Agnishom Chattopadhyay Agnishom

Analysis Books (top most is most recommended)

Understanding Analysis - Stephen Abott

BV Rao's notes on Analysis I

Episode 1

Objective: To understand the basic philosophy of Haskell, to know the distinction between functional programming and other paradigms of programming, setting up the haskell interpreter, getting acquinted to the basic syntax, basic understanding of the type system, currying

The Haskell Philosophy

Read any one of these (but not necessarily all three)

Prelude (CIS 194: Introduction to Haskell (Fall 2016))
Read the sections:

We viewed computation just as the process of rewriting. Is this notion powerful enough? Can we use such a model to compute whatever we like?
- It turns out that we can. Functional programming is based on an abstraction called the Lambda Calculus
- To have a sense of the multitude of the strange systems that are really just as powerful as traditional computers, see Esoteric Languages. BrainF and FRACTRAN are particularly interesting. Rule 110 could be an honorable mention
- Having said that, Haskell could be a pleasant and practical language to program in.
In class, we defined plus in terms of succ.
- Can you define mult standing for multiplication, in terms of plus
  - Install the Haskell interpreter on your device and check if your program works. Alternately, use the repl.it environment online.
C

	{-# LANGUAGE NoMonomorphismRestriction #-}
	{-# LANGUAGE FlexibleContexts #-}
	{-# LANGUAGE TypeFamilies #-}

	import Diagrams.Prelude
	import Diagrams.Backend.SVG.CmdLine

	rules :: Diagram B
	rules = foldr1 (<>) hands
	where

	module Lib where

	import Data.Graph
	import Data.Vector
	import Data.Map

	newtype State = State Int

	data Transition = Transition { addV :: [Int],
	toState :: State

	import requests
	import json


	# replace the access_token with your own. You can get one at https://developers.facebook.com/tools/explorer/?method=GET&path=cmiconfessionz%2Ffeed&version=v3.0
	starturl = "https://graph.facebook.com/v3.0/cmiconfessionz/feed?access_token="

	cururl = starturl

	confessionData = []

	{-# OPTIONS_GHC -Wall #-}

	{-# LANGUAGE DataKinds #-}
	{-# LANGUAGE FunctionalDependencies #-}
	{-# LANGUAGE DeriveGeneric #-}
	{-# LANGUAGE FlexibleInstances #-}
	{-# LANGUAGE GeneralizedNewtypeDeriving #-}
	{-# LANGUAGE MultiParamTypeClasses #-}
	{-# LANGUAGE OverloadedStrings #-}
	{-# LANGUAGE RankNTypes #-}

	public static void main(String[] args)
	{
	int l = 3;
	Conveyor conveyor = new Conveyor();
	Thread nonHazardous[] = new Thread[l];
	Thread hazardous[] = new Thread[l];

	//populate
	for (int i = 0; i < l; i++){
	nonHazardous[i] = new Thread(new Item(conveyor, i*10, 3000, false));


	-- Just an utility function to calculate [root(x)]
	intSqrt :: Integer -> Integer
	intSqrt n = acc 1 n n
	where
	acc a b n
	\| a == (b-1) = a
	\| m*m > n = acc a m n
	\| m*m <= n = acc m b n
	where

	Diag = {M \| M does not accept M}
	HP = {(M, x) \| M accepts x}
	Co-Univ = {M \| there exists w such that M does not accept w}

	Claim: HP <= Diag <= Co-Univ

	Reduction from HP to Diag

	Say HP has input (M, x)
	Design Turing Machine N such that: