{-# OPTIONS --without-K --safe #-}
module Function.Base where
open import Level
open import Strict
private
variable
a b c d e : Level
A : Set a
B : Set b
C : Set c
D : Set d
E : Set e
id : A → A
id x = x
const : A → B → A
const x = λ _ → x
constᵣ : A → B → B
constᵣ _ = id
infixr 9 _∘_ _∘₂_
infixl 8 _ˢ_
infixl 0 _|>_
infix 0 case_return_of_
infixr -1 _$_ _$!_
_∘_ : ∀ {A : Set a} {B : A → Set b} {C : {x : A} → B x → Set c} →
(∀ {x} (y : B x) → C y) → (g : (x : A) → B x) →
((x : A) → C (g x))
f ∘ g = λ x → f (g x)
{-# INLINE _∘_ #-}
_∘₂_ : ∀ {A₁ : Set a} {A₂ : A₁ → Set d}
{B : (x : A₁) → A₂ x → Set b}
{C : {x : A₁} → {y : A₂ x} → B x y → Set c} →
({x : A₁} → {y : A₂ x} → (z : B x y) → C z) →
(g : (x : A₁) → (y : A₂ x) → B x y) →
((x : A₁) → (y : A₂ x) → C (g x y))
f ∘₂ g = λ x y → f (g x y)
flip : ∀ {A : Set a} {B : Set b} {C : A → B → Set c} →
((x : A) (y : B) → C x y) → ((y : B) (x : A) → C x y)
flip f = λ y x → f x y
{-# INLINE flip #-}
_$_ : ∀ {A : Set a} {B : A → Set b} →
((x : A) → B x) → ((x : A) → B x)
f $ x = f x
{-# INLINE _$_ #-}
_$!_ : ∀ {A : Set a} {B : A → Set b} →
((x : A) → B x) → ((x : A) → B x)
_$!_ = flip force
_|>_ : ∀ {A : Set a} {B : A → Set b} →
(a : A) → (∀ a → B a) → B a
_|>_ = flip _$_
{-# INLINE _|>_ #-}
_ˢ_ : ∀ {A : Set a} {B : A → Set b} {C : (x : A) → B x → Set c} →
((x : A) (y : B x) → C x y) →
(g : (x : A) → B x) →
((x : A) → C x (g x))
f ˢ g = λ x → f x (g x)
{-# INLINE _ˢ_ #-}
_$- : ∀ {A : Set a} {B : A → Set b} → ((x : A) → B x) → ({x : A} → B x)
f $- = f _
{-# INLINE _$- #-}
λ- : ∀ {A : Set a} {B : A → Set b} → ({x : A} → B x) → ((x : A) → B x)
λ- f = λ x → f
{-# INLINE λ- #-}
case_return_of_ : ∀ {A : Set a} (x : A) (B : A → Set b) →
((x : A) → B x) → B x
case x return B of f = f x
{-# INLINE case_return_of_ #-}
infixr 9 _∘′_ _∘₂′_
infixl 0 _|>′_
infix 0 case_of_
infixr -1 _$′_ _$!′_
_∘′_ : (B → C) → (A → B) → (A → C)
f ∘′ g = _∘_ f g
_∘₂′_ : (C → D) → (A → B → C) → (A → B → D)
f ∘₂′ g = _∘₂_ f g
_$′_ : (A → B) → (A → B)
_$′_ = _$_
_$!′_ : (A → B) → (A → B)
_$!′_ = _$!_
_|>′_ : A → (A → B) → B
_|>′_ = _|>_
case_of_ : A → (A → B) → B
case x of f = case x return _ of f
{-# INLINE case_of_ #-}
infixl 1 _⟨_⟩_
infixl 0 _∋_
_⟨_⟩_ : A → (A → B → C) → B → C
x ⟨ f ⟩ y = f x y
_∋_ : (A : Set a) → A → A
A ∋ x = x
typeOf : {A : Set a} → A → Set a
typeOf {A = A} _ = A
it : {A : Set a} → {{A}} → A
it {{x}} = x
infixr 0 _-⟪_⟫-_ _-⟨_⟫-_
infixl 0 _-⟪_⟩-_
infixr 1 _-⟨_⟩-_ ∣_⟫-_ ∣_⟩-_
infixl 1 _on_ _on₂_ _-⟪_∣ _-⟨_∣
_-⟪_⟫-_ : (A → B → C) → (C → D → E) → (A → B → D) → (A → B → E)
f -⟪ _*_ ⟫- g = λ x y → f x y * g x y
_-⟪_∣ : (A → B → C) → (C → B → D) → (A → B → D)
f -⟪ _*_ ∣ = f -⟪ _*_ ⟫- constᵣ
∣_⟫-_ : (A → C → D) → (A → B → C) → (A → B → D)
∣ _*_ ⟫- g = const -⟪ _*_ ⟫- g
_-⟨_∣ : (A → C) → (C → B → D) → (A → B → D)
f -⟨ _*_ ∣ = f ∘₂ const -⟪ _*_ ∣
∣_⟩-_ : (A → C → D) → (B → C) → (A → B → D)
∣ _*_ ⟩- g = ∣ _*_ ⟫- g ∘₂ constᵣ
_-⟪_⟩-_ : (A → B → C) → (C → D → E) → (B → D) → (A → B → E)
f -⟪ _*_ ⟩- g = f -⟪ _*_ ⟫- ∣ constᵣ ⟩- g
_-⟨_⟫-_ : (A → C) → (C → D → E) → (A → B → D) → (A → B → E)
f -⟨ _*_ ⟫- g = f -⟨ const ∣ -⟪ _*_ ⟫- g
_-⟨_⟩-_ : (A → C) → (C → D → E) → (B → D) → (A → B → E)
f -⟨ _*_ ⟩- g = f -⟨ const ∣ -⟪ _*_ ⟫- ∣ constᵣ ⟩- g
_on₂_ : (C → C → D) → (A → B → C) → (A → B → D)
_*_ on₂ f = f -⟪ _*_ ⟫- f
_on_ : (B → B → C) → (A → B) → (A → A → C)
_*_ on f = f -⟨ _*_ ⟩- f
_-[_]-_ = _-⟪_⟫-_
{-# WARNING_ON_USAGE _-[_]-_
"Warning: Function._-[_]-_ was deprecated in v1.4.
Please use _-⟪_⟫-_ instead."
#-}