statement stringlengths 5 1.82k | proof stringlengths 0 5.57k | type stringclasses 4
values | symbolic_name stringlengths 1 58 | library stringclasses 164
values | filename stringclasses 562
values | imports listlengths 0 99 | deps listlengths 0 64 | docstring stringclasses 1
value | source_url stringclasses 1
value | commit stringclasses 1
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|---|---|---|---|---|---|---|---|---|---|---|
_◁_ : ∀ {ℓ} {A : I → Type ℓ} {a₀ a₀' : A i0} {a₁ : A i1}
→ a₀ ≡ a₀' → PathP A a₀' a₁ → PathP A a₀ a₁ | function | _◁_ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | ||
_▷_ : ∀ {ℓ} {A : I → Type ℓ} {a₀ : A i0} {a₁ a₁' : A i1}
→ PathP A a₀ a₁ → a₁ ≡ a₁' → PathP A a₀ a₁' | function | _▷_ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | ||
◁◁-▷▷-filler
: ∀ {ℓ} {A : I → Type ℓ} {a₀ a₀' : A i0} {a₁ a₁' : A i1}
→ (p : a₀ ≡ a₀') (q : PathP A a₀' a₁) (r : a₁ ≡ a₁')
→ SquareP (λ i j → A j) (sym p) q (p ◁◁ q ▷▷ r) r | ◁◁-▷▷-filler p q r j i = hfill (∂ i) j (_◁◁_▷▷_.sys p q r i) | function | ◁◁-▷▷-filler | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"SquareP",
"hfill",
"sym"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
∙-filler' : ∀ {ℓ} {A : Type ℓ} {x y z : A}
→ (p : x ≡ y) (q : y ≡ z)
→ Square (sym p) q (p ∙ q) refl | ∙-filler' {x = x} {y} {z} p q j i =
hcomp (∂ i ∨ ~ j) λ where
k (i = i0) → p (~ j)
k (i = i1) → q k
k (j = i0) → q (i ∧ k)
k (k = i0) → p (i ∨ ~ j) | function | ∙-filler' | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Square",
"hcomp",
"refl",
"sym"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
_∙₂_ : ∀ {ℓ} {A : Type ℓ} {a00 a01 a02 a10 a11 a12 : A}
{p : a00 ≡ a01} {p' : a01 ≡ a02}
{q : a00 ≡ a10} {s : a01 ≡ a11} {t : a02 ≡ a12}
{r : a10 ≡ a11} {r' : a11 ≡ a12}
→ Square p q s r
→ Square p' s t r'
→ Square (p ∙ p') q t (r ∙ r') | function | _∙₂_ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Square",
"r'"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | ||
_∙'_ : {x y z : A} (p : x ≡ y) (q : y ≡ z) → x ≡ z | _∙'_ {x = x} p q = transport (λ i → x ≡ q i) p | function | _∙'_ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"transport"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
∙∙-unique
: ∀ {ℓ} {A : Type ℓ} {w x y z : A}
→ (p : w ≡ x) (q : x ≡ y) (r : y ≡ z)
→ (α β : Σ[ s ∈ (w ≡ z) ] Square (sym p) q s r)
→ α ≡ β | ∙∙-unique {w = w} {x} {y} {z} p q r (α , α-fill) (β , β-fill) =
λ i → (λ j → square i j) , (λ j k → cube i j k)
where
cube : (i j : I) → p (~ j) ≡ r j
cube i j k = hfill (∂ i ∨ ∂ k) j λ where
l (i = i0) → α-fill l k
l (i = i1) → β-fill l k
l (k = i0) → p (~ l)
l (k = i1) → r l
... | function | ∙∙-unique | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Square",
"hfill",
"sym"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
∙∙-contract : ∀ {ℓ} {A : Type ℓ} {w x y z : A}
→ (p : w ≡ x) (q : x ≡ y) (r : y ≡ z)
→ (β : Σ[ s ∈ (w ≡ z) ] Square (sym p) q s r)
→ (p ∙∙ q ∙∙ r , ∙∙-filler p q r) ≡ β | ∙∙-contract p q r β = ∙∙-unique p q r _ β | function | ∙∙-contract | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Square",
"sym",
"∙∙-filler",
"∙∙-unique"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
∙-unique
: ∀ {ℓ} {A : Type ℓ} {x y z : A} {p : x ≡ y} {q : y ≡ z}
→ (r : x ≡ z)
→ Triangle p r q
→ r ≡ p ∙ q | ∙-unique {p = p} {q} r square i =
∙∙-unique refl p q (_ , square) (_ , (∙-filler p q)) i .fst | function | ∙-unique | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Triangle",
"refl",
"∙-filler",
"∙∙-unique"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
∙∙-unique' : ∀ {ℓ} {A : Type ℓ} {w x y z : A}
→ {p : w ≡ x} {q : x ≡ y} {r : y ≡ z} {s : w ≡ z}
→ (β : Square (sym p) q s r)
→ s ≡ p ∙∙ q ∙∙ r | ∙∙-unique' β i = ∙∙-contract _ _ _ (_ , β) (~ i) .fst | function | ∙∙-unique' | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Square",
"sym",
"∙∙-contract"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
ap-square
: ∀ {ℓ ℓ'} {A : Type ℓ} {B : A → Type ℓ'} {a00 a01 a10 a11 : A}
{p : a00 ≡ a01} {q : a00 ≡ a10} {s : a01 ≡ a11} {r : a10 ≡ a11}
→ (f : (a : A) → B a)
→ (α : Square p q s r)
→ SquareP (λ i j → B (α i j)) (ap f p) (ap f q) (ap f s) (ap f r) | ap-square f α i j = f (α i j) | function | ap-square | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Square",
"SquareP",
