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.
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):
    normalized 𝑛·0·1 := ⟦ φ ↦ ∅, gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧  # Φ.number
    𝑛·0·2 := 5.0
    𝑛·0·3 := ⟦ φ ↦ Φ.bytes( φ ↦ 40-14-00-00-00-00-00-00:Δ ), gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧
    normalized 𝑛·0·4 := ⟦ x ↦ ∅, λ ⤍ L_number_gt ⟧  # 𝑛·0·3.gt
    𝑛·0·5 := 𝑛·0·2.gt( x ↦ 0.0 )
    𝑛·0·6 := ⟦ x ↦ 0.0, λ ⤍ L_number_gt ⟧
    𝔼(L_number_gt):
      𝔻(ξ.ρ):
        𝕄(ξ.ρ):
          𝑛·1·1 := 5.0
          𝑛·1·2 := ⟦ φ ↦ Φ.bytes( φ ↦ 40-14-00-00-00-00-00-00:Δ ), gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧
          morphed 𝑛·1·3 := 𝑛·1·2
        boxed 𝑛·1·4 := 𝑛·1·3.φ
        normalized 𝑛·1·5 := Φ.bytes( φ ↦ 40-14-00-00-00-00-00-00:Δ )  # 𝑛·1·4
        𝕄(𝑛·1·4):
          normalized 𝑛·1·6 := ∅:φ  # Φ.bytes
          𝑛·1·7 := Φ.bytes( φ ↦ 40-14-00-00-00-00-00-00:Δ )
          𝑛·1·8 := 40-14-00-00-00-00-00-00:Δ:φ
          morphed 𝑛·1·9 := 𝑛·1·8
        boxed 𝑛·1·10 := 𝑛·1·9.φ
        normalized 𝑛·1·11 := 40-14-00-00-00-00-00-00:Δ  # 𝑛·1·10
        𝛿·1·1 := 40-14-00-00-00-00-00-00  # 5.0
      𝛿1·1 := 𝛿·1·1  # 𝔻(ξ.ρ)
      𝔻(ξ.x):
        𝕄(ξ.x):
          𝑛·1·12 := 0.0
          𝑛·1·13 := ⟦ φ ↦ Φ.bytes( φ ↦ 00-00-00-00-00-00-00-00:Δ ), gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧
          morphed 𝑛·1·14 := 𝑛·1·13
        boxed 𝑛·1·15 := 𝑛·1·14.φ
        normalized 𝑛·1·16 := Φ.bytes( φ ↦ 00-00-00-00-00-00-00-00:Δ )  # 𝑛·1·15
        𝕄(𝑛·1·15):
          𝑛·1·17 := Φ.bytes( φ ↦ 00-00-00-00-00-00-00-00:Δ )
          𝑛·1·18 := 00-00-00-00-00-00-00-00:Δ:φ
          morphed 𝑛·1·19 := 𝑛·1·18
        boxed 𝑛·1·20 := 𝑛·1·19.φ
        normalized 𝑛·1·21 := 00-00-00-00-00-00-00-00:Δ  # 𝑛·1·20
        𝛿·1·2 := 00-00-00-00-00-00-00-00  # 0.0
      𝛿2·1 := 𝛿·1·2  # 𝔻(ξ.x)
      𝑛·1·22 := Φ.bool( φ ↦ 𝜎1:λ )  # 𝑛
      𝕄(𝑛·1·22):
        normalized 𝑛·1·23 := ⟦ φ ↦ ∅, if(then, else) ↦ L_fork:λ ⟧  # Φ.bool
        𝑛·1·24 := Φ.bool( φ ↦ 𝜎1:λ )
        𝑛·1·25 := ⟦ φ ↦ 𝜎1:λ, if(then, else) ↦ L_fork:λ ⟧
        morphed 𝑛·1·26 := 𝑛·1·25
      𝑛·1·27 := 𝑛·1·26  # 𝕄(𝑛·1·22)
    normalized 𝑛·0·7 := ⟦ then ↦ ∅, else ↦ ∅, λ ⤍ L_fork ⟧  # 𝑛·1·27.if
    𝑛·0·8 := 𝑛·1·24.if( then ↦ 1.0.plus( 2.0 ) )
    𝑛·0·9 := ⟦ then ↦ 1.0.plus( 2.0 ), else ↦ ∅, λ ⤍ L_fork ⟧
    𝑛·0·10 := 𝑛·0·8( else ↦ 1.0.plus( 2.0 ) )
    𝑛·0·11 := ⟦ then ↦ 1.0.plus( 2.0 ), else ↦ 1.0.plus( 2.0 ), λ ⤍ L_fork ⟧
    𝔼(L_fork):
      𝔻(ξ.ρ):
        𝕄(ξ.ρ):
          𝑛·2·1 := Φ.bool( φ ↦ 𝜎1:λ )
          𝑛·2·2 := ⟦ φ ↦ 𝜎1:λ, if(then, else) ↦ L_fork:λ ⟧
