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Add _⟨$⟩_ operator for Function bundle #2144

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6 changes: 6 additions & 0 deletions CHANGELOG.md
Original file line number Diff line number Diff line change
Expand Up @@ -3114,6 +3114,12 @@ Additions to existing modules
execState : State s a → s → s
```

* Added new application operator synonym to `Function.Bundles`:
```agda
_⟨$⟩_ : Func From To → Carrier From → Carrier To
_⟨$⟩_ = Func.to
```

* Added new proofs in `Function.Construct.Symmetry`:
```
bijective : Bijective ≈₁ ≈₂ f → Symmetric ≈₂ → Transitive ≈₂ → Congruent ≈₁ ≈₂ f → Bijective ≈₂ ≈₁ f⁻¹
Expand Down
13 changes: 13 additions & 0 deletions src/Function/Bundles.agda
Original file line number Diff line number Diff line change
Expand Up @@ -66,6 +66,7 @@ module _ (From : Setoid a ℓ₁) (To : Setoid b ℓ₂) where
open IsCongruent isCongruent public
using (module Eq₁; module Eq₂)


record Injection : Set (a ⊔ b ⊔ ℓ₁ ⊔ ℓ₂) where
field
to : A → B
Expand Down Expand Up @@ -472,3 +473,15 @@ module _ {A : Set a} {B : Set b} where
, strictlyInverseʳ⇒inverseʳ to invʳ
)

------------------------------------------------------------------------
-- Other
------------------------------------------------------------------------

-- Alternative syntax for the application of functions

module _ {From : Setoid a ℓ₁} {To : Setoid b ℓ₂} where
open Setoid

infixl 5 _⟨$⟩_
_⟨$⟩_ : Func From To → Carrier From → Carrier To
_⟨$⟩_ = Func.to