"ap"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
ap-∙∙ : (f : A → B) {x y z w : A} (p : x ≡ y) (q : y ≡ z) (r : z ≡ w)
→ ap f (p ∙∙ q ∙∙ r) ≡ ap f p ∙∙ ap f q ∙∙ ap f r | ap-∙∙ f p q r = ∙∙-unique' (ap-square f (∙∙-filler p q r)) | function | ap-∙∙ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"ap",
"ap-square",
"∙∙-filler",
"∙∙-unique'"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
ap-∙ : (f : A → B) {x y z : A} (p : x ≡ y) (q : y ≡ z)
→ ap f (p ∙ q) ≡ ap f p ∙ ap f q | ap-∙ f p q = ap-∙∙ f refl p q | function | ap-∙ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"ap",
"ap-∙∙",
"refl"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
ap₂-∙∙
: ∀ {ℓ ℓ' ℓ''} {A : Type ℓ} {B : Type ℓ'} {C : Type ℓ''}
→ (f : A → B → C)
→ {a b c d : A} (α : a ≡ b) (β : b ≡ c) (γ : c ≡ d)
→ {w x y z : B} (ξ : w ≡ x) (ψ : x ≡ y) (ω : y ≡ z)
→ ap₂ f (α ∙∙ β ∙∙ γ) (ξ ∙∙ ψ ∙∙ ω) ≡ ap₂ f α ξ ∙∙ ap₂ f β ψ ∙∙ ap₂ f γ ω | ap₂-∙∙ f α β γ ξ ψ ω = ∙∙-unique' λ i j → f (∙∙-filler α β γ i j) (∙∙-filler ξ ψ ω i j) | function | ap₂-∙∙ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"ap₂",
"∙∙-filler",
"∙∙-unique'"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
ap₂-∙
: ∀ {ℓ ℓ' ℓ''} {A : Type ℓ} {B : Type ℓ'} {C : Type ℓ''}
→ (f : A → B → C)
→ {a b c : A} (α : a ≡ b) (β : b ≡ c)
→ {w x y : B} (ξ : w ≡ x) (ψ : x ≡ y)
→ ap₂ f (α ∙ β) (ξ ∙ ψ) ≡ ap₂ f α ξ ∙ ap₂ f β ψ | ap₂-∙ f α β ξ ψ = ap₂-∙∙ f refl α β refl ξ ψ | function | ap₂-∙ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"ap₂",
"ap₂-∙∙",
"refl"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
PathP≡Path : ∀ {ℓ} (P : I → Type ℓ) (p : P i0) (q : P i1)
→ PathP P p q ≡ Path (P i1) (transport (λ i → P i) p) q | PathP≡Path P p q i = PathP (λ j → P (i ∨ j)) (transport-filler (λ j → P j) p i) q | function | PathP≡Path | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Path",
"transport",
"transport-filler"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
PathP≡Path⁻ : ∀ {ℓ} (P : I → Type ℓ) (p : P i0) (q : P i1)
→ PathP P p q ≡ Path (P i0) p (transport (λ i → P (~ i)) q) | PathP≡Path⁻ P p q i = PathP (λ j → P (~ i ∧ j)) p (transport-filler (λ j → P (~ j)) q i) | function | PathP≡Path⁻ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Path",
"transport",
"transport-filler"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
coe0→1 : ∀ {ℓ} (A : I → Type ℓ) → A i0 → A i1 | coe0→1 A a = transp (λ i → A i) i0 a | function | coe0→1 | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
coe1→0 : ∀ {ℓ} (A : I → Type ℓ) → A i1 → A i0 | coe1→0 A a = transp (λ i → A (~ i)) i0 a | function | coe1→0 | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
coe0→i : ∀ {ℓ : I → Level} (A : ∀ i → Type (ℓ i)) (i : I) → A i0 → A i | coe0→i A i a = transp (λ j → A (i ∧ j)) (~ i) a | function | coe0→i | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Level"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
coe1→i : ∀ {ℓ : I → Level} (A : ∀ i → Type (ℓ i)) (i : I) → A i1 → A i | coe1→i A i a = transp (λ j → A (i ∨ ~ j)) i a | function | coe1→i | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Level"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
coei→0 : ∀ {ℓ : I → Level} (A : ∀ i → Type (ℓ i)) (i : I) → A i → A i0 | coei→0 A i a = transp (λ j → A (i ∧ ~ j)) (~ i) a | function | coei→0 | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Level"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
coei→1 : ∀ {ℓ : I → Level} (A : ∀ i → Type (ℓ i)) (i : I) → A i → A i1 | coei→1 A i a = transp (λ l → A (i ∨ l)) i a | function | coei→1 | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Level"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
to-from-pathp
: ∀ {ℓ} {A : I → Type ℓ} {x y} (p : PathP A x y) → to-pathp (from-pathp p) ≡ p | to-from-pathp {A = A} {x} {y} p i j = hcomp-unique (∂ j)
(λ { k (k = i0) → coe0→i A j x
; k (j = i0) → x
; k (j = i1) → coei→1 A k (p k)
})
(λ k → inS (transp (λ l → A (j ∧ (k ∨ l))) (~ j ∨ k) (p (j ∧ k))))
i | function | to-from-pathp | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"coe0→i",
"coei→1",
"hcomp-unique"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
from-to-pathp
: ∀ {ℓ} {A : I → Type ℓ} {x y} (p : coe0→1 A x ≡ y)
→ from-pathp {A = A} (to-pathp p) ≡ p | from-to-pathp {A = A} {x} {y} p i j =
hcomp (∂ i ∨ ∂ j) λ where
k (k = i0) →
coei→1 A (j ∨ ~ i) $
