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{-# LANGUAGE MultiParamTypeClasses #-} | |
{-# LANGUAGE FlexibleInstances #-} | |
{-# LANGUAGE DefaultSignatures #-} | |
{-# LANGUAGE FlexibleContexts #-} | |
{-# LANGUAGE ScopedTypeVariables #-} | |
{-# LANGUAGE DeriveGeneric #-} | |
{-# LANGUAGE TypeOperators #-} | |
{-# LANGUAGE UndecidableInstances #-} | |
{-# LANGUAGE AllowAmbiguousTypes #-} | |
{-# LANGUAGE TypeApplications #-} |
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{-# LANGUAGE | |
AllowAmbiguousTypes, | |
DeriveGeneric, | |
EmptyCase, | |
TypeOperators, | |
FlexibleInstances, | |
FlexibleContexts, | |
MultiParamTypeClasses, | |
PolyKinds, | |
TypeApplications, |
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#![cfg_attr(not(creusot),feature(stmt_expr_attributes,proc_macro_hygiene))] | |
use ::std::vec; | |
extern crate creusot_contracts; | |
use creusot_contracts::*; | |
#[requires(t@.len() == n@)] | |
#[ensures(result ==> exists<i0: Int> exists<j0: Int> 0 <= i0 && i0 < j0 && j0 < n@ && t@[i0] == t@[j0])] | |
#[ensures(!result ==> forall<i0 : Int> forall<j0 : Int> 0 <= i0 && i0 < n@ && i0 < j0 && j0 < n@ ==> t@[i0] != t@[j0])] |
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From Coq Require Import List. | |
Fixpoint map_In {A B : Type} (xs : list A) : (forall x, In x xs -> B) -> list B := | |
match xs return (forall x, In x xs -> B) -> list B with | |
| nil => fun _ => nil | |
| cons x xs' => fun f => cons (f x (or_introl eq_refl)) (map_In xs' (fun x' In_x'_xs' => f x' (or_intror In_x'_xs'))) | |
end. |
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{-# LANGUAGE | |
RankNTypes, | |
TypeOperators #-} | |
-- | User-defined handlers. | |
module Bluefin.Handlers | |
( Sig | |
, Handler | |
, with |
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(* formalization attached to my answer to https://cstheory.stackexchange.com/questions/53855/can-we-use-relational-parametricity-to-simplify-the-type-forall-a-a-to-a *) | |
From Coq Require Import Lia. | |
Definition U : Type := forall A : Type, ((A -> A) -> A) -> A. | |
(* Try enumerating solutions by hand. After the initial [intros], | |
we can either complete the term with [exact xi], | |
or continue deeper with [apply f; intros xi]. *) | |
Goal U. | |
Proof. |
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#!/usr/bin/env cabal | |
{- cabal: | |
build-depends: base, effectful-core | |
-} | |
-- Usage: cabal run Coroutine.hs | |
{-# LANGUAGE | |
DataKinds, | |
FlexibleContexts, |
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(* https://proofassistants.stackexchange.com/questions/3841/assistance-using-destruct-on-an-equality-proof-for-functors/3843 *) | |
(* Proof of associativity of functor composition without UIP *) | |
(* 1. Intuition: treat equality as a proper algebraic structure: | |
think of it as a category (aka. the discrete category), not an equivalence relation. *) | |
(* 1a. An equality between morphisms, f = g, becomes the existence of a morphism between f and g. *) | |
(* 1b. In the definition of a category, homsets are thus categories. | |
The resulting structure is known as a 2-category. https://ncatlab.org/nlab/show/2-category | |
You can kepp applying the same generalization to the morphism category, resulting |
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{-# LANGUAGE BangPatterns #-} | |
import Criterion | |
import Criterion.Main | |
import Data.List (inits, scanl') | |
import Data.Primitive.Array | |
import GHC.Exts (RealWorld) | |
import System.IO.Unsafe | |
-- base implementation, using queues |
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(* A trick to print the simplified type of something *) | |
Definition type_of {A : Type} (a : A) : Type := A. | |
Arguments type_of _ /. | |
Notation simpl_type_of a := ltac:(let A := eval simpl in (type_of a) in exact A). | |
(* Example *) | |
Parameter p : forall x, 3 + x = x. |
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