Start Lecture #1

Chapter 0: Administrivia

I start at Chapter 0 so that when we get to chapter 1, the numbering will agree with the text.

0.1: Contact Information

0.2: Course Web Page

There is a web site for the course. You can find it from my home page listed above.

0.3: Textbook

The course text is Aho, Lam, Sethi, and Ullman: Compilers: Principles, Techniques, and Tools, second edition

0.4: Computer Accounts and Mailman Mailing List

0.5: Grades

Your grade will be a function of your final exam and laboratory assignments (see below). I am not yet sure of the exact weightings for each lab and the final, but the final will be roughly half the grade (very likely between 40% and 60%).

0.6: The Upper Left Board

I use the upper left board for lab/homework assignments and announcements. I should never erase that board. If you see me start to erase an announcement, please let me know.

I try very hard to remember to write all announcements on the upper left board and I am normally successful. If, during class, you see that I have forgotten to record something, please let me know. HOWEVER, if I forgot and no one reminds me, the assignment has still been given.

0.7: Homeworks and Labs

I make a distinction between homeworks and labs.

Labs are

Homeworks are

0.7.1: Homework Numbering

Homeworks are numbered by the class in which they are assigned. So any homework given today is homework #1. Even if I do not give homework today, the homework assigned next class will be homework #2. Unless I explicitly state otherwise, all homeworks assignments can be found in the class notes. So the homework present in the notes for lecture #n is homework #n (even if I inadvertently forgot to write it to the upper left board).

0.7.2: Doing Labs on non-NYU Systems

You may solve lab assignments on any system you wish, but ...

0.7.3: Obtaining Help with the Labs

Good methods for obtaining help include

  1. Asking me during office hours (see web page for my hours).
  2. Asking the mailing list.
  3. Asking another student, but ...
  4. ... Your lab must be your own.
    That is, each student must submit a unique lab. Naturally, simply changing comments, variable names, etc. does not produce a unique lab. See the Academic Integrity Policy below.

0.7.4: Computer Language Used for Labs

You may write your lab in Java, C, or C++. Other languages may be possible, but please ask in advance. I need to ensure that the TA is comfortable with the language.

0.8: A Grade of Incomplete

The rules for incompletes and grade changes are set by the school and not the department or individual faculty member. The rules set by GSAS state:

The assignment of the grade Incomplete Pass(IP) or Incomplete Fail(IF) is at the discretion of the instructor. If an incomplete grade is not changed to a permanent grade by the instructor within one year of the beginning of the course, Incomplete Pass(IP) lapses to No Credit(N), and Incomplete Fail(IF) lapses to Failure(F).

Permanent grades may not be changed unless the original grade resulted from a clerical error.

0.9: An Introductory Compiler Course with a Programming Prerequisite

0.9.1: An Introductory Course ...

I do not assume you have had a compiler course as an undergraduate, and I do not assume you have had experience developing/maintaining a compiler.

If you have already had a compiler class, this course is probably not appropriate. For example, if you can explain the following concepts/terms, the course is probably too elementary for you.

0.9.2: ... with a Programming Prerequisite

I do assume you are an experienced programmer. There will be non-trivial programming assignments during this course. Indeed, you will write a compiler for a simple programming language.

I also assume that you have at least a passing familiarity with assembler language. In particular, your compiler may need to produce assembler language, but probably it will produce an intermediate language consisting of 3-address code. We will also be using addressing modes found in typical assemblers. We will not, however, write significant assembly-language programs.

0.10: Academic Integrity Policy

The CS policy on academic integrity, which applies to all graduate courses in the department, can be found here .

An Interlude from Chapter 2

I present this snippet from chapter 2 here (it appears where it belongs as well), since it is self-contained and needed for lab number 1, which I wish to assign today.

2.3.4: (depth-first) Tree Traversals

When performing a depth-first tree traversal, it is clear in what order the leaves are to be visited, namely left to right. In contrast there are several choices as to when to visit an interior (i.e. non-leaf) node. The traversal can visit an interior node

  1. Before visiting any of its children.
  2. Between visiting its children.
  3. After visiting all of its children.

I do not like the book's pseudocode as I feel the names chosen confuse the traversal with visiting the nodes. I prefer the pseudocode below, which uses the following conventions.

    traverse (n : treeNode)
        if leaf(n)                      -- visit leaves once; base of recursion
        else                            -- interior node, at least 1 child
           -- visit(n)                  -- visit node PRE visiting any children
           traverse(first child)        -- recursive call
           while (more children remain) -- excluding first child
               -- visit(n)              -- visit node IN-between visiting children
               traverse (next child)    -- recursive call
           -- visit(n)                  -- visit node POST visiting all children

Note the following properties

  1. As written, with the last three visit()s commented out, only the leaves are visited and those visits are in left to right order.

