program design, design patterns, type theory, and other buzzwords. amr sabry عمرو صبرى...

Program Design,Design Patterns,

Type Theory,and other buzzwords.

Amr Sabry

صبرى عمروIndiana University

October 22, 2001 Design Patterns and Type Theory2

Playing Music

Building Structures

Programming

(define fact

(lambda (n)

(if (zero? n)

(* n (fact (sub1 n))))))

Levels of Abstraction

As programmers we must deal with different levels of abstraction

Write little pieces of code, encapsulate them by hiding the irrelevant details, and describing their behavior in concise terms.

Use these encapsulations as building blocks for the next

layers of abstraction, etc.

Outline

Part I

Abstraction and Reuse

Part II

Abstraction and Safety

Part I

Abstraction and Reuse

Do we want to “reuse” code? YES!!!

We earlier said:

Write little pieces of code, encapsulate them by hiding

the irrelevant details, and describing their behavior in concise terms.

What is “irrelevant” depends on how the code will be used!!!

Which is an abstraction of a human?

Reuse (unanticipated)

If we choose one particular abstraction, then we essentially rule out some future uses of the software.

Unfortunately people like to modify software after the fact in unpredictable ways!

Architecture and Design Patterns

Christopher Alexander

Design of a building is tied to the anticipated uses and must be flexible to accommodate other emerging uses.

The uses are captured in pattern languages and all buildings are the result of applying sets of rules (or pattern languages - sets of related patterns)

Alexander's Patterns

a pattern is a formalized instruction that says: "if you encounter this problem, then solve it like that" patterns are the means to an end or rules of thumb patterns are used in combination, with cross-referencing, enabling decisions to be made in a reasonable

Software Design Patterns "These patterns solve specific design problems ...

make object-oriented designs more flexible, elegant and ultimately reusable ... basing new designs on prior experience ... without having to rediscover them ... “ (Gamma et al. 1995)

Warning!

Lots of details to follow!

A Design Problem

McSabry food chain needs a program to keep track of the food items it sells.

Initially, McSabry will focus on: ice cream, hotdogs, and pizza.

For each food item, we will need to keep track of its cost and selling price so that we can compute the profit from sales.

An Initial Java Design

FoodItem

IceCream Hotdog Pizza

CostPrice

Java Implementation

abstract class FoodItem { abstract int cost (); abstract int price();}

class HotDog … { … }

class Pizza … { … }

class IceCream extends FoodItem {

int cost () { return 1; }

int price () { return 5; }}

Sales and Profit

class Profit { int profit (FoodItem[] sales) { int totcost = 0; int totprice = 0; for (int i=0; i<sales.length; i++) { totcost += sales[i].cost(); totprice += sales[i].price(); } return totprice – totcost; }}

McSabry expands…

McSabry decides to add Vegetables to its food items.

We need to modify the design and the program!

Updated Design

FoodItem

CostPrice

Vegetables

Updated Implementation

class Vegetables extends FoodItem {

int cost () { return 2; }

int price () { return 4; }

Code already written does NOT have to change at all!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Unfortunately McSabry discovered recently that the FDA requires that the company reports the number of calories in every food item.

Need to modify the design and program again!

Updated Design

FoodItem

CostPriceCalories

Vegetables

Updated Implementation

Must go back and change EVERY class that we have written.

Scale this to millions of line of code

Let’s revise our original design…

The problem

We did not anticipate reuse in one dimension.

How could we modify the design to accommodate growth not only in new food items but also in new operations on food items.

Solution: the Visitor Pattern.

Visitor Pattern

FoodItem

acceptVegetables

FoodVis

CostVis PriceVis CaloriesVis

visitIceCreamvisitHotDogvisitPizzavisitVegetables

Implementation

class IceCream extends FoodItem {

int accept (FoodVis fv) { return fv.visitIceCream(); }

class PriceVis extends FoodVis { int visitIceCream () { return 5; } int visitVegetables () { return 4; } …}

Extensible Reusable Code

Possible to add new operations on food items without changing any existing code.

With another small modification, it is possible to add more food items without changing any existing code.

Summary of Part I

Before we can “abstract” we must decide what is “relevant” and what is “irrelevant.” Need design experience, patterns, etc.

Most CS courses teach abstraction. Focus on reuse comes in class that focus on programming in the large, software engineering, and OO design.

Part II

Abstraction and Safety

Programming with Abstractions

Assuming we have already decided what is relevant and what is irrelevant, how do really hide the irrelevant details and be sure they will not somehow leak out?

Types are a syntactic discipline for enforcing levels of abstractions [Reynolds]

Not comments

Part of the programming language

Checked and enforced by the compiler

Interfaces (from Java 2)

public interface Collection { boolean add (Object o); bollean addAll (Collection c); void clear (); boolean contains (Object o); boolean containsAll (Collection c); boolean equals (Object o); int hashCode (); boolean isEmpty (); Iterator iterator (); boolean remove (Object o); boolean removeAll (Collection c); boolean retainAll (Collection c); int size (); Object[] toArray (); Object[] toArray (Object[] a);}

Type Safety

Informal:

If the compiler determines that some expression has type T, then it will have type T at runtime.

No unanticipated errors.

Bad example:

Compiler determines that e has type int

Hence ok to write 1+e

But e evaluates to an array of booleans.

