phino-0.0.165: test-resources/evaluate-packs/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):
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 ).plus( 𝑛·1·12 ) )
𝑛·0·9 := ⟦ then ↦ 1.0.plus( 2.0 ).plus( 𝑛·1·12 ), else ↦ ∅, λ ⤍ L_fork ⟧
𝑛·0·10 := 𝑛·0·8( else ↦ 3.0.plus( 4.0 ).plus( 𝑛·1·12 ) )
𝑛·0·11 := ⟦ then ↦ 1.0.plus( 2.0 ).plus( 𝑛·1·12 ), else ↦ 3.0.plus( 4.0 ).plus( 𝑛·1·12 ), 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 ⟧
𝔼(L_number_plus):
𝔻(ξ.ρ):
𝕄(ξ.ρ):
𝑛·3·1 := 1.0
𝑛·3·2 := ⟦ 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 ⟧
morphed 𝑛·3·3 := 𝑛·3·2
boxed 𝑛·3·4 := 𝑛·3·3.φ
normalized 𝑛·3·5 := Φ.bytes( φ ↦ 3F-F0-00-00-00-00-00-00:Δ ) # 𝑛·3·4
𝕄(𝑛·3·4):
𝑛·3·6 := Φ.bytes( φ ↦ 3F-F0-00-00-00-00-00-00:Δ )
𝑛·3·7 := 3F-F0-00-00-00-00-00-00:Δ:φ
morphed 𝑛·3·8 := 𝑛·3·7
boxed 𝑛·3·9 := 𝑛·3·8.φ
normalized 𝑛·3·10 := 3F-F0-00-00-00-00-00-00:Δ # 𝑛·3·9
𝛿·3·1 := 3F-F0-00-00-00-00-00-00 # 1.0
𝛿1·3 := 𝛿·3·1 # 𝔻(ξ.ρ)
𝔻(ξ.x):
𝕄(ξ.x):
𝑛·3·11 := 2.0
𝑛·3·12 := ⟦ φ ↦ Φ.bytes( φ ↦ 40-00-00-00-00-00-00-00:Δ ), gt(x) ↦ L_number_gt:λ, 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 ↦ 40-00-00-00-00-00-00-00:Δ ) # 𝑛·3·14
𝕄(𝑛·3·14):
𝑛·3·16 := Φ.bytes( φ ↦ 40-00-00-00-00-00-00-00:Δ )
𝑛·3·17 := 40-00-00-00-00-00-00-00:Δ:φ
morphed 𝑛·3·18 := 𝑛·3·17
boxed 𝑛·3·19 := 𝑛·3·18.φ
normalized 𝑛·3·20 := 40-00-00-00-00-00-00-00:Δ # 𝑛·3·19
𝛿·3·2 := 40-00-00-00-00-00-00-00 # 2.0
𝛿2·3 := 𝛿·3·2 # 𝔻(ξ.x)
𝑛·3·21 := Φ.number( φ ↦ 𝜎2:λ ) # 𝑛
𝕄(𝑛·3·21):
𝑛·3·22 := Φ.number( φ ↦ 𝜎2:λ )
𝑛·3·23 := ⟦ φ ↦ 𝜎2:λ, gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧
morphed 𝑛·3·24 := 𝑛·3·23
𝑛·3·25 := 𝑛·3·24 # 𝕄(𝑛·3·21)
normalized 𝑛·2·11 := ⟦ x ↦ ∅, λ ⤍ L_number_plus ⟧ # 𝑛·3·25.plus
𝑛·2·12 := 𝑛·3·22.plus( x ↦ 𝑛·1·12 )
𝑛·2·13 := ⟦ x ↦ 𝑛·1·12, λ ⤍ L_number_plus ⟧
morphed 𝑛·2·14 := 𝑛·2·13
𝕄(ξ.else):
𝑛·2·15 := 3.0
𝑛·2·16 := ⟦ 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·2·17 := ⟦ x ↦ ∅, λ ⤍ L_number_plus ⟧ # 𝑛·2·16.plus
𝑛·2·18 := 𝑛·2·15.plus( x ↦ 4.0 )
𝑛·2·19 := ⟦ x ↦ 4.0, λ ⤍ L_number_plus ⟧
𝔼(L_number_plus):
𝔻(ξ.ρ):
𝕄(ξ.ρ):
𝑛·4·1 := 3.0
𝑛·4·2 := ⟦ 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 ⟧
morphed 𝑛·4·3 := 𝑛·4·2
boxed 𝑛·4·4 := 𝑛·4·3.φ
normalized 𝑛·4·5 := Φ.bytes( φ ↦ 40-08-00-00-00-00-00-00:Δ ) # 𝑛·4·4
