cuts-a-recursion-running-through-evaluate-lines.yaml

# SPDX-FileCopyrightText: Copyright (c) 2025 Objectionary.com
# SPDX-License-Identifier: MIT
---
# yamllint disable rule:line-length
# A recursion that runs through 'evaluate' lines alone, under
# '--acyclic=proven'. 'L_loop' morphs 'next' to the very formation it was
# fired from, and its 'evaluate' line fires that formation again. The line
# enters the formation the way 'ml' does, so the second firing is cut before
# it opens and writes a 'looped' line where its block would have stood
# (#1882). The budget of firings is there only to end the run if the cut
# is ever lost again.
symbolic: |
  - λ: L_loop
    morph:
      𝑛1: $.next
    evaluate:
      𝑛2: 𝑛1
    𝑛: 𝑛2
location: 'Q.app'
acyclic: proven
firings: 5
input: '⟦ loop ↦ ⟦ next ↦ Φ.loop, λ ⤍ L_loop ⟧, app ↦ Φ.loop.φ ⟧'
result: '⟦ next ↦ Φ.loop, λ ⤍ L_loop ⟧.φ'
protocol: |
  𝕄(Φ.app):
    𝔼(L_loop):
      𝑛1·1 := ⟦ next ↦ Φ.loop, λ ⤍ L_loop ⟧  # 𝕄(ξ.next)
      looped(⟦ next ↦ Φ.loop, λ ⤍ L_loop ⟧)  # 𝔼(𝑛1), proven