diff options
| -rw-r--r-- | LiftGet.agda | 23 |
1 files changed, 10 insertions, 13 deletions
diff --git a/LiftGet.agda b/LiftGet.agda index 3c07fd7..982277f 100644 --- a/LiftGet.agda +++ b/LiftGet.agda @@ -8,7 +8,7 @@ open import Data.List.Properties using (length-map) open import Data.Product using (∃ ; _,_ ; proj₁ ; proj₂) open import Function using (_∘_ ; flip ; const) open import Relation.Binary.Core using (_≡_) -open import Relation.Binary.PropositionalEquality using (_≗_ ; sym ; cong ; refl) +open import Relation.Binary.PropositionalEquality using (_≗_ ; sym ; cong ; refl ; subst) open Relation.Binary.PropositionalEquality.≡-Reasoning using (begin_ ; _≡⟨_⟩_ ; _∎) get-type : Set₁ @@ -44,14 +44,11 @@ length-toList : {A : Set} {n : ℕ} → (v : Vec A n) → length (toList v) ≡ length-toList []V = refl length-toList (x ∷V xs) = cong suc (length-toList xs) -vec-length : {A : Set} {n m : ℕ} → n ≡ m → Vec A n → Vec A m -vec-length refl v = v - toList-fromList : {A : Set} → (l : List A) → toList (fromList l) ≡ l toList-fromList [] = refl toList-fromList (x ∷ xs) = cong (_∷_ x) (toList-fromList xs) -vec-length-same : {A : Set} → (l : List A) → {n : ℕ} → (p : length l ≡ n) → toList (vec-length p (fromList l)) ≡ l +vec-length-same : {A : Set} → (l : List A) → {n : ℕ} → (p : length l ≡ n) → toList (subst (Vec A) p (fromList l)) ≡ l vec-length-same l refl = toList-fromList l getList-to-getVec-length-property : (get : get-type) → {C : Set} → {m : ℕ} → (v : Vec C m) → length (get (toList v)) ≡ length (get (replicate m tt)) @@ -67,7 +64,7 @@ getList-to-getVec get = getlen , get' where getlen : ℕ → ℕ getlen = getList-to-getlen get get' : {C : Set} {m : ℕ} → Vec C m → Vec C (getlen m) - get' v = vec-length (getList-to-getVec-length-property get v) (fromList (get (toList v))) + get' {C} v = subst (Vec C) (getList-to-getVec-length-property get v) (fromList (get (toList v))) {- -- We cannot formulate the first commutation property, because the type of @@ -77,12 +74,12 @@ get-commut-1 get l = ? -} get-trafo-1 : (get : get-type) → {B : Set} → getVec-to-getList (proj₂ (getList-to-getVec get)) {B} ≗ get {B} -get-trafo-1 get l = begin +get-trafo-1 get {B} l = begin getVec-to-getList (proj₂ (getList-to-getVec get)) l ≡⟨ refl ⟩ toList (proj₂ (getList-to-getVec get) (fromList l)) ≡⟨ refl ⟩ - toList (vec-length (getList-to-getVec-length-property get (fromList l)) (fromList (get (toList (fromList l))))) + toList (subst (Vec B) (getList-to-getVec-length-property get (fromList l)) (fromList (get (toList (fromList l))))) ≡⟨ vec-length-same (get (toList (fromList l))) (getList-to-getVec-length-property get (fromList l)) ⟩ get (toList (fromList l)) ≡⟨ cong get (toList-fromList l) ⟩ @@ -122,16 +119,16 @@ get-trafo-2-getlen getlen get n = begin getlen n ∎ getVec-getlen : {getlen₁ getlen₂ : ℕ → ℕ} → (get : getV-type getlen₁) → getlen₁ ≗ getlen₂ → getV-type getlen₂ -getVec-getlen get p {B} {n} v = vec-length (p n) (get v) +getVec-getlen get p {B} {n} v = subst (Vec B) (p n) (get v) get-trafo-2-get : (getlen : ℕ → ℕ) → (get : getV-type getlen) → {B : Set} {n : ℕ} → proj₂ (getList-to-getVec (getVec-to-getList get)) {B} {n} ≗ getVec-getlen get (sym ∘ (get-trafo-2-getlen getlen get)) -get-trafo-2-get getlen get v = begin +get-trafo-2-get getlen get {B} v = begin proj₂ (getList-to-getVec (getVec-to-getList get)) v ≡⟨ refl ⟩ - vec-length (getList-to-getVec-length-property (getVec-to-getList get) v) (fromList (toList (get (fromList (toList v))))) + subst (Vec B) (getList-to-getVec-length-property (getVec-to-getList get) v) (fromList (toList (get (fromList (toList v))))) ≡⟨ {!!} ⟩ - vec-length (sym (get-trafo-2-getlen getlen get (vec-len v))) (vec-length (cong getlen (length-toList v)) (get (fromList (toList v)))) + subst (Vec B) (sym (get-trafo-2-getlen getlen get (vec-len v))) (subst (Vec B) (cong getlen (length-toList v)) (get (fromList (toList v)))) ≡⟨ {!!} ⟩ - vec-length (sym (get-trafo-2-getlen getlen get (vec-len v))) (get v) + subst (Vec B) (sym (get-trafo-2-getlen getlen get (vec-len v))) (get v) ≡⟨ refl ⟩ getVec-getlen get (sym ∘ (get-trafo-2-getlen getlen get)) v ∎ |