transp (λ l → A (j ∨ (~ i ∧ l))) (i ∨ j) $
coe0→i A j x
k (j = i0) → slide (k ∨ ~ i)
k (j = i1) → p k
k (i = i0) → coei→1 A j $ hfill (∂ j) k λ where
k (k = i0) → coe0→i A ... | function | from-to-pathp | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"coe0→1",
"coe0→i",
"coei→1",
"hcomp",
"hfill"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
hcomp-unique : ∀ {ℓ} {A : Type ℓ} φ
(u : ∀ i → Partial (φ ∨ ~ i) A)
→ (h2 : ∀ i → A [ _ ↦ (λ { (i = i0) → u i0 1=1
; (φ = i1) → u i 1=1 }) ])
→ hcomp φ u ≡ outS (h2 i1) | hcomp-unique φ u h2 i =
hcomp (φ ∨ i) λ where
k (k = i0) → u i0 1=1
k (i = i1) → outS (h2 k)
k (φ = i1) → u k 1=1 | function | hcomp-unique | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"hcomp"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
hlid-unique : ∀ {ℓ} {A : Type ℓ} φ
(u : ∀ i → Partial (φ ∨ ~ i) A)
→ (h1 h2 : ∀ i → A [ _ ↦ (λ { (i = i0) → u i0 1=1
; (φ = i1) → u i 1=1 }) ])
→ outS (h1 i1) ≡ outS (h2 i1) | hlid-unique φ u h1 h2 i =
hcomp (φ ∨ ∂ i) λ where
k (k = i0) → u i0 1=1
k (i = i0) → outS (h1 k)
k (i = i1) → outS (h2 k)
k (φ = i1) → u k 1=1 | function | hlid-unique | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"hcomp"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
≡⟨⟩-syntax : ∀ {ℓ} {A : Type ℓ} (x : A) {y z} → y ≡ z → x ≡ y → x ≡ z | ≡⟨⟩-syntax x q p = p ∙ q | function | ≡⟨⟩-syntax | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
≡⟨⟩≡⟨⟩-syntax
: ∀ {ℓ} {A : Type ℓ} (w x : A) {y z}
→ (p : w ≡ x)
→ (q : x ≡ y)
→ (r : y ≡ z)
→ w ≡ z | ≡⟨⟩≡⟨⟩-syntax w x p q r = p ∙∙ q ∙∙ r | function | ≡⟨⟩≡⟨⟩-syntax | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
_≡˘⟨_⟩_ : ∀ {ℓ} {A : Type ℓ} (x : A) {y z : A} → y ≡ x → y ≡ z → x ≡ z | function | _≡˘⟨_⟩_ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | ||
_≡⟨⟩_ : ∀ {ℓ} {A : Type ℓ} (x : A) {y : A} → x ≡ y → x ≡ y | function | _≡⟨⟩_ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | ||
_∎ : ∀ {ℓ} {A : Type ℓ} (x : A) → x ≡ x | function | _∎ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | ||
along : ∀ {ℓ} {A : I → Type ℓ} {x : A i0} {y : A i1} → (i : I) → PathP A x y → A i | along i p = p i | function | along | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
+-associative : (x y z : Nat) → x + (y + z) ≡ (x + y) + z | +-associative zero y z = refl
+-associative (suc x) y z =
suc (x + (y + z)) ≡⟨ ap suc (+-associative x y z) ⟩
suc ((x + y) + z) ∎ | function | +-associative | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Nat",
"ap",
"refl",
"suc",
"zero"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
Σ-pathp
: ∀ {ℓ ℓ'} {A : I → Type ℓ} {B : ∀ i → A i → Type ℓ'}
→ {x : Σ _ (B i0)} {y : Σ _ (B i1)}
→ (p : PathP A (x .fst) (y .fst))
→ PathP (λ i → B i (p i)) (x .snd) (y .snd)
→ PathP (λ i → Σ (A i) (B i)) x y | Σ-pathp p q i = p i , q i | function | Σ-pathp | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
Σ-path : ∀ {a b} {A : Type a} {B : A → Type b}
→ {x y : Σ A B}
→ (p : x .fst ≡ y .fst)
→ subst B p (x .snd) ≡ (y .snd)
→ x ≡ y | Σ-path {A = A} {B} {x} {y} p q = Σ-pathp p (to-pathp q) | function | Σ-path | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"subst",
"Σ-pathp"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
happly : ∀ {a b} {A : Type a} {B : A → Type b}
{f g : (x : A) → B x}
→ f ≡ g → (x : A) → f x ≡ g x | happly p x i = p i x | function | happly | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
funext : ∀ {a b} {A : Type a} {B : A → Type b}
{f g : (x : A) → B x}
→ ((x : A) → f x ≡ g x) → f ≡ g | funext p i x = p x i | function | funext | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
homotopy-natural : ∀ {a b} {A : Type a} {B : Type b}
→ {f g : A → B}
→ (H : (x : A) → f x ≡ g x)
→ {x y : A} (p : x ≡ y)
→ H x ∙ ap g p ≡ ap f p ∙ H y | homotopy-natural {f = f} {g = g} H {x} {y} p = ∙-unique _ λ i j →
hcomp (~ i ∨ ∂ j) λ where
k (k = i0) → H x (j ∧ i)
k (i = i0) → f (p (j ∧ k))
k (j = i0) → f x
k (j = i1) → H (p k) i | function | homotopy-natural | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"ap",
"hcomp",
"∙-unique"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
double-composite
: ∀ {ℓ} {A : Type ℓ}
→ {x y z w : A}
→ (p : x ≡ y) (q : y ≡ z) (r : z ≡ w)
→ p ∙∙ q ∙∙ r ≡ p ∙ q ∙ r | double-composite p q r i j =
hcomp (i ∨ ∂ j) λ where
k (i = i1) → ∙-filler' p (q ∙ r) k j