  2. If you uncomment just the first (interior node) visit, you get a preorder traversal, in which each node is visited before (i.e., pre) visiting any of its children.

  3. If you uncomment just the last visit, you get a postorder traversal, in which each node is visited after (i.e., post) visiting all of its children.

  4. If you uncomment only the middle visit, you get an inorder traversal, in which the node is visited (in-) between visiting its children.

    Inorder traversals are normally defined only for binary trees, i.e., trees in which every interior node has exactly two children. Although the code with only the middle visit uncommented works for any tree, we will, like everyone else, reserve the name inorder traversal for binary trees. In the case of binary search trees (everything in the left subtree is smaller than the root of that subtree, which in tern is smaller than everything in the corresponding right subtree) an inorder traversal visits the values of the nodes in (numerical) order.

  5. If you uncomment two of the three visits, you get a traversal without a name.

  6. euler tour If you uncomment all of the three visits, you get an Euler-tour traversal.

    To explain the name Euler-tour traversal, recall that an Eulerian tour on a directed graph is one that traverses each edge once. If we view the tree on the right as undirected and replace each edge with two arcs, one in each direction, we see that the pink curve is indeed an Eulerian tour. It is easy to see that the curve visits the nodes in the order of the pseudocode (with all visits uncommented).

    Normally, the Euler-tour traversal is defined only for a binary tree, but this time I will differ from convention and use the pseudocode above to define Euler-tour traversal for all trees.

    Note the following points about our Euler-tour traversal.

Do the Euler-tour traversal for the tree in the notes and then for a binary tree.

Lab 1 assigned. See the home page.

Roadmap of the Course

  1. Chapter 1 touches on all the material.

  2. Chapter 2 constructs (the front end of) a simple compiler.

  3. Chapters 3-8 fill in the (considerable) gaps, as well as the presenting the beginnings of the compiler back end.

  4. I always spend too much time on introductory chapters, but will try not to.

Chapter 1: Introduction to Compiling

Homework Read chapter 1.

1.1: Language Processors

A Compiler is a translator from one language, the input or source language, to another language, the output or target language.

Often, but not always, the target language is an assembler language or the machine language for a computer processor.

Note that using a compiler requires a two step process to run a program.

  1. Execute the compiler (and possibly an assembler) to translate the source program into a machine language program.
  2. Execute the resulting machine language program, supplying appropriate input.

This should be compared with an interpreter, which accepts the source language program and the appropriate input, and itself produces the program output.

Sometimes both compilation and interpretation are used. For example, consider typical Java implementations. The (Java) source code is translated (i.e., compiled) into bytecodes, the machine language for an idealized virtual machine, the Java Virtual Machine or JVM. Then an interpreter of the JVM (itself normally called a JVM) accepts the bytecodes and the appropriate input, and produces the output. This technique was quite popular in academia, with the Pascal programming language and P-code.

Homework: 1, 2, 4

Remark: Unless otherwise stated, homeworks are from the book and specifically from the end of the second level section we are discussing. Even more specifically, we are in section 1.1, so you are to do the first, second, and fourth problem at the end of section 1.1. These three problems are numbered 1.1.1, 1.1.2, and 1.1.4 in the book.

The compilation tool chain

For large programs, the compiler is actually part of a multistep tool chain

[preprocessor] → [compiler] → [assembler] → [linker] → [loader]

We will be primarily focused on the second element of the chain, the compiler. Our target language will be assembly language. I give a very short description of the other components, including some historical comments.


Preprocessors are normally fairly simple as in the C language, providing primarily the ability to include files and expand macros. There are exceptions, however. IBM's PL/I, another Algol-like language had quite an extensive preprocessor, which made available at preprocessor time, much of the PL/I language itself (e.g., loops and I believe procedure calls).

Some preprocessors essentially augment the base language, to add additional capabilities. One could consider them as compilers in their own right, having as source this augmented language (say Fortran augmented with statements for multiprocessor execution in the guise of Fortran comments) and as target the original base language (in this case Fortran). Often the preprocessor inserts procedure calls to implement the extensions at runtime.


Assembly code is an mnemonic version of machine code in which names, rather than binary values, are used for machine instructions, and memory addresses.