𝕄(𝑛·4·4):
𝑛·4·6 := Φ.bytes( φ ↦ 40-08-00-00-00-00-00-00:Δ )
𝑛·4·7 := 40-08-00-00-00-00-00-00:Δ:φ
morphed 𝑛·4·8 := 𝑛·4·7
boxed 𝑛·4·9 := 𝑛·4·8.φ
normalized 𝑛·4·10 := 40-08-00-00-00-00-00-00:Δ # 𝑛·4·9
𝛿·4·1 := 40-08-00-00-00-00-00-00 # 3.0
𝛿1·4 := 𝛿·4·1 # 𝔻(ξ.ρ)
𝔻(ξ.x):
𝕄(ξ.x):
𝑛·4·11 := 4.0
𝑛·4·12 := ⟦ φ ↦ Φ.bytes( φ ↦ 40-10-00-00-00-00-00-00:Δ ), gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧
morphed 𝑛·4·13 := 𝑛·4·12
boxed 𝑛·4·14 := 𝑛·4·13.φ
normalized 𝑛·4·15 := Φ.bytes( φ ↦ 40-10-00-00-00-00-00-00:Δ ) # 𝑛·4·14
𝕄(𝑛·4·14):
𝑛·4·16 := Φ.bytes( φ ↦ 40-10-00-00-00-00-00-00:Δ )
𝑛·4·17 := 40-10-00-00-00-00-00-00:Δ:φ
morphed 𝑛·4·18 := 𝑛·4·17
boxed 𝑛·4·19 := 𝑛·4·18.φ
normalized 𝑛·4·20 := 40-10-00-00-00-00-00-00:Δ # 𝑛·4·19
𝛿·4·2 := 40-10-00-00-00-00-00-00 # 4.0
𝛿2·4 := 𝛿·4·2 # 𝔻(ξ.x)
𝑛·4·21 := Φ.number( φ ↦ 𝜎3:λ ) # 𝑛
𝕄(𝑛·4·21):
𝑛·4·22 := Φ.number( φ ↦ 𝜎3:λ )
𝑛·4·23 := ⟦ φ ↦ 𝜎3:λ, gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧
morphed 𝑛·4·24 := 𝑛·4·23
𝑛·4·25 := 𝑛·4·24 # 𝕄(𝑛·4·21)
normalized 𝑛·2·20 := ⟦ x ↦ ∅, λ ⤍ L_number_plus ⟧ # 𝑛·4·25.plus
𝑛·2·21 := 𝑛·4·22.plus( x ↦ 𝑛·1·12 )
𝑛·2·22 := ⟦ x ↦ 𝑛·1·12, λ ⤍ L_number_plus ⟧
morphed 𝑛·2·23 := 𝑛·2·22
joined 𝜎4 := 𝛿1·2 ? 𝜎2 : 𝜎3
𝑛·2·24 := ⟦ x ↦ 𝑛·1·12, λ ⤍ L_number_plus ⟧
𝔼(L_number_plus):
𝔻(ξ.ρ):
𝕄(ξ.ρ):
𝑛·5·1 := Φ.number( φ ↦ 𝜎4:λ )
𝑛·5·2 := ⟦ φ ↦ 𝜎4:λ, gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧
morphed 𝑛·5·3 := 𝑛·5·2
boxed 𝑛·5·4 := 𝑛·5·3.φ
normalized 𝑛·5·5 := 𝜎4:λ # 𝑛·5·4
𝛿·5·1 := 𝔻(𝜎4:λ)
𝛿1·5 := 𝛿·5·1 # 𝔻(ξ.ρ)
𝔻(ξ.x):
𝕄(ξ.x):
𝑛·5·6 := Φ.number( φ ↦ 𝑛·1·17 )
𝑛·5·7 := ⟦ φ ↦ 𝑛·1·17, gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧
morphed 𝑛·5·8 := 𝑛·5·7
boxed 𝑛·5·9 := 𝑛·5·8.φ
normalized 𝑛·5·10 := 𝑛·1·17 # 𝑛·5·9
𝕄(𝑛·5·9):
𝑛·5·11 := Φ.bytes( φ ↦ 00-00-00-00-00-00-00-00:Δ )
𝑛·5·12 := 00-00-00-00-00-00-00-00:Δ:φ
morphed 𝑛·5·13 := 𝑛·5·12
boxed 𝑛·5·14 := 𝑛·5·13.φ
normalized 𝑛·5·15 := 00-00-00-00-00-00-00-00:Δ # 𝑛·5·14
𝛿·5·2 := 00-00-00-00-00-00-00-00 # 0.0
𝛿2·5 := 𝛿·5·2 # 𝔻(ξ.x)
𝑛·5·16 := Φ.number( φ ↦ 𝜎5:λ ) # 𝑛
𝕄(𝑛·5·16):
𝑛·5·17 := Φ.number( φ ↦ 𝜎5:λ )
𝑛·5·18 := ⟦ φ ↦ 𝜎5:λ, gt(x) ↦ L_number_gt:λ, plus(x) ↦ L_number_plus:λ ⟧
morphed 𝑛·5·19 := 𝑛·5·18
𝑛·5·20 := 𝑛·5·19 # 𝕄(𝑛·5·16)
normalized 𝑛·0·12 := 𝜎5:λ # 𝑛·5·20.φ
morphed 𝑛·0·13 := 𝑛·0·12