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module RoseTree where

open import Level
open import Data.List as List
open import Data.Unit
open import Data.Product

data RoseTree {ℓ : Level} (A : Set ℓ) : Set ℓ where
  node : (a : A) (ts : List (RoseTree A)) → RoseTree A

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{-# LANGUAGE KindSignatures            #-}
{-# LANGUAGE DataKinds                 #-}
{-# LANGUAGE GADTs                     #-}
{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE TypeFamilies              #-}
{-# LANGUAGE TypeOperators             #-}
{-# LANGUAGE UndecidableInstances      #-}
{-# LANGUAGE PolyKinds                 #-}

module ImperativeDSL where

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module State where

open import Data.Unit
open import Data.Product
open import Function
open import Relation.Binary.PropositionalEquality

_⟶_ : {I : Set} (X Y : I → Set) → Set
X ⟶ Y = ∀ {i} → X i → Y i

gallais

-- Slight variant of https://gist.github.com/AndrasKovacs/9597994

{-
    Copyright (C) 2014 András Kovács

    Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TO

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module STLC (Atom : Set) (_≠_ : Atom → Atom → Set) where

open import Data.Empty
open import Data.Product as P hiding (_,_)
open import Data.List 
open import Function hiding (_∋_)

data ★ : Set where
  ι : ★
  _⊳_ : ★ → ★ → ★

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module Sums where

open import Data.Nat
open import Data.Fin using (Fin; module Fin)
open import Function

sum : (k : ℕ) (f : Fin k → ℕ) → ℕ
sum zero    f = 0
sum (suc k) f = f Fin.zero + sum k (f ∘ Fin.suc)

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{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleInstances     #-}
{-# LANGUAGE FlexibleContexts      #-}
{-# LANGUAGE UndecidableInstances  #-}
{-# LANGUAGE TypeFamilies          #-}
{-# LANGUAGE DataKinds             #-}
{-# LANGUAGE TypeOperators         #-}
{-# LANGUAGE ScopedTypeVariables   #-}
{-# LANGUAGE PolyKinds             #-}

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{-# LANGUAGE RecordWildCards #-}

module AllContexts where

import Data.List

data Context a = Context
  { before :: [a]
  , focus  :: a
  , after  :: [a]

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(*
   We don't really care about the data constructors here
   but they are needed, cf:
   https://sympa.inria.fr/sympa/arc/caml-list/2013-10/msg00190.html
 *)
type zero    = Zero
type 'a succ = Succ

(*
   []   has length 0

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{-# OPTIONS_GHC -fdefer-type-errors #-}
{-# LANGUAGE RankNTypes             #-}

module NumList where

import Data.Void

type NumList a = Num a => [a]

first :: NumList a -> a