copumpkin

module Types where

open import Level
open import Function
open import Algebra
open import Data.Empty
open import Data.Unit
open import Data.Sum as Sum
open import Data.Product as Prod
open import Relation.Binary

copumpkin

module FinVector-cons (T : Set) where

data Nat : Set where
  zero : Nat
  suc  : Nat → Nat

data Fin : Nat → Set where
  zero : ∀ {n} → Fin (suc n)
  suc  : ∀ {n} → Fin n → Fin (suc n)

copumpkin

module Topology where

import Level
open import Function
open import Data.Empty
open import Data.Unit
open import Data.Nat hiding (_⊔_)
open import Data.Fin
open import Data.Product
open import Relation.Nullary

copumpkin

module Prime where

open import Coinduction

open import Data.Empty
open import Data.Nat
open import Data.Nat.Properties
open import Data.Nat.Divisibility
open import Data.Fin hiding (pred; _+_; _<_; _≤_; compare)
open import Data.Fin.Props hiding (_≟_)

copumpkin

module Primes where

open import Level using (_⊔_)
open import Coinduction
open import Function
open import Data.Empty
open import Data.Unit
open import Data.Nat
open import Data.Nat.Properties
open import Data.Nat.Divisibility

copumpkin

{-# LANGUAGE ExistentialQuantification, TypeOperators #-}
module Fold where
 
import Control.Applicative
import Control.Functor.Contra
 
import Data.Array.Vector
import qualified Data.Foldable as Foldable
 
data Fold b c = forall a. Fold (a -> b -> a) a (a -> c)

copumpkin

# Very alpha still, but getting there...

# Yeah, I like it this way
require 'pp'
require 'set'
require 'zlib'
require 'base64'
require 'socket'
require 'openssl'
require 'stringio'

copumpkin

module Grothendieck where

open import Level using (_⊔_)
open import Function
open import Algebra
open import Algebra.Structures
open import Data.Product
import Relation.Binary.EqReasoning as EqReasoning

copumpkin

{-# LANGUAGE GADTs, RankNTypes, TypeFamilies, DataKinds, PolyKinds, TypeOperators, ScopedTypeVariables #-}

-- Lots of ways you can phrase this, but this works for me
-- For folks who haven't seen it before, this is "the essence of the sum type" and sigma stands for sum.
-- You see it far more often in dependent types than elsewhere because it becomes a lot more pleasant to
-- work with there, but it's doable in other contexts too. Think of the first parameter to the data
-- constructor as a generalized "tag" as we talk about in "tagged union", and the second parameter is the
-- "payload". It turns out that you can represent any simple sum type you could write in Haskell this way
-- by using a finite and enumerable `f`, but things can get more unusual when `f` isn't either. In such
-- cases, it's often easier to think of this as the essence of existential types.

copumpkin

module Unify where

-- Translated from http://strictlypositive.org/unify.ps.gz

open import Data.Empty
import Data.Maybe as Maybe
open Maybe hiding (map)
open import Data.Nat
open import Data.Fin
open import Data.Product hiding (map)