k (j = i0) → p (~ k)
k (j = i1) → r (i ∨ k)
k (k = i0) → ∙-filler q r i j | function | double-composite | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"hcomp",
"∙-filler",
"∙-filler'"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
transport-path : ∀ {ℓ} {A : Type ℓ} {x y x' y' : A}
→ (p : x ≡ y)
→ (left : x ≡ x') → (right : y ≡ y')
→ transport (λ i → left i ≡ right i) p ≡ sym left ∙ p ∙ right | transport-path {A = A} {x} {y} {x'} {y'} p left right =
lemma ∙ double-composite _ _ _ | function | transport-path | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"double-composite",
"sym",
"transport"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
subst-path-left : ∀ {ℓ} {A : Type ℓ} {x y x' : A}
→ (p : x ≡ y)
→ (left : x ≡ x')
→ subst (λ e → e ≡ y) left p ≡ sym left ∙ p | subst-path-left {y = y} p left =
subst (λ e → e ≡ y) left p ≡⟨⟩
transport (λ i → left i ≡ y) p ≡⟨ transport-path p left refl ⟩
sym left ∙ p ∙ refl ≡⟨ ap (sym left ∙_) (sym (∙-filler _ _)) ⟩
sym left ∙ p ∎ | function | subst-path-left | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"ap",
"refl",
"subst",
"sym",
"transport",
"transport-path",
"∙-filler"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
subst-path-right : ∀ {ℓ} {A : Type ℓ} {x y y' : A}
→ (p : x ≡ y)
→ (right : y ≡ y')
→ subst (λ e → x ≡ e) right p ≡ p ∙ right | subst-path-right {x = x} p right =
subst (λ e → x ≡ e) right p ≡⟨⟩
transport (λ i → x ≡ right i) p ≡⟨ transport-path p refl right ⟩
sym refl ∙ p ∙ right ≡⟨⟩
refl ∙ p ∙ right ≡⟨ sym (∙-filler' _ _) ⟩
p ∙ right ∎ | function | subst-path-right | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"refl",
"subst",
"sym",
"transport",
"transport-path",
"∙-filler'"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
subst-path-both : ∀ {ℓ} {A : Type ℓ} {x x' : A}
→ (p : x ≡ x)
→ (adj : x ≡ x')
→ subst (λ x → x ≡ x) adj p ≡ sym adj ∙ p ∙ adj | subst-path-both p adj = transport-path p adj adj | function | subst-path-both | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"subst",
"sym",
"transport-path"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
Square≡double-composite-path : ∀ {ℓ} {A : Type ℓ}
→ {w x y z : A}
→ {p : x ≡ w} {q : x ≡ y} {s : w ≡ z} {r : y ≡ z}
→ Square p q s r ≡ (sym p ∙∙ q ∙∙ r ≡ s) | Square≡double-composite-path {p = p} {q} {s} {r} k =
PathP (λ i → p (i ∨ k) ≡ r (i ∨ k))
(∙∙-filler (sym p) q r k) s | function | Square≡double-composite-path | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Square",
"sym",
"∙∙-filler"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
J' : ∀ {ℓ₁ ℓ₂} {A : Type ℓ₁}
(P : (x y : A) → x ≡ y → Type ℓ₂)
→ (∀ x → P x x refl)
→ {x y : A} (p : x ≡ y)
→ P x y p | J' P prefl {x} p = transport (λ i → P x (p i) λ j → p (i ∧ j)) (prefl x) | function | J' | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"refl",
"transport"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
J₂
: ∀ {ℓa ℓb ℓp} {A : Type ℓa} {B : Type ℓb} {xa : A} {xb : B}
→ (P : ∀ ya yb → xa ≡ ya → xb ≡ yb → Type ℓp)
→ P xa xb refl refl
→ ∀ {ya yb} p q → P ya yb p q | J₂ P prr p q = transport (λ i → P (p i) (q i) (λ j → p (i ∧ j)) (λ j → q (i ∧ j))) prr | function | J₂ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"refl",
"transport"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
invert-sides : ∀ {ℓ} {A : Type ℓ} {x y z : A} (p : x ≡ y) (q : x ≡ z)
→ Square q p (sym q) (sym p) | invert-sides {x = x} p q i j = hcomp (∂ i ∨ ∂ j) λ where
k (i = i0) → p (k ∧ j)
k (i = i1) → q (~ j ∧ k)
k (j = i0) → q (i ∧ k)
k (j = i1) → p (~ i ∧ k)
k (k = i0) → x | function | invert-sides | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"Square",
"hcomp",
"sym"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
sym-∙-filler : ∀ {ℓ} {A : Type ℓ} {x y z : A} (p : x ≡ y) (q : y ≡ z) → I → I → I → A | sym-∙-filler {A = A} {z = z} p q i j k =
hfill (∂ i) k λ where
l (i = i0) → q (l ∨ j)
l (i = i1) → p (~ l ∧ j)
l (l = i0) → invert-sides q (sym p) i j | function | sym-∙-filler | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"hfill",
"invert-sides",
"sym"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
sym-∙ : ∀ {ℓ} {A : Type ℓ} {x y z : A} (p : x ≡ y) (q : y ≡ z) → sym (p ∙ q) ≡ sym q ∙ sym p | sym-∙ p q i j = sym-∙-filler p q j i i1 | function | sym-∙ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"sym",
