kanak

Richard Bird - Introduction to Functional Programming using Haskell [2ed]
Chapter 02: Simple Datatypes

> module Bird02 where
> import Data.Char (chr, ord)

================================================================================
2.1 Booleans

> data Bool' = False' | True'

kanak

Richard Bird - Introduction to Functional Programming using Haskell [2ed]
Chapter 01: Fundamental Concepts

> module Bird01 where
> import Prelude hiding (pi, signum, abs)

================================================================================
1.1 Sessions and Scripts

Some definitions from the book. I've used more general type signatures.

kanak

{- Discrete Mathematics Using a Computer
   Chapter 13: Circuit Simulation
   
   Story: verify circuit properties using math because actually building and 
          testing is expensive.
-}
module Main where
import Data.List (intersperse)

-- Signal is anything that can be manipulated by circuits

kanak

{- Discrete Mathematics Using a Computer
   Chapter 12: AVL Trees

   AVL Trees: Self-balancing binary trees.
-}
module AVL where

data SearchTree k d = Leaf
                    | Node k d (SearchTree k d) (SearchTree k d)
                    deriving (Show)

kanak

{- Discrete Mathematics Using a Computer
   Chapter 11: Functions
-}

module Functions where
import Data.Tuple (swap)

-- =============================================================================
-- 11.1 The Graph of a Function

kanak

{- Discrete Mathematics Using a Computer
   Chapter 10: Relations
-}

module Relations where
import List (nub)
import Stdm (setEq, union, isWeakest, isGreatest, isQuasiOrder, isLinearOrder)
import Data.Tuple (swap)

-- =============================================================================

kanak

{- Discrete Mathematics Using a Computer
   Chapter 09: Inductively Defined Sets
-}

module IndSet where

-- =============================================================================
-- 9.1: The Idea Behind Induction

{- Suppose we have know that:

kanak

{- Discrete Mathematics Using a Computer
   Chapter 08: Sets
-}

module Sets where

type Set a = [a]
-- Note, this definition prevents us from having heterogeneous sets
-- TODO: use hlist (http://homepages.cwi.nl/~ralf/HList/) ?

kanak

#+TITLE: DiscreteMathComputer 07-Predicate Logic
#+DATE:
#+LATEX_HEADER: \usepackage{fullpage}
#+OPTIONS: H:3 toc:nil

* Introduction: Why Predicates Logic
  - Want to make the statement that everything has a certain property
    + e.g. "All men are mortal"
  - Propositional Logic doesn't provide us any structure to express this
    + e.g. could say "P = all men are mortal"

kanak

{- Discrete Math Using a Computer
   Chapter 6: Propositional Logic
  Review Exercise
-}

import Stdm

--------------------------------------------------------------------------------
-- Exercise 34: Prove A ^ ~A |- False