Merge pull request #8 from ionathanch/patch-1

Create Fib.agda

1 files changed, 19 insertions, 0 deletions

diff --git a/entries/ionchy/agda/Fib.agda b/entries/ionchy/agda/Fib.agda
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+
+open import Agda.Builtin.Nat
+open import Agda.Builtin.List
+open import Agda.Builtin.Reflection
+
+data Fib : Nat → Nat → Set where
+  instance F0 : Fib 0 0
+  instance F1 : Fib 1 1
+  instance Fk : ∀ {k n m} → ⦃ Fib k n ⦄ → ⦃ Fib (suc k) m ⦄ → Fib (suc (suc k)) (n + m)
+
+fib' : ∀ k {n} → ⦃ Fib k n ⦄ → Nat
+fib' k {n} ⦃ fib ⦄ = n
+
+macro
+  fib : Term → Term → TC _
+  fib t hole = unify hole (def (quote fib') (arg i t ∷ []))
+    where i = arg-info visible (modality relevant quantity-ω)
+
+{- Get the [n]th Fibonacci number by normalization via C-n `fib [n]`. -}