"sym-∙-filler"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
_$ₚ_ : ∀ {ℓ₁ ℓ₂} {A : Type ℓ₁} {B : A → Type ℓ₂} {f g : ∀ x → B x}
→ f ≡ g → ∀ x → f x ≡ g x | function | _$ₚ_ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | ||
_≠_ : ∀ {ℓ} {A : Type ℓ} → A → A → Type ℓ | function | _≠_ | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | ||
(p ∙∙ q ∙∙ r) i = hcomp (∂ i) sys module ∙∙-sys where
sys : ∀ j → Partial (∂ i ∨ ~ j) _
sys j (i = i0) = p (~ j)
sys j (i = i1) = r j
sys j (j = i0) = q i | p ∙ q = refl ∙∙ p ∙∙ q
(p ◁◁ q ▷▷ r) i = hcomp (∂ i) sys module _◁◁_▷▷_ where
sys : ∀ j → Partial (∂ i ∨ ~ j) _
sys j (i = i0) = p (~ j)
sys j (i = i1) = r j
sys j (j = i0) = q i
p ◁ q = p ◁◁ q ▷▷ refl
p ▷ q = refl ◁◁ p ▷▷ q | function | p | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"_◁◁_▷▷_",
"hcomp",
"refl"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
(α ∙₂ β) i j = ((λ i → α i j) ∙ (λ i → β i j)) i | function | α | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | ||
x ≡˘⟨ p ⟩ q = (sym p) ∙ q | x ≡⟨⟩ x≡y = x≡y
x ∎ = refl
x ≠ y = ¬ x ≡ y | function | x | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [
"refl",
"sym"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
(f $ₚ x) i = f i x
{-# INLINE _$ₚ_ #-} | function | f | 1Lab | src/1Lab/Path.lagda.md | [
"1Lab.Type",
"Prim.Data.Bool",
"Prim.Extension",
"Prim.Interval",
"Prim.Kan"
] | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | ||
Map-TC : Map (eff TC) | Map-TC .Map.map f x = P.bindTC x λ x → P.returnTC (f x) | function | Map-TC | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Map"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
Idiom-TC : Idiom (eff TC) | Idiom-TC .Idiom.pure = P.returnTC
Idiom-TC .Idiom._<*>_ f g = P.bindTC f λ f → P.bindTC g λ g → pure (f g) | function | Idiom-TC | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Idiom"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
Bind-TC : Bind (eff TC) | Bind-TC .Bind._>>=_ = P.bindTC | function | Bind-TC | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Bind"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
Alt-TC : Alt (eff TC) | Alt-TC .Alt.fail = P.typeError mempty
Alt-TC .Alt._<|>_ = P.catchTC | function | Alt-TC | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Alt"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
Args : Type | Args = List (Arg Term) | function | Args | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Arg",
"List",
"Term"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
Fun : ∀ {ℓ ℓ'} → Type ℓ → Type ℓ' → Type (ℓ ⊔ ℓ') | Fun A B = A → B | function | Fun | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
idfun : ∀ {ℓ} (A : Type ℓ) → A → A | idfun A x = x | function | idfun | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
under-abs : ∀ {ℓ} {A : Type ℓ} → Term → TC A → TC A | under-abs (lam v (abs nm _)) m = extend-context nm (arg (arginfo v (modality relevant quantity-ω)) unknown) m
under-abs (pi a (abs nm _)) m = extend-context nm a m
under-abs _ m = m | function | under-abs | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Term",
"abs",
"pi"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
extend-context* : ∀ {a} {A : Type a} → Telescope → TC A → TC A | extend-context* [] a = a
extend-context* ((nm , tm) ∷ xs) a = extend-context nm tm (extend-context* xs a) | function | extend-context* | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Telescope",
"[]",
"xs"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
new-meta : Term → TC Term | new-meta ty = do
mv ← check-type unknown ty
debugPrint "tactic.meta" 70
[ "Created new meta " , termErr mv , " of type " , termErr ty ]
pure mv | function | new-meta | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Term"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
new-meta' : Term → TC (Meta × Term) | new-meta' ty = do
tm@(meta mv _) ← check-type unknown ty
where _ → typeError "impossible new-meta'"
debugPrint "tactic.meta" 70
[ "Created new meta " , termErr tm , " of type " , termErr tm ]
pure (mv , tm) | function | new-meta' | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Term"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
block-on-meta : ∀ {a} {A : Type a} → Meta → TC A | block-on-meta m = blockTC (blocker-meta m) | function | block-on-meta | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
