fires-a-formation-once-however-often-it-is-met.yaml

# SPDX-FileCopyrightText: Copyright (c) 2025 Objectionary.com
# SPDX-License-Identifier: MIT
---
# yamllint disable rule:line-length
# The memo of '--acyclic=plausible': 𝔼 is a function of the formation it
# fires, so two bindings spelling one term fire one formation twice, and a
# run firing it afresh each time mints two symbols for one value and fires
# everything under the second once more (#1476). The 'evaluate' lines of
# 'L_pair' fire 'a' and then 'b', which spell the very same sum. Under the
# mode the second firing takes what the first answered: it reduces nothing,
# mints nothing and lands 'b' on the very symbol 'a' came to. The protocol
# still writes the firing of 'b' at its own site, with the answer the firing
# of 'a' made, named after the line that made it, and with no operand line
# under it, since none was reduced (#1874).
symbolic: |
  - λ: L_number_plus
    dataize:
      𝛿1: $.ρ
      𝛿2: $.x
    𝑛: Φ.number( φ ↦ ⟦ λ ⤍ 𝜎 ⟧ )
  - λ: L_pair
    morph:
      𝑛1: $.a
      𝑛2: $.b
    evaluate:
      𝑛3: 𝑛1
      𝑛4: 𝑛2
    𝑛: ⟦ φ ↦ ⟦ a ↦ 𝑛3, b ↦ 𝑛4 ⟧ ⟧
location: 'Q.p'
acyclic: plausible
input: >
  ⟦ bytes(φ) ↦ ⟦⟧,
    number(φ) ↦ ⟦ plus(ρ, x) ↦ ⟦ λ ⤍ L_number_plus ⟧ ⟧,
    p ↦ ⟦
      a ↦ 7.plus( 5.plus( 6 ) ),
      b ↦ 7.plus( 5.plus( 6 ) ),
      λ ⤍ L_pair ⟧.φ ⟧
result: >
  ⟦ a ↦ ⟦ φ ↦ 𝜎2:λ, plus(x) ↦ L_number_plus:λ ⟧,
    b ↦ ⟦ φ ↦ 𝜎2:λ, plus(x) ↦ L_number_plus:λ ⟧ ⟧
protocol: |
  𝕄(Φ.p):
    𝔼(L_pair):
      𝕄(ξ.a):
        normalized 𝑛·1·1 := ⟦ φ ↦ ∅, plus(x) ↦ L_number_plus:λ ⟧  # Φ.number
        𝑛·1·2 := 7.0
        𝑛·1·3 := ⟦ φ ↦ Φ.bytes( φ ↦ 40-1C-00-00-00-00-00-00:Δ ), plus(x) ↦ L_number_plus:λ ⟧
        normalized 𝑛·1·4 := ⟦ x ↦ ∅, λ ⤍ L_number_plus ⟧  # 𝑛·1·3.plus
        𝑛·1·5 := 𝑛·1·2.plus( x ↦ 5.0.plus( 6.0 ) )
        𝑛·1·6 := ⟦ x ↦ 5.0.plus( 6.0 ), λ ⤍ L_number_plus ⟧
        morphed 𝑛·1·7 := 𝑛·1·6
      𝑛1·1 := 𝑛·1·6  # 𝕄(ξ.a)
      𝕄(ξ.b):
        𝑛·1·8 := 7.0
        𝑛·1·9 := ⟦ φ ↦ Φ.bytes( φ ↦ 40-1C-00-00-00-00-00-00:Δ ), plus(x) ↦ L_number_plus:λ ⟧
        normalized 𝑛·1·10 := ⟦ x ↦ ∅, λ ⤍ L_number_plus ⟧  # 𝑛·1·9.plus
        𝑛·1·11 := 𝑛·1·8.plus( x ↦ 5.0.plus( 6.0 ) )
        𝑛·1·12 := ⟦ x ↦ 5.0.plus( 6.0 ), λ ⤍ L_number_plus ⟧
        morphed 𝑛·1·13 := 𝑛·1·12
      𝑛2·1 := 𝑛·1·12  # 𝕄(ξ.b)
      𝔼(L_number_plus):  # 𝔼(𝑛1)
        𝔻(ξ.ρ):
          𝕄(ξ.ρ):
            𝑛·2·1 := 7.0
            𝑛·2·2 := ⟦ φ ↦ Φ.bytes( φ ↦ 40-1C-00-00-00-00-00-00:Δ ), plus(x) ↦ L_number_plus:λ ⟧
            morphed 𝑛·2·3 := 𝑛·2·2
          boxed 𝑛·2·4 := 𝑛·2·3.φ
          normalized 𝑛·2·5 := Φ.bytes( φ ↦ 40-1C-00-00-00-00-00-00:Δ )  # 𝑛·2·4
          𝕄(𝑛·2·4):
            normalized 𝑛·2·6 := ∅:φ  # Φ.bytes
            𝑛·2·7 := Φ.bytes( φ ↦ 40-1C-00-00-00-00-00-00:Δ )
            𝑛·2·8 := 40-1C-00-00-00-00-00-00:Δ:φ
            morphed 𝑛·2·9 := 𝑛·2·8
          boxed 𝑛·2·10 := 𝑛·2·9.φ
