joins-two-sides-that-differ-only-in-symbols.yaml

# SPDX-FileCopyrightText: Copyright (c) 2025 Objectionary.com
# SPDX-License-Identifier: MIT
---
# yamllint disable rule:line-length
# A join brings both of its sides to a normal form through 𝕄 first (#1954).
# Each side here is a call of 'plus' over the answer of another 'plus', which
# 𝕄 fires: 𝜎2 on the left, 𝜎3 on the right, and nothing else tells the two
# sides apart. So the join mints 𝜎4, writes that 𝜎4 is 𝜎2 when the condition
# holds and 𝜎3 when it does not, and answers the joined call, whose ρ holds
# 𝜎4; the last 'plus' reads 𝜎4.
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 ).plus( 0 ), 3.plus( 4 ).plus( 0 ) ).φ ⟧
result: '𝜎5: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 ).plus( 𝑛·1·3 ) )
    𝑛·0·4 := 𝑛·0·3( else ↦ 3.plus( 4 ).plus( 𝑛·1·3 ) )
    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 )
        𝔼(L_number_plus):
          𝔻(Φ.a🌵4):
            𝕄(Φ.a🌵4):
              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🌵5):
            𝕄(Φ.a🌵5):
              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)
        𝑛·2·4 := 𝑛·3·6.plus( x ↦ 𝑛·1·3 )
      𝕄(Φ.a🌵6):
        𝑛·2·5 := 3
        𝑛·2·6 := 𝑛·2·5.plus( x ↦ 4 )
        𝔼(L_number_plus):
          𝔻(Φ.a🌵7):
            𝕄(Φ.a🌵7):
              𝑛·4·1 := 3
              𝑛·4·2 := Φ.bytes( φ ↦ 40-08-00-00-00-00-00-00:Δ )
            𝛿·4·1 := 40-08-00-00-00-00-00-00  # 3.0
          𝛿1·4 := 𝛿·4·1  # 𝔻(ξ.ρ)
          𝔻(Φ.a🌵8):
            𝕄(Φ.a🌵8):
              𝑛·4·3 := 4
              𝑛·4·4 := Φ.bytes( φ ↦ 40-10-00-00-00-00-00-00:Δ )
            𝛿·4·2 := 40-10-00-00-00-00-00-00  # 4.0
          𝛿2·4 := 𝛿·4·2  # 𝔻(ξ.x)
          𝑛·4·5 := Φ.number( φ ↦ 𝜎3:λ )  # 𝑛
          𝕄(𝑛·4·5):
            𝑛·4·6 := Φ.number( φ ↦ 𝜎3:λ )
          𝑛·4·7 := 𝑛·4·6  # 𝕄(𝑛·4·5)
        𝑛·2·7 := 𝑛·4·6.plus( x ↦ 𝑛·1·3 )
      joined 𝜎4 := 𝛿1·2 ? 𝜎2 : 𝜎3
      𝑛·2·8 := ⟦ x ↦ 𝑛·1·3, λ ⤍ L_number_plus ⟧  # 𝕄(ξ.then), 𝕄(ξ.else)
    𝔼(L_number_plus):
      𝔻(Φ.a🌵9):
        𝕄(Φ.a🌵9):
          𝑛·5·1 := Φ.number( φ ↦ 𝜎4:λ )
      𝛿1·5 := 𝔻(𝜎4:λ)  # 𝔻(ξ.ρ)
      𝔻(Φ.a🌵10):
        𝕄(Φ.a🌵10):
          𝑛·5·2 := Φ.number( φ ↦ 𝑛·1·4 )
          𝑛·5·3 := Φ.bytes( φ ↦ 00-00-00-00-00-00-00-00:Δ )
        𝛿·5·1 := 00-00-00-00-00-00-00-00  # 0.0
      𝛿2·5 := 𝛿·5·1  # 𝔻(ξ.x)
      𝑛·5·4 := Φ.number( φ ↦ 𝜎5:λ )  # 𝑛
      𝕄(𝑛·5·4):
        𝑛·5·5 := Φ.number( φ ↦ 𝜎5:λ )
      𝑛·5·6 := 𝑛·5·5  # 𝕄(𝑛·5·4)