Problem 1 of Project Euler (#85)

ProjectEuler/Problem1.agda

@@ -0,0 +1,35 @@
+{-# OPTIONS --warning=error --safe #-}
+
+open import LogicalFormulae
+open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
+open import Numbers.Naturals.Semiring
+open import Numbers.Naturals.Order
+open import Lists.Lists
+open import Numbers.Primes.PrimeNumbers
+open import Decidable.Relations
+open import Numbers.BinaryNaturals.Definition
+open import Numbers.BinaryNaturals.Addition
+
+module ProjectEuler.Problem1 where
+
+numbers<N : (N : ℕ) → List ℕ
+numbers<N zero = []
+numbers<N (succ N) = N :: numbers<N N
+
+filter' : {a b : _} {A : Set a} {f : A → Set b} (decidable : (x : A) → (f x) || (f x → False)) → List A → List A
+filter' {f} decid [] = []
+filter' {f} decid (x :: xs) with decid x
+filter' {f} decid (x :: xs) | inl fx = x :: filter' decid xs
+filter' {f} decid (x :: xs) | inr Notfx = filter' decid xs
+
+filtered : (N : ℕ) → List ℕ
+filtered N = filter' (orDecidable (divisionDecidable 3) (divisionDecidable 5)) (numbers<N N)
+
+ans : ℕ → ℕ
+ans n = binNatToN (fold _+B_ (NToBinNat 0) (map NToBinNat (filtered n)))
+
+t : ans 10 ≡ 23
+t = refl
+
+--q : ans 1000 ≡ 0 -- takes about 15secs for me to reduce the term that fills this hole
+--q = refl