answers-the-same-under-acyclic.yaml

# SPDX-FileCopyrightText: Copyright (c) 2025 Objectionary.com
# SPDX-License-Identifier: MIT
---
# yamllint disable rule:line-length
# A program that does not loop answers the same with '_acyclic' as without it.
# The guard remembers the terms the frames above have open, so only a genuine
# return to one of them trips it; a term merely reduced twice in two places
# does not.
symbolic: |
  - λ: L_number_plus
    dataize:
      𝛿1: $.ρ
      𝛿2: $.x
    𝑛: Φ.number( φ ↦ ⟦ λ ⤍ 𝜎 ⟧ )
location: 'Q.@'
acyclic: proven
input: >
  ⟦ bytes(φ) ↦ ⟦⟧,
    number(φ) ↦ ⟦ plus(ρ, x) ↦ ⟦ λ ⤍ L_number_plus ⟧ ⟧,
    φ ↦ 5.plus( 6 ).φ ⟧
result: '𝜎1:λ'
protocol: |
  𝕄(Φ.φ):
    normalized 𝑛·0·1 := ⟦ φ ↦ ∅, 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 ), plus(x) ↦ L_number_plus:λ ⟧
    normalized 𝑛·0·4 := ⟦ x ↦ ∅, λ ⤍ L_number_plus ⟧  # 𝑛·0·3.plus
    𝑛·0·5 := 𝑛·0·2.plus( x ↦ 6.0 )
    𝑛·0·6 := ⟦ x ↦ 6.0, λ ⤍ L_number_plus ⟧
    𝔼(L_number_plus):
      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 ), 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 := 6.0
          𝑛·1·13 := ⟦ φ ↦ Φ.bytes( φ ↦ 40-18-00-00-00-00-00-00:Δ ), 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 ↦ 40-18-00-00-00-00-00-00:Δ )  # 𝑛·1·15
        𝕄(𝑛·1·15):
          𝑛·1·17 := Φ.bytes( φ ↦ 40-18-00-00-00-00-00-00:Δ )
          𝑛·1·18 := 40-18-00-00-00-00-00-00:Δ:φ
          morphed 𝑛·1·19 := 𝑛·1·18
        boxed 𝑛·1·20 := 𝑛·1·19.φ
        normalized 𝑛·1·21 := 40-18-00-00-00-00-00-00:Δ  # 𝑛·1·20
        𝛿·1·2 := 40-18-00-00-00-00-00-00  # 6.0
      𝛿2·1 := 𝛿·1·2  # 𝔻(ξ.x)
      𝑛·1·22 := Φ.number( φ ↦ 𝜎1:λ )  # 𝑛
      𝕄(𝑛·1·22):
        𝑛·1·23 := Φ.number( φ ↦ 𝜎1:λ )
        𝑛·1·24 := ⟦ φ ↦ 𝜎1:λ, plus(x) ↦ L_number_plus:λ ⟧
        morphed 𝑛·1·25 := 𝑛·1·24
      𝑛·1·26 := 𝑛·1·25  # 𝕄(𝑛·1·22)
    normalized 𝑛·0·7 := 𝜎1:λ  # 𝑛·1·26.φ
    morphed 𝑛·0·8 := 𝑛·0·7