          normalized 𝑛·2·11 := 40-1C-00-00-00-00-00-00:Δ  # 𝑛·2·10
          𝛿·2·1 := 40-1C-00-00-00-00-00-00  # 7.0
        𝛿1·2 := 𝛿·2·1  # 𝔻(ξ.ρ)
        𝔻(ξ.x):
          𝕄(ξ.x):
            𝑛·2·12 := 5.0
            𝑛·2·13 := ⟦ φ ↦ Φ.bytes( φ ↦ 40-14-00-00-00-00-00-00:Δ ), 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 ↦ 6.0 )
            𝑛·2·16 := ⟦ x ↦ 6.0, λ ⤍ L_number_plus ⟧
            morphed 𝑛·2·17 := 𝑛·2·16
          𝔼(L_number_plus):
            𝔻(ξ.ρ):
              𝕄(ξ.ρ):
                𝑛·3·1 := 5.0
                𝑛·3·2 := ⟦ φ ↦ Φ.bytes( φ ↦ 40-14-00-00-00-00-00-00:Δ ), 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 ↦ 40-14-00-00-00-00-00-00:Δ )  # 𝑛·3·4
              𝕄(𝑛·3·4):
                𝑛·3·6 := Φ.bytes( φ ↦ 40-14-00-00-00-00-00-00:Δ )
                𝑛·3·7 := 40-14-00-00-00-00-00-00:Δ:φ
                morphed 𝑛·3·8 := 𝑛·3·7
              boxed 𝑛·3·9 := 𝑛·3·8.φ
              normalized 𝑛·3·10 := 40-14-00-00-00-00-00-00:Δ  # 𝑛·3·9
              𝛿·3·1 := 40-14-00-00-00-00-00-00  # 5.0
            𝛿1·3 := 𝛿·3·1  # 𝔻(ξ.ρ)
            𝔻(ξ.x):
              𝕄(ξ.x):
                𝑛·3·11 := 6.0
                𝑛·3·12 := ⟦ φ ↦ Φ.bytes( φ ↦ 40-18-00-00-00-00-00-00:Δ ), 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 ↦ 40-18-00-00-00-00-00-00:Δ )  # 𝑛·3·14
              𝕄(𝑛·3·14):
                𝑛·3·16 := Φ.bytes( φ ↦ 40-18-00-00-00-00-00-00:Δ )
                𝑛·3·17 := 40-18-00-00-00-00-00-00:Δ:φ
                morphed 𝑛·3·18 := 𝑛·3·17
              boxed 𝑛·3·19 := 𝑛·3·18.φ
              normalized 𝑛·3·20 := 40-18-00-00-00-00-00-00:Δ  # 𝑛·3·19
              𝛿·3·2 := 40-18-00-00-00-00-00-00  # 6.0
            𝛿2·3 := 𝛿·3·2  # 𝔻(ξ.x)
            𝑛·3·21 := Φ.number( φ ↦ 𝜎1:λ )  # 𝑛
            𝕄(𝑛·3·21):
              𝑛·3·22 := Φ.number( φ ↦ 𝜎1:λ )
              𝑛·3·23 := ⟦ φ ↦ 𝜎1:λ, plus(x) ↦ L_number_plus:λ ⟧
              morphed 𝑛·3·24 := 𝑛·3·23
            𝑛·3·25 := 𝑛·3·24  # 𝕄(𝑛·3·21)
            memoized 𝑛·2·16 ⇛ 𝑛·3·25
          boxed 𝑛·2·18 := 𝑛·3·25.φ
          normalized 𝑛·2·19 := 𝜎1:λ  # 𝑛·2·18
          𝛿·2·2 := 𝔻(𝜎1:λ)
        𝛿2·2 := 𝛿·2·2  # 𝔻(ξ.x)
        𝑛·2·20 := Φ.number( φ ↦ 𝜎2:λ )  # 𝑛
        𝕄(𝑛·2·20):
          𝑛·2·21 := Φ.number( φ ↦ 𝜎2:λ )
          𝑛·2·22 := ⟦ φ ↦ 𝜎2:λ, plus(x) ↦ L_number_plus:λ ⟧
          morphed 𝑛·2·23 := 𝑛·2·22
        𝑛·2·24 := 𝑛·2·23  # 𝕄(𝑛·2·20)
        memoized 𝑛·1·12 ⇛ 𝑛·2·24
      𝑛3·1 := 𝑛·2·24  # 𝔼(𝑛1)
      𝔼(L_number_plus):  # 𝔼(𝑛2)
        recalled 𝑛·1·12 ⇒ 𝑛·2·24
        𝑛·4·1 := 𝑛·2·21  # 𝑛
        𝑛·4·2 := 𝑛3·1  # 𝕄(𝑛·4·1)
      𝑛4·1 := 𝑛·4·2  # 𝔼(𝑛2)
      𝑛·1·14 := ⟦ a ↦ 𝑛·4·2, b ↦ 𝑛·4·2 ⟧:φ  # 𝑛
      𝕄(𝑛·1·14):
        morphed 𝑛·1·15 := ⟦ a ↦ 𝑛·4·2, b ↦ 𝑛·4·2 ⟧:φ
      𝑛·1·16 := 𝑛·1·15  # 𝕄(𝑛·1·14)
      memoized 𝑛·1·17 ⇛ 𝑛·1·16  # ⟦ a ↦ 𝑛·2·1.plus( 𝑛·3·1.plus( 𝑛·3·11 ) ), b ↦ 𝑛·2·1.plus( 𝑛·3·1.plus( 𝑛·3·11 ) ), λ ⤍ L_pair ⟧
    normalized 𝑛·0·1 := ⟦ a ↦ 𝑛·4·2, b ↦ 𝑛·4·2 ⟧  # 𝑛·1·16.φ
    morphed 𝑛·0·2 := 𝑛·0·1