diff options
Diffstat (limited to 'Examples.agda')
| -rw-r--r-- | Examples.agda | 27 |
1 files changed, 9 insertions, 18 deletions
diff --git a/Examples.agda b/Examples.agda index bda3ae1..ca65835 100644 --- a/Examples.agda +++ b/Examples.agda @@ -1,14 +1,11 @@ module Examples where -open import Data.Nat using (ℕ ; zero ; suc ; _+_ ; ⌈_/2⌉ ; pred) +open import Data.Nat using (ℕ ; zero ; suc ; _+_ ; ⌈_/2⌉) open import Data.Nat.Properties using (cancel-+-left) import Algebra.Structures -open Algebra.Structures.IsCommutativeSemiring Data.Nat.Properties.isCommutativeSemiring using (+-isCommutativeMonoid) -open Algebra.Structures.IsCommutativeMonoid +-isCommutativeMonoid using () renaming (comm to +-comm) open import Data.List using (List ; length) renaming ([] to []L ; _∷_ to _∷L_) open import Data.Vec using (Vec ; [] ; _∷_ ; reverse ; _++_ ; tail ; take ; drop) open import Function using (id) -open import Function.Injection using () renaming (Injection to _↪_ ; id to id↪) open import Relation.Binary.PropositionalEquality using (_≡_ ; refl ; cong) renaming (setoid to EqSetoid) open import Generic using (≡-to-Π) @@ -20,10 +17,10 @@ open GetTypes.PartialVecVec using (Get) open FreeTheorems.PartialVecVec using (assume-get) reverse' : Get -reverse' = assume-get id↪ (≡-to-Π id) reverse +reverse' = assume-get (≡-to-Π id) (≡-to-Π id) reverse double' : Get -double' = assume-get id↪ (≡-to-Π g) f +double' = assume-get (≡-to-Π id) (≡-to-Π g) f where g : ℕ → ℕ g zero = zero g (suc n) = suc (suc (g n)) @@ -32,25 +29,19 @@ double' = assume-get id↪ (≡-to-Π g) f f (x ∷ v) = x ∷ x ∷ f v double'' : Get -double'' = assume-get id↪ (≡-to-Π _) (λ v → v ++ v) - -suc-injection : EqSetoid ℕ ↪ EqSetoid ℕ -suc-injection = record { to = ≡-to-Π suc; injective = cong pred } +double'' = assume-get (≡-to-Π id) (≡-to-Π _) (λ v → v ++ v) tail' : Get -tail' = assume-get suc-injection (≡-to-Π id) tail - -n+-injection : ℕ → EqSetoid ℕ ↪ EqSetoid ℕ -n+-injection n = record { to = ≡-to-Π (_+_ n); injective = cancel-+-left n } +tail' = assume-get (≡-to-Π suc) (≡-to-Π id) tail take' : ℕ → Get -take' n = assume-get (n+-injection n) (≡-to-Π _) (take n) +take' n = assume-get (≡-to-Π (_+_ n)) (≡-to-Π _) (take n) drop' : ℕ → Get -drop' n = assume-get (n+-injection n) (≡-to-Π _) (drop n) +drop' n = assume-get (≡-to-Π (_+_ n)) (≡-to-Π _) (drop n) sieve' : Get -sieve' = assume-get id↪ (≡-to-Π _) f +sieve' = assume-get (≡-to-Π id) (≡-to-Π _) f where f : {A : Set} {n : ℕ} → Vec A n → Vec A ⌈ n /2⌉ f [] = [] f (x ∷ []) = x ∷ [] @@ -67,7 +58,7 @@ intersperse s (x ∷ []) = x ∷ [] intersperse s (x ∷ y ∷ v) = x ∷ s ∷ intersperse s (y ∷ v) intersperse' : Get -intersperse' = assume-get suc-injection (≡-to-Π intersperse-len) f +intersperse' = assume-get (≡-to-Π suc) (≡-to-Π intersperse-len) f where f : {A : Set} {n : ℕ} → Vec A (suc n) → Vec A (intersperse-len n) f (s ∷ v) = intersperse s v |