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runmingl
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Nov 26, 2023
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| ≤⟨ ( | ||
| {! !} | ||
| -- ≤⁻-mono {Π _ λ _ → cost} {cost} (bind cost (mapreduce _ _ _ t₁ f g z ∥ mapreduce _ _ _ t₂ f g z)) | ||
| -- {λ (s₁ , s₂) → | ||
| -- bind cost (f a) λ b → | ||
| -- bind cost (g b s₂) λ s₃ → | ||
| -- funext | ||
| -- $ λ-mono-≤⁻ λ (s₁ , s₂) → | ||
| -- ≤⁻-mono (bind cost (f a)) $ λ-mono-≤⁻ λ b → | ||
| -- ≤⁻-mono (bind cost (g b s₂)) $ λ-mono-≤⁻ λ s₃ → | ||
| -- g-bound {s₁} {s₃} | ||
| ) ⟩ | ||
| ≤⟨ bind-monoʳ-≤⁻ ((mapreduce/seq _ _ _ t₁ f g z) ∥ (mapreduce/seq _ _ _ t₂ f g z)) (λ (s₁ , s₂) → | ||
| bind-monoʳ-≤⁻ (f a) (λ b → | ||
| bind-monoʳ-≤⁻ (g b s₂) (λ s₃ → g-bound))) ⟩ |
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The problem we ran into earlier can (and should) be solved via bind-monoʳ-≤⁻ and bind-monoˡ-≤⁻.
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This should supersede #34 by porting everything from calf to decalf.