vlam : String → Term → Term | vlam nam body = lam visible (abs nam body) | function | vlam | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Term",
"abs"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
infer-hidden : Nat → Args → Args | infer-hidden zero xs = xs
infer-hidden (suc n) xs = unknown h∷ infer-hidden n xs | function | infer-hidden | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Args",
"Nat",
"suc",
"xs",
"zero"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
infer-tel : Telescope → Args | infer-tel tel = (λ (_ , arg ai _) → arg ai unknown) <$> tel | function | infer-tel | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Args",
"Telescope"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
“refl” : Term | “refl” = def (quote refl) []
-- Run a TC computation and reset the state after. If the returned value
-- makes references to metas generated in the reset computation, you'll
-- probably get __IMPOSSIBLE__s! | function | “refl” | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Term",
"[]",
"refl"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
resetting : ∀ {ℓ} {A : Type ℓ} → TC A → TC A | resetting k = run-speculative ((_, false) <$> k) | function | resetting | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
unifies? : Term → Term → TC Bool | unifies? `x `y = run-speculative ((unify `x `y >> pure (true , true)) <|> pure (false , false)) | function | unifies? | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Bool",
"Term"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
checks? : Term → Term → TC (Maybe Term) | checks? tm tp = run-speculative (check-type tm tp <&> (λ tm → (just tm , true)) <|> pure (nothing , false)) | function | checks? | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Maybe",
"Term"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
all-metas-in : Term → List Blocker | all-metas-in tm = go tm [] where
go : Term → List Blocker → List Blocker
go* : List (Arg Term) → List Blocker → List Blocker
go (var _ args) acc = go* args acc
go (con _ args) acc = go* args acc
go (def _ args) acc = go* args acc
go (lam _ (abs _ t)) acc = go t a... | function | all-metas-in | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Arg",
"Blocker",
"List",
"Term",
"[]",
"abs",
"go",
"go*",
"pi",
"xs"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
wait-for-type : Term → TC Term | function | wait-for-type | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Term"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | ||
wait-just-a-bit : Term → TC Term | wait-just-a-bit (meta m _) = block-on-meta m
wait-just-a-bit tm = pure tm | function | wait-just-a-bit | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Term",
"block-on-meta"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
blocking-meta : Term → Maybe Blocker | blocking-meta (var x as) = nothing
blocking-meta (con c as) = nothing
blocking-meta (def f as) = blocking-meta* as
blocking-meta (lam v t) = nothing
blocking-meta (pat-lam _ as) = blocking-meta* as
blocking-meta (pi a (abs _ b)) = blocking-meta b
blocking-meta (agda-sort s) = nothing
block... | function | blocking-meta | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Blocker",
"Maybe",
"Term",
"abs",
"blocking-meta*",
"pi"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
blocking-meta* : List (Arg Term) → Maybe Blocker | blocking-meta* (arg (arginfo visible _) tm ∷ _) = blocking-meta tm
blocking-meta* (arg (arginfo instance' _) tm ∷ _) = blocking-meta tm
blocking-meta* (arg (arginfo hidden _) tm ∷ as) = blocking-meta* as
blocking-meta* [] = nothing | function | blocking-meta* | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Arg",
"Blocker",
"List",
"Maybe",
"Term",
"[]",
"blocking-meta"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
reduceB : Term → TC Term | reduceB tm = do
tm' ← reduce tm
case blocking-meta tm' of λ where
(just b) → blockTC b
nothing → pure tm'
-- The first argument decides whether we want a PathP. | function | reduceB | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Term",
"blocking-meta",
"case"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
unapply-path' : Bool → Term → TC (Maybe (Term × Term × Term)) | unapply-path' true red@(def (quote PathP) (l h∷ T v∷ x v∷ y v∷ [])) = do
