add examples

2 files changed, 40 insertions, 0 deletions

diff --git a/Everything.agda b/Everything.agda
index 7399254..e1734a9 100644
--- a/Everything.agda
+++ b/Everything.agda
@@ -10,3 +10,4 @@ import BFF
 import Bidir
 import LiftGet
 import Precond
+import Examples
diff --git a/Examples.agda b/Examples.agda
new file mode 100644
index 0000000..70628a5
--- /dev/null
+++ b/Examples.agda
@@ -0,0 +1,39 @@
+module Examples where
+
+open import Data.Nat using (ℕ ; zero ; suc ; _⊓_ ; _∸_)
+open import Data.Vec using (Vec ; [] ; _∷_ ; reverse ; _++_)
+
+import GetTypes
+import FreeTheorems
+
+open GetTypes.VecVec using (Get)
+open FreeTheorems.VecVec using (assume-get)
+
+reverse' : Get
+reverse' = assume-get reverse
+
+double' : Get
+double' = assume-get f
+  where g : ℕ → ℕ
+        g zero = zero
+        g (suc n) = suc (suc (g n))
+        f : {A : Set} {n : ℕ} → Vec A n → Vec A (g n)
+        f []      = []
+        f (x ∷ v) = x ∷ x ∷ f v
+
+double'' : Get
+double'' = assume-get (λ v → v ++ v)
+
+take' : ℕ → Get
+take' n = assume-get (f n)
+  where f : (n : ℕ) → {A : Set} {m : ℕ} → Vec A m → Vec A (m ⊓ n)
+        f n       []       = []
+        f zero    (x ∷ xs) = []
+        f (suc n) (x ∷ xs) = x ∷ f n xs
+
+drop' : ℕ → Get
+drop' n = assume-get (f n)
+  where f : (n : ℕ) → {A : Set} {m : ℕ} → Vec A m → Vec A (m ∸ n)
+        f zero    xs       = xs
+        f (suc n) []       = []
+        f (suc n) (x ∷ xs) = f n xs