Some processors have fairly regular operations and as a result assembly code for them can be fairly natural and not-too-hard to understand. Other processors, in particular Intel's x86 line, have let us charitably say more interesting instructions with certain registers used for certain things.

My laptop has one of these latter processors (pentium 4) so my gcc compiler produces code that from a pedagogical viewpoint is less than ideal. If you have a mac with a ppc processor (newest macs are x86), your assembly language is cleaner. NYU's ACF features sun computers with sparc processors, which also have regular instruction sets.

Two pass assembly

No matter what the assembly language is, an assembler needs to assign memory locations to symbols (called identifiers) and use the numeric location address in the target machine language produced. Of course the same address must be used for all occurrences of a given identifier and two different identifiers must (normally) be assigned two different locations.

The conceptually simplest way to accomplish this is to make two passes over the input (read it once, then read it again from the beginning). During the first pass, each time a new identifier is encountered, an address is assigned and the pair (identifier, address) is stored in a symbol table. During the second pass, whenever an identifier is encountered, its address is looked up in the symbol table and this value is used in the generated machine instruction.


Linkers, a.k.a. linkage editors combine the output of the assembler for several different compilations. That is the horizontal line of the diagram above should really be a collection of lines converging on the linker. The linker has another input, namely libraries, but to the linker the libraries look like other programs compiled and assembled. The two primary tasks of the linker are

  1. Relocating relative addresses.
  2. Resolving external references (such as the procedure xor() above).
Relocating relative addresses

The assembler processes one file at a time. Thus the symbol table produced while processing file A is independent of the symbols defined in file B, and conversely. Thus, it is likely that the same address will be used for different symbols in each program. The technical term is that the (local) addresses in the symbol table for file A are relative to file A; they must be relocated by the linker. This is accomplished by adding the starting address of file A (which in turn is the sum of the lengths of all the files processed previously in this run) to the relative address.

Resolving external references

Assume procedure f, in file A, and procedure g, in file B, are compiled (and assembled) separately. Assume also that f invokes g. Since the compiler and assembler do not see g when processing f, it appears impossible for procedure f to know where in memory to find g.

The solution is for the compiler to indicated in the output of the file A compilation that the address of g is needed. This is called a use of g. When processing file B, the compiler outputs the (relative) address of g. This is called the definition of g. The assembler passes this information to the linker.

The simplest linker technique is to again make two passes. During the first pass, the linker records in its external symbol table (a table of external symbols, not a symbol table that is stored externally) all the definitions encountered. During the second pass, every use can be resolved by access to the table.

I cover the linker in more detail when I teach 2250, OS Design. You can find my class notes for OS Design starting at my home page.


After the linker has done its work, the resulting executable file can be loaded by the operating system into central memory. The details are OS dependent. With early single-user operating systems all programs would be loaded into a fixed address (say 0) and the loader simply copies the file to memory. Today it is much more complicated since (parts of) many programs reside in memory at the same time. Hence the compiler/assembler/linker cannot know the real location for an identifier. Indeed, this real location can change.

More information is given in any OS course.


1.2: The Structure of a Compiler

Modern compilers contain two (large) parts, each of which is often subdivided. These two parts are the front end, shown in green on the right and the back end, shown in pink.

The front end analyzes the source program, determines its constituent parts, and constructs an intermediate representation of the program. Typically the front end is independent of the target language.

The back end synthesizes the target program from the intermediate representation produced by the front end. Typically the back end is independent of the source language.

This front/back division very much reduces the work for a compiling system that can handle several (N) source languages and several (M) target languages. Instead of NM compilers, we need N front ends and M back ends. For gcc (originally abbreviating Gnu C Compiler, but now abbreviating Gnu Compiler Collection), N=7 and M~30 so the savings are considerable.

Other analyzers and synthesizers

Other compiler like applications also use analysis and synthesis. Some examples include

  1. Pretty printer: Can be considered a real compiler with the target language a formatted version of the source.
  2. Interpreter. The synthesis traverses the intermediate code and executes the operation at each node (rather than generating machine code to do such).

Multiple Phases

The front and back end are themselves each divided into multiple phases. Conceptually, the input to each phase is the output of the previous. Sometime a phase changes the representation of the input. For example, the lexical analyzer converts a character stream input into a token stream output. Sometimes the representation is unchanged. For example, the machine-dependent optimizer transforms target-machine code into (hopefully improved) target-machine code.

The diagram is definitely not drawn to scale, in terms of effort or lines of code. In practice, the optimizers dominate.