Example in C (I)

[From Intensional Equality for Continuations by Andrew Appel]

A function in a high-level programming language is just the address of an instruction at the machine level. In C one can mix high-level functions and unsigned numbers!!!

Warning!

Lots of details to follow!

Example in C (II)

cMain (int ac, char*av[]) { int i,j; (void) srandom (atoi (av[1])); for (i=0; i < 10000000; i++) { j = quickroot (random()); } exit(0);}

eMain() {}

unsigned mycaller[] = { 0x81c3e008,0x9010001f };

Example in C (III)

int quickroot (int i) { static x = 0; if (x) return cbrt (i); x=1; { unsigned *p, *q, caller; union { unsigned *z; unsigned (*f)(); } u; u.z = mycaller; caller = u.f();

if (caller <= (unsigned)main ||

caller >= (unsigned)main +

(unsigned)eMain -

(unsigned)cMain)

return quickroot(i);

exit(0);

What’s going on?

Layout: If main == cMain then

do nothing

If main is anything else then call the real cbrt function

quickroot

Why is this Bad?

The types don’t hide anything!

Unanticipated errors can happen

Evaluation can even proceed with nonsense

No abstraction

Why is it REALLY Bad?

From Securing Java, John Wiley & Sons, Inc.

The Java language is designed to enforce type safety. This means that programs are prevented from

accessing memory in inappropriate ways… Type safety means that a program cannot perform an operation on an object unless that operation is valid for that object.

Type safety is the most essential element of Java’s security… In our experience, every type safety violation has created an opportunity for an untrusted applet to break out of Java’s security restrictions.

Safety with a Straightjacket

Pascal was safe (almost!)

Pascal’s type system was very limited (a function that sorts an array of ints cannot sort an array of floats)

Need expressive type system that is safe.

Here lies Pascal: A Language

Chocked by its Type System

An Expressive & Safe Type System: Haskell

Lookup :: (Eq a) =>

a -> [(a,b)] -> Maybe b

lookup key [] = Nothing

lookup key ((x,y):xys)

| key == x = Just y

| otherwise = lookup key ys

There are even more advanced type systems but they are not part of “mainstream” programming languages

Hot research topic with new proposals emerging every year

Haskell primitive types

[Based on tutorial on haskell.org] 5 :: Integer ‘a’ :: Char inc :: Integer -> Integer

inc n = n+1 [1,2,3] :: [Integer] (‘b’,4) :: (Char, Integer)

Polymorphic Types

length :: forall a. [a] -> Integer

length [] = 0

length (x:xs) = 1 + length xs

length [1,2,3] 3 length [‘a’, ‘b’, ‘c’] 3 length [[1,5], [2,5], [3,5]] 3

User-Defined Types

data Bool = False | True data Color = Red | Green | Blue | Indigo data Point a = Pt a a

Pt 2.0 3.0 :: Point Float Pt ‘a’ ‘b’ :: Point Char Pt True False :: Point Bool Pt ‘a’ 1 :: TYPE ERROR

Recursive Types

data Tree a = Leaf a | Branch (Tree a) (Tree a)

Branch :: Tree a -> Tree a -> Tree a Leaf :: a -> Tree a

fringe :: Tree a -> [a]

fringe (Leaf x) = [x]

fringe (Branch left right) = fringe left ++ fringe right

Type Classes

class Eq a where (==) :: a -> a -> Bool instance Eq Integer where x == y = x `integerEq` y instance Eq Float where x == y = x `floatEq` y instance (Eq a) => Eq (Tree a) where Leaf a == Leaf b = a == b (Branch l1 r1) == (Branch l2 r2) = (l1 == l2) && (r1 == r2) _ == _ = False

Modules

module Tree (Tree(Leaf,Branch), fringe) where

fringe :: Tree a -> [a] fringe (Leaf x) = [x] fringe (Branch l r) = fringe l ++ fringe r

module Main (main) where

import Tree( Tree(Leaf,Branch), fringe)

main = print (fringe (Branch (Leaf 1) (Leaf 2)))

Existential Types

module TreeADT (Tree, leaf, branch, cell, left, right, isLeaf) where-- We know there exists a type Tree but representation is HIDDEN

leaf = Leafbranch = Branchcell (Leaf a) = aleft (Branch l r) = l right (Branch l r) = risLeaf (Leaf _) = TrueisLeaf _ = False

Monads & Memory Encapsulation

new :: forall a. a -> ST s (Ref s a) read :: forall a. Ref s a -> ST s a write :: forall a. Ref s a -> a -> ST s () runST :: forall a. (forall s. ST s a) -> a

If (runST e) typechecks then:– e does not use any memory allocated from the outside– The memory allocated by e is not visible on the outside.

Can evaluate e on a local processor Can immediately reclaim the memory used by e etc

And so on …

Parametricity Theorem for Haskell (informal)

If a program typechecks then it is likely to be correct!!!!!!

Intuition: Assume I tell you a term has type forall a. a -> a, what could it be?

The only sensible term of this type is the function f defined as:

f x = x

The Sky is the Limit!

The type system becomes a programming language of its own

Programs at the type level are proofs about the “regular” programs

Proof-Carrying Code: An emerging industry!

Conclusion

Abstraction is at the heart of CS

Finding the right abstractions is hard: engineering aspect of Programming

Expressing and enforcing rich abstractions: theoretical foundations of Programming Languages

program design, design patterns, type theory, and other buzzwords. amr sabry عمرو صبرى...

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