( else ↦ 1.plus( 2 ) )
    𝔼(L_fork):
      𝔻(Φ.a🌵2):
        𝕄(Φ.a🌵2):
          𝑛·2·1 := Φ.bool( φ ↦ 𝜎1:λ )
      𝛿1·2 := 𝔻(𝜎1:λ)  # 𝔻(ξ.ρ)
      𝕄(Φ.a🌵3):
        𝑛·2·2 := 1
        𝑛·2·3 := 𝑛·2·2.plus( x ↦ 2 )
      𝕄(Φ.a🌵4):
        𝑛·2·4 := 1
        𝑛·2·5 := 𝑛·2·4.plus( x ↦ 2 )
      𝑛·2·6 := 𝑛·2·5  # 𝕄(ξ.then), 𝕄(ξ.else)
    𝔼(L_number_plus):
      𝔻(Φ.a🌵5):
        𝕄(Φ.a🌵5):
          𝑛·3·1 := 1
          𝑛·3·2 := Φ.bytes( φ ↦ 3F-F0-00-00-00-00-00-00:Δ )
        𝛿·3·1 := 3F-F0-00-00-00-00-00-00  # 1.0
      𝛿1·3 := 𝛿·3·1  # 𝔻(ξ.ρ)
      𝔻(Φ.a🌵6):
        𝕄(Φ.a🌵6):
          𝑛·3·3 := 2
          𝑛·3·4 := Φ.bytes( φ ↦ 40-00-00-00-00-00-00-00:Δ )
        𝛿·3·2 := 40-00-00-00-00-00-00-00  # 2.0
      𝛿2·3 := 𝛿·3·2  # 𝔻(ξ.x)
      𝑛·3·5 := Φ.number( φ ↦ 𝜎2:λ )  # 𝑛
      𝕄(𝑛·3·5):
        𝑛·3·6 := Φ.number( φ ↦ 𝜎2:λ )
      𝑛·3·7 := 𝑛·3·6  # 𝕄(𝑛·3·5)