pure (just (T , x , y))
unapply-path' false red@(def (quote PathP) (l h∷ T v∷ x v∷ y v∷ [])) = do
domain ← new-meta (def (quote Type) (l v∷ []))
ty ← pure (def (quote Path) (domain v∷ x v∷ y v∷ []))
debugPrint "tactic" 50
[ "(no reduct... | function | unapply-path' | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Bool",
"Maybe",
"Path",
"Term",
"[]",
"abs",
"argN",
"domain",
"new-meta",
"new-meta'",
"pi",
"wait-for-type"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
unapply-path unapply-pathp : Term → TC (Maybe (Term × Term × Term)) | unapply-path = unapply-path' false | function | unapply-path | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Maybe",
"Term",
"unapply-path'",
"unapply-pathp"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
get-boundary : Term → TC (Maybe (Term × Term)) | get-boundary tm = unapply-path tm >>= λ where
(just (_ , x , y)) → pure (just (x , y))
nothing → pure nothing | function | get-boundary | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Maybe",
"Term",
"unapply-path"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
Has-visibility-Telescope : Has-visibility Telescope | Has-visibility-Telescope .set-visibility v tel = ×-map₂ (set-visibility v) <$> tel | function | Has-visibility-Telescope | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Has-visibility",
"Telescope",
"×-map₂"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
debug! : ∀ {ℓ} {A : Type ℓ} → Term → TC A | debug! tm = typeError ("[DEBUG]: " ∷ termErr tm ∷ []) | function | debug! | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Term",
"[]"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
quote-repr-macro : ∀ {ℓ} {A : Type ℓ} → A → Term → TC ⊤ | quote-repr-macro a hole = do
tm ← quoteTC a
repr ← quoteTC tm
typeError $ "The term\n "
∷ termErr tm
∷ "\nHas quoted representation\n "
∷ termErr repr ∷ [] | function | quote-repr-macro | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Term",
"[]"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
quote-repr! : ∀ {ℓ ℓ'} {A : Type ℓ} {B : Type ℓ'} → A → Term → TC ⊤ | quote-repr! a = quote-repr-macro a | function | quote-repr! | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Term",
"quote-repr-macro"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
unify-loudly : Term → Term → TC ⊤ | unify-loudly a b = do
debugPrint "tactic" 50 $ termErr a ∷ " =? " ∷ termErr b ∷ []
unify a b | function | unify-loudly | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"Term",
"[]"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
... | [] = pure tm | ... | it = blockTC (blocker-all it) | function | ... | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"[]",
"it"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
unapply-pathp = unapply-path' true | function | unapply-pathp | 1Lab | src/1Lab/Reflection.lagda.md | [
"1Lab.Type.Sigma",
"1Lab.Path",
"1Lab.Type",
"Data.Product.NAry",
"Data.String.Show",
"Data.Bool.Base",
"Data.List.Base",
"Data.Dec.Base",
"Data.Vec.Base",
"Meta.Append",
"Data.String.Base",
"Meta.Traversable",
"Data.Float.Base",
"Data.Maybe.Base",
"Data.Word.Base",
"Meta.Idiom",
"Me... | [
"unapply-path'"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | ||
Ω : Type where
constructor el
field
∣_∣ : Type
is-tr : is-prop ∣_∣ | record | Ω | 1Lab | src/1Lab/Resizing.lagda.md | [
"1Lab.Function.Surjection",
"1Lab.Path.IdentitySystem",
"1Lab.Reflection.HLevel",
"1Lab.HLevel.Universe",
"1Lab.Extensionality",
"1Lab.HLevel.Closure",
"1Lab.Reflection",
"1Lab.Truncation",
"1Lab.Univalence",
"1Lab.Inductive",
"1Lab.HLevel",
"1Lab.Equiv",
"1Lab.Path",
"1Lab.Type",
"Data.... | [
"is-prop"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | ||
□ {ℓ} (A : Type ℓ) : Type where
inc : A → □ A
squash : (x y : □ A) → x ≡ y | data | □ | 1Lab | src/1Lab/Resizing.lagda.md | [
"1Lab.Function.Surjection",
"1Lab.Path.IdentitySystem",
"1Lab.Reflection.HLevel",
"1Lab.HLevel.Universe",
"1Lab.Extensionality",
"1Lab.HLevel.Closure",
"1Lab.Reflection",
"1Lab.Truncation",
"1Lab.Univalence",
"1Lab.Inductive",
"1Lab.HLevel",
"1Lab.Equiv",
"1Lab.Path",
"1Lab.Type",
"Data.... | [
"inc",
"squash"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | ||
