COS 441 Exam StuffCOS 441 Exam Stuff

David Walker

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LogisticsLogistics

• take-home exam will become available on the course web site Jan 15-18

• write down when you download & when you turn in • email to kenny or deliver to his office by hand

• you have 24 hours to complete the exam

• content: anything from class, assignments, or assigned textbook readings

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Content: Pre-midtermContent: Pre-midterm

• Judgments, inductive definitions, proofs by induction (Chapter 3)

• Intuitionistic logic: formulas, proofs, proof checking & the Curry-Howard isomorphism

• Untyped lambda calculus, operational semantics, properties, encodings (Chapter 5)

• Typed lambda calculus: syntax, operational semantics, typing rules, properties including type safety, progress, preservation, canonical forms, substitution, inversion principles, etc. (Chapter 8,9,11)

• Typed datastructures: tuples, sums (Chapter 11) • Implementation of programming language concepts

(syntax, substitution, operational semantics, type checking)

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Content: Post-midtermContent: Post-midterm

• recursive types (Chap 20.1, 20.2)• effectful computations:  references, exceptions, semantics

using evaluation contexts (Chap 13,14; evaluation contexts note above)

• quantified types:  universal polymorphism, existential types, type inference (Chap 22.1-22.6, 23.1-23.5, 24)

• subtyping: subtyping relations, co-, contra-, and in-variance, subsumption rule, proving soundness of declarative system, showing subtyping rules are “bad”, don’t worry about relating declarative and algorithmic subtyping formally (Chap 15.1-5, 16.1-3)

• class-based, object-oriented languages:  featherweight Java (Chap 19.1-19.5)

• applications of operational semantics & type systems:  stack inspection

• stuff we cover today in lecture• implementation of any of the concepts above

Typed Assembly LanguageTyped Assembly Language

David Walker

Slides stolen from:Greg Morrisett

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TypesTypes

“Type systems for programming languages are a syntactic mechanism for enforcing abstraction.”

J. Reynolds

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What is TAL?What is TAL?

A type system for assembly language(s):•built-in abstractions (tuple,code)

•operators to build new abstractions (,,)

•annotations on assembly code

•an abstraction checker

Thm: well-annotated code cannot violate abstractions.

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What We Did What We Did [popl 98, toplas 99 & [popl 98, toplas 99 & others]others]

Theory:• small RISC-style assembly language

• compiler from System F to TAL

• soundness and preservation theorems

Practice:• most of IA32 (32-bit Intel x86)

• more type constructors • everything you can think of and more

• safe C compiler • ~40,000LOC & compiles itself

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Why Type Assembly?Why Type Assembly?

Theory:•simplifies proofs of compiler correctness

•deeper understanding of compilation

Practice:•compiler debugging

•software-based protection

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Type-Based Protection (JVM)Type-Based Protection (JVM)

Java Source

javac

JVM bytecodes

JVM verifier System Interface

Binary

Optimizer

Low-Level IL

SystemBinary

“Kernel”

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JVM Pros & ConsJVM Pros & Cons

Pros:•portable•hype: $, tools, libraries, books, training

Cons:•trusted computing base includes JIT•requires many run-time tests

• “down” casts, arrays, null pointers, etc.

•only suitable for Java (too high-level)•no formal spec (when we started with TAL)

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Ideally:Ideally:

Your favoritelanguage

Low-Level IL(SSA)

optimizer

machine code

verifier System Interface

SystemBinary“Kernel”

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Rest of the Lecture: Rest of the Lecture: ExamplesExamples•TAL core types:

•bytes, tuples, code,

•Control-Flow:•calling conventions, stacks, exns

• I won’t get to:•closures, objects, modules, type

analysis, ADTs

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Simple Built-In TypesSimple Built-In Types

•Bytes: b1, b2, b4

•Tuples: (11,…,n

n)

•Code: {r1:1,…, rn:n}

• like a pre-condition

•argument type of function

•no return type because code doesn’t really return, just jumps somewhere else...

•Polymorphic types: ., .

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Simple LoopSimple Loopsum: {ecx:b4, ebx:{eax:b4}} ; int sum(int

x) {mov eax,0 ; int a = 0;jmp test ;

loop: {eax:b4, ecx:b4, ebx:{eax:b4}} ; while(!x) {add eax,ecx ; a += x;dec ecx ; x--;FALLTHRU ; }

test: {eax:b4, ecx:b4, ebx:{eax:b4}} ;cmp ecx,0 ;jne loop ; return(a);jmp ebx ; }

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Allocation:Allocation:

mkpair: {eax:b4, ebx:{eax:(b41, b41)}}

mov ecx,eaxMALLOC eax,8,(b4, b4) ; eax : (b40,

b40)mov [eax+0],ecx ; eax : (b41,

b40)mov [eax+4],ecx ; eax : (b41,

b41)jmp ebx

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Callee-Saves RegisterCallee-Saves Register

addone: .{eax:b4, ecx:, ebx:{eax:b4, ecx:}}inc eax ; x+1jmp ebx ; return

main: {ebx:{eax:b4}}mov eax,3 mov ecx,ebx ; save main’s return addressmov ebx,done jmp addone[{eax:b4}]

done: {eax:b4,ecx:{eax:b4}}inc eaxjmp ecx

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In General:In General:

Need to save more stuff (e.g., locals):

MALLOC ecx,4n,(1,…,n) ; frame for storage

mov [ecx+0],r1… ; save locals

mov [ecx+4n-4],rnjmp addone[(1,…,n)]

Heap-AllocatedActivation Records

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StacksStacks

Want to use stack for activation frames.

Stack types: ::= nil | :: | | 1 @ 2

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Typing Stack OperationsTyping Stack Operations

{ esp: } { esp: 1::2

::…::i:: }

sub esp,i*4 add esp,i*4{ esp: b40::b40::…::b40:: } { esp :

{ r: , esp: 1::2

::…::i:: } { r: , esp: }

mov [esp+i*4],r push r{ r: , esp: 1

::2::…::1:: } { r: esp: 1:: }

{ esp: 1::2

::…::i1:: } { esp: 1:: }

mov r,[esp+i*4] pop r{ r: i, esp: 1

::2::…::i

1:: } { r: esp: }

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Recursion thru Stack Recursion thru Stack VariablesVariablesfact: .{eax:b4, esp:{eax:b4, esp:}::}

cmp eax,1 jne L[]

retnL:’.{eax:b4, esp:{eax:b4, esp:’}::’}

push eax dec eaxcall fact[b4::{eax:b4, esp:’}::’]pop ecximul eax,ecxretn

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Fact FactFact Fact

fact: .{eax:b4, esp:{eax:b4, esp:}::}

Because is abstract, fact cannot read or write this portion of the stack.

Caller’s frame is protected from callee…

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Other TAL FeaturesOther TAL Features

•Module system• interfaces, implementations, ADTs

•Sum type/datatype support •Fancy arrays/vector typing• (Higher Order) Type constructors•Fault tolerance checking•Other people still writing papers

about more ...

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Long Term?Long Term?

Low-level, portable, safe language:• OO-support of Java

• typing support of ML

• programmer control of C• good model of space• good model of running time• many optimizations expressible in the language

Microsoft research working on a new compiler (Phoenix) to generate TAL