diverges-on-two-sides-that-do-not-join.yaml

# SPDX-FileCopyrightText: Copyright (c) 2025 Objectionary.com
# SPDX-License-Identifier: MIT
---
# yamllint disable rule:line-length
# A join on a condition nobody decided: the condition comes down through 𝔻
# and answers a symbol nobody has decided. The join brings both sides to a
# normal form through 𝕄 first, each a call of 'plus' nobody has fired
# (#1954). The calls add other numbers, so no join makes one term of them,
# and the firing writes 'diverged' with the metas of the formations the two
# applications made, instead of splitting the run (#1996). Its comment tells
# that the two copies of 'plus' first differ at the ρ the protocol hides, and
# that the join names no function to fabricate a formation with (#2043).
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 ), 3.plus( 4 ) ).φ ⟧
fails: "No entry of --symbolic answers the λ function 'L_fork'"
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 ↦ 3.0.plus( 4.0 ) )
    𝑛·0·11 := ⟦ then ↦ 1.0.plus( 2.0 ), else ↦ 3.0.plus( 4.0 ), 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 := 3.0
        𝑛·2·13 := ⟦ φ ↦ Φ.bytes( φ ↦ 40-08-00-00-00-00-00-00: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 ↦ 4.0 )
        𝑛·2·16 := ⟦ x ↦ 4.0, λ ⤍ L_number_plus ⟧
        morphed 𝑛·2·17 := 𝑛·2·16
      diverged 𝑛·2·10 vs 𝑛·2·16  # cannot join: at .ρ the left side has ρ ↦ 𝑛·2·6 and the right side has ρ ↦ 𝑛·2·12; cannot fabricate: the join names no otherwise