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Adds "pushforward" to Relation.Unary #2840

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Adds "pushforward" to Relation.Unary #2840

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bc1d795
add predicate pushforward
bsaul Oct 22, 2025
648d3a8
update changelog
bsaul Oct 22, 2025
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5 changes: 5 additions & 0 deletions CHANGELOG.md
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Expand Up @@ -180,6 +180,11 @@ Additions to existing modules
contradiction′ : ¬ A → A → Whatever
```

* In `Relation.Unary`
```agda
_⊣_ : (A → B) → Pred A ℓ → Pred B _
```

* In `System.Random`:
```agda
randomIO : IO Bool
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7 changes: 6 additions & 1 deletion src/Relation/Unary.agda
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Expand Up @@ -202,7 +202,7 @@ Decidable P = ∀ x → Dec (P x)
-- Operations on sets

infix 10 ⋃ ⋂
infixr 9 _⊢_
infixr 9 _⊢_ _⊣_
infixr 8 _⇒_
infixr 7 _∩_
infixr 6 _∪_
Expand Down Expand Up @@ -266,6 +266,11 @@ P ⊥′ Q = P ∩ Q ⊆′ ∅
_⊢_ : (A → B) → Pred B ℓ → Pred A ℓ
f ⊢ P = λ x → P (f x)

-- Pushforward.
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I think a certain amount of the discussion on the PR should go in comments here. At least that would give a hope of someone finding this via just plain 'grep'.


_⊣_ : (A → B) → Pred A ℓ → Pred B _
f ⊣ P = λ b → ∃ λ a → f a ≡ b × P a
Comment on lines +271 to +272
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@jamesmckinna jamesmckinna Oct 25, 2025 •
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In a spirit of 'compromise', and taking @gallais 's nudge about relative position wrt the turnstile, suggest instead:

Suggested change
_⊣_ : (A → B) → Pred A ℓ → Pred B _
f ⊣ P = λ b → ∃ λ a → f a ≡ b × P a
∃[_]⊢_ : (A → B) → Pred A ℓ → Pred B ℓ
∃[ f ]⊢ P = λ b → ∃ λ a → f a ≡ b × P a

so that one can also then add (plus fixing up the fixity declarations! sigh...)

∀[_]⊢_ : (A → B) → Pred A ℓ → Pred B ℓ
∀[ f ]⊢ P = λ b → ∀ a → f a ≡ b → P a

per Lawvere, and consider refinements of this in a setoidal context downstream?


------------------------------------------------------------------------
-- Predicate combinators

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