          morphed 𝑛·2·3 := 𝑛·1·27
        boxed 𝑛·2·4 := 𝑛·2·3.φ
        normalized 𝑛·2·5 := 𝜎1:λ  # 𝑛·2·4
        𝛿·2·1 := 𝔻(𝜎1:λ)
      𝛿1·2 := 𝛿·2·1  # 𝔻(ξ.ρ)
      𝕄(ξ.then):
        𝑛·2·6 := 1.0
        𝑛·2·7 := ⟦ φ ↦ Φ.bytes( φ ↦ 3F-F0-00-00-00-00-00-00:Δ ), gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧
        normalized 𝑛·2·8 := ⟦ x ↦ ∅, λ ⤍ L_number_plus ⟧  # 𝑛·2·7.plus
        𝑛·2·9 := 𝑛·2·6.plus( x ↦ 2.0 )
        𝑛·2·10 := ⟦ x ↦ 2.0, λ ⤍ L_number_plus ⟧
        morphed 𝑛·2·11 := 𝑛·2·10
      𝕄(ξ.else):
        𝑛·2·12 := 1.0
        𝑛·2·13 := ⟦ φ ↦ Φ.bytes( φ ↦ 3F-F0-00-00-00-00-00-00:Δ ), gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧
        normalized 𝑛·2·14 := ⟦ x ↦ ∅, λ ⤍ L_number_plus ⟧  # 𝑛·2·13.plus
        𝑛·2·15 := 𝑛·2·12.plus( x ↦ 2.0 )
        𝑛·2·16 := ⟦ x ↦ 2.0, λ ⤍ L_number_plus ⟧
        morphed 𝑛·2·17 := 𝑛·2·16
      𝑛·2·18 := 𝑛·2·16
    𝔼(L_number_plus):
      𝔻(ξ.ρ):
        𝕄(ξ.ρ):
          𝑛·3·1 := 1.0
          𝑛·3·2 := ⟦ φ ↦ Φ.bytes( φ ↦ 3F-F0-00-00-00-00-00-00:Δ ), gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧
          morphed 𝑛·3·3 := 𝑛·3·2
        boxed 𝑛·3·4 := 𝑛·3·3.φ
        normalized 𝑛·3·5 := Φ.bytes( φ ↦ 3F-F0-00-00-00-00-00-00:Δ )  # 𝑛·3·4
        𝕄(𝑛·3·4):
          𝑛·3·6 := Φ.bytes( φ ↦ 3F-F0-00-00-00-00-00-00:Δ )
          𝑛·3·7 := 3F-F0-00-00-00-00-00-00:Δ:φ
          morphed 𝑛·3·8 := 𝑛·3·7
        boxed 𝑛·3·9 := 𝑛·3·8.φ
        normalized 𝑛·3·10 := 3F-F0-00-00-00-00-00-00:Δ  # 𝑛·3·9
        𝛿·3·1 := 3F-F0-00-00-00-00-00-00  # 1.0
      𝛿1·3 := 𝛿·3·1  # 𝔻(ξ.ρ)
      𝔻(ξ.x):
        𝕄(ξ.x):
          𝑛·3·11 := 2.0
          𝑛·3·12 := ⟦ φ ↦ Φ.bytes( φ ↦ 40-00-00-00-00-00-00-00:Δ ), gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧
          morphed 𝑛·3·13 := 𝑛·3·12
        boxed 𝑛·3·14 := 𝑛·3·13.φ
        normalized 𝑛·3·15 := Φ.bytes( φ ↦ 40-00-00-00-00-00-00-00:Δ )  # 𝑛·3·14
        𝕄(𝑛·3·14):
          𝑛·3·16 := Φ.bytes( φ ↦ 40-00-00-00-00-00-00-00:Δ )
          𝑛·3·17 := 40-00-00-00-00-00-00-00:Δ:φ
          morphed 𝑛·3·18 := 𝑛·3·17
        boxed 𝑛·3·19 := 𝑛·3·18.φ
        normalized 𝑛·3·20 := 40-00-00-00-00-00-00-00:Δ  # 𝑛·3·19
        𝛿·3·2 := 40-00-00-00-00-00-00-00  # 2.0
      𝛿2·3 := 𝛿·3·2  # 𝔻(ξ.x)
      𝑛·3·21 := Φ.number( φ ↦ 𝜎2:λ )  # 𝑛
      𝕄(𝑛·3·21):
        𝑛·3·22 := Φ.number( φ ↦ 𝜎2:λ )
        𝑛·3·23 := ⟦ φ ↦ 𝜎2:λ, gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧
        morphed 𝑛·3·24 := 𝑛·3·23
      𝑛·3·25 := 𝑛·3·24  # 𝕄(𝑛·3·21)
    normalized 𝑛·0·12 := 𝜎2:λ  # 𝑛·3·25.φ
    morphed 𝑛·0·13 := 𝑛·0·12