H-Level-□ : ∀ {ℓ} {T : Type ℓ} {n} → H-Level (□ T) (suc n) | H-Level-□ = prop-instance squash | function | H-Level-□ | 1Lab | src/1Lab/Resizing.lagda.md | [
"1Lab.Function.Surjection",
"1Lab.Path.IdentitySystem",
"1Lab.Reflection.HLevel",
"1Lab.HLevel.Universe",
"1Lab.Extensionality",
"1Lab.HLevel.Closure",
"1Lab.Reflection",
"1Lab.Truncation",
"1Lab.Univalence",
"1Lab.Inductive",
"1Lab.HLevel",
"1Lab.Equiv",
"1Lab.Path",
"1Lab.Type",
"Data.... | [
"H-Level",
"prop-instance",
"squash",
"suc"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
Ω-hlevel-proj : hlevel-projection (quote Ω.∣_∣) | Ω-hlevel-proj .has-level = quote Ω.is-tr
Ω-hlevel-proj .get-level x = pure (quoteTerm (suc zero))
Ω-hlevel-proj .get-argument (arg _ t ∷ _) = pure t
Ω-hlevel-proj .get-argument _ = typeError [] | function | Ω-hlevel-proj | 1Lab | src/1Lab/Resizing.lagda.md | [
"1Lab.Function.Surjection",
"1Lab.Path.IdentitySystem",
"1Lab.Reflection.HLevel",
"1Lab.HLevel.Universe",
"1Lab.Extensionality",
"1Lab.HLevel.Closure",
"1Lab.Reflection",
"1Lab.Truncation",
"1Lab.Univalence",
"1Lab.Inductive",
"1Lab.HLevel",
"1Lab.Equiv",
"1Lab.Path",
"1Lab.Type",
"Data.... | [
"[]",
"hlevel-projection",
"suc",
"zero"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
Ω-ua : {A B : Ω} → (∣ A ∣ → ∣ B ∣) → (∣ B ∣ → ∣ A ∣) → A ≡ B | Ω-ua {A} {B} f g i .∣_∣ = ua (prop-ext! f g) i
Ω-ua {A} {B} f g i .is-tr =
is-prop→pathp (λ i → is-prop-is-prop {A = ua (prop-ext! f g) i})
(A .is-tr) (B .is-tr) i | function | Ω-ua | 1Lab | src/1Lab/Resizing.lagda.md | [
"1Lab.Function.Surjection",
"1Lab.Path.IdentitySystem",
"1Lab.Reflection.HLevel",
"1Lab.HLevel.Universe",
"1Lab.Extensionality",
"1Lab.HLevel.Closure",
"1Lab.Reflection",
"1Lab.Truncation",
"1Lab.Univalence",
"1Lab.Inductive",
"1Lab.HLevel",
"1Lab.Equiv",
"1Lab.Path",
"1Lab.Type",
"Data.... | [
"is-prop-is-prop",
"is-prop→pathp",
"prop-ext!",
"ua"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
H-Level-Ω : ∀ {n} → H-Level Ω (2 + n) | H-Level-Ω = basic-instance 2 $ retract→is-hlevel 2
(λ r → el ∣ r ∣ (r .is-tr))
(λ r → el ∣ r ∣ (r .is-tr))
(λ x → Ω-ua id id)
(n-Type-is-hlevel {lzero} 1) | function | H-Level-Ω | 1Lab | src/1Lab/Resizing.lagda.md | [
"1Lab.Function.Surjection",
"1Lab.Path.IdentitySystem",
"1Lab.Reflection.HLevel",
"1Lab.HLevel.Universe",
"1Lab.Extensionality",
"1Lab.HLevel.Closure",
"1Lab.Reflection",
"1Lab.Truncation",
"1Lab.Univalence",
"1Lab.Inductive",
"1Lab.HLevel",
"1Lab.Equiv",
"1Lab.Path",
"1Lab.Type",
"Data.... | [
"H-Level",
"basic-instance",
"id",
"lzero",
"n-Type-is-hlevel",
"retract→is-hlevel",
"Ω-ua"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
□-map : ∀ {ℓ ℓ'} {A : Type ℓ} {B : Type ℓ'}
→ (A → B) → □ A → □ B | □-map f (inc x) = inc (f x)
□-map f (squash x y i) = squash (□-map f x) (□-map f y) i | function | □-map | 1Lab | src/1Lab/Resizing.lagda.md | [
"1Lab.Function.Surjection",
"1Lab.Path.IdentitySystem",
"1Lab.Reflection.HLevel",
"1Lab.HLevel.Universe",
"1Lab.Extensionality",
"1Lab.HLevel.Closure",
"1Lab.Reflection",
"1Lab.Truncation",
"1Lab.Univalence",
"1Lab.Inductive",
"1Lab.HLevel",
"1Lab.Equiv",
"1Lab.Path",
"1Lab.Type",
"Data.... | [
"inc",
"squash"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
□-rec : ∀ {ℓ ℓ'} {A : Type ℓ} {B : Type ℓ'} → is-prop B → (A → B) → □ A → B | □-rec bp f (inc x) = f x
□-rec bp f (squash x y i) = bp (□-rec bp f x) (□-rec bp f y) i | function | □-rec | 1Lab | src/1Lab/Resizing.lagda.md | [
"1Lab.Function.Surjection",
"1Lab.Path.IdentitySystem",
"1Lab.Reflection.HLevel",
"1Lab.HLevel.Universe",
"1Lab.Extensionality",
"1Lab.HLevel.Closure",
"1Lab.Reflection",
"1Lab.Truncation",
"1Lab.Univalence",
"1Lab.Inductive",
"1Lab.HLevel",
"1Lab.Equiv",
"1Lab.Path",
"1Lab.Type",
"Data.... | [
"inc",
"is-prop",
"squash"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c | |
elΩ : ∀ {ℓ} (T : Type ℓ) → Ω | elΩ T .∣_∣ = □ T
elΩ T .is-tr = squash | function | elΩ | 1Lab | src/1Lab/Resizing.lagda.md | [
"1Lab.Function.Surjection",
"1Lab.Path.IdentitySystem",
"1Lab.Reflection.HLevel",
"1Lab.HLevel.Universe",
"1Lab.Extensionality",
"1Lab.HLevel.Closure",
"1Lab.Reflection",
"1Lab.Truncation",
"1Lab.Univalence",
"1Lab.Inductive",
"1Lab.HLevel",
"1Lab.Equiv",
"1Lab.Path",
"1Lab.Type",
"Data.... | [
"squash"
] | https://github.com/plt-amy/1lab | e5a99a399a3c58922adef713f38314805810937c |
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