Conceptually, there are three phases of analysis with the output of one phase the input of the next. Each of these phases changes the representation of the program being compiled. The phases are called lexical analysis or scanning, which transforms the program from a string of characters to a string of tokens; syntax analysis or parsing, which transforms the program into some kind of syntax tree; and semantic analysis, which decorates the tree with semantic information.

Note that the above classification is conceptual; in practice more efficient representations may be used. For example, instead of having all the information about the program in the tree, tree nodes may point to symbol table entries. Thus the information about the variable counter is stored once and pointed to at each occurrence.

1.2.1: Lexical Analysis (or Scanning)

The character stream input is grouped into meaningful units called lexemes, which are then mapped into tokens, the latter constituting the output of the lexical analyzer. For example, any one of the following C statements

    x3 = y + 3;
    x3  =   y   +   3   ;
    x3   =y+ 3  ;
but not
    x 3 = y + 3;
would be grouped into the lexemes x3, =, y, +, 3, and ;.

A token is a <token-name,attribute-value> pair. For example

  1. The lexeme x3 would be mapped to a token such as <id,1>. The name id is short for identifier. The value 1 is the index of the entry for x3 in the symbol table produced by the compiler. This table is used gather information about the identifiers and to pass this information to subsequent phases.
  2. The lexeme = would be mapped to the token <=>. In reality it is probably mapped to a pair, whose second component is ignored. The point is that there are many different identifiers so we need the second component, but there is only one assignment symbol =.
  3. The lexeme y is mapped to the token <id,2>
  4. The lexeme + is mapped to the token <+>.
  5. The lexeme 3 is somewhat interesting and is discussed further in subsequent chapters. It is mapped to <number,something>, but what is the something. On the one hand there is only one 3 so we could just use the token <number,3>. However, there can be a difference between how this should be printed (e.g., in an error message produced by subsequent phases) and how it should be stored (fixed vs. float vs. double). Perhaps the token should point to the symbol table where an entry for this kind of 3 is stored. Another possibility is to have a separate numbers table.
  6. The lexeme ; is mapped to the token <;>.

Note that non-significant blanks are normally removed during scanning. In C, most blanks are non-significant. That does not mean the blanks are unnecessary. Consider

    int x;
The blank between int and x is clearly necessary, but it does not become part of any token. Blanks inside strings are an exception, they are part of the token (or more likely the table entry pointed to by the second component of the token).

Note that we can define identifiers, numbers, and the various symbols and punctuation without using recursion (compare with parsing below).


1.2.2: Syntax Analysis (or Parsing)

Parsing involves a further grouping in which tokens are grouped into grammatical phrases, which are often represented in a parse tree. For example

    x3 = y + 3;
would be parsed into the tree on the right.

This parsing would result from a grammar containing rules such as

    asst-stmt → id = expr ;
    expr      → number
              |  id
              |  expr + expr

Note the recursive definition of expression (expr). Note also the hierarchical decomposition in the figure on the right.

The division between scanning and parsing is somewhat arbitrary, in that some tasks can be accomplished by either. However, if a recursive definition is involved, it is considered parsing not scanning. syntax tree

Often we utilize a simpler tree called the syntax tree (more properly the abstract syntax tree with operators as interior nodes and operands as the children of the operator. The syntax tree on the right corresponds to the parse tree above it. We expand on this point later.

(Technical point.) The syntax tree shown represents an assignment expression not an assignment statement. In C an assignment statement includes the trailing semicolon. That is, in C (unlike in Algol) the semicolon is a statement terminator not a statement separator.

1.2.3: Semantic Analysis


There is more to a front end than simply syntax. The compiler needs semantic information, e.g., the types (integer, real, pointer to array of integers, etc) of the objects involved. This enables checking for semantic errors and inserting type conversion where necessary.

For example, if y was declared to be a real and x3 an integer, we need to insert (unary, i.e., one operand) conversion operators inttoreal and realtoint as shown on the right.

In this class we will use three-address-code for our intermediate language; another possibility that is used is some kind of syntax tree.

1.2.4: Intermediate code generation

Many compilers internally generate intermediate code for an idealized machine. For example, the intermediate code generated would assume that the target has an unlimited number of registers and that any register can be used for any operation. You can just as well think of this model as a machine with no registers, but which permits operations to be directly performed on memory locations. Another common assumption is that machine operations take (up to) three operands: two source and one target.

With these assumptions of a machine with an unlimited number of registers and instructions with three operands, one generates three-address code by walking the semantic tree. Our example C instruction would produce

    temp1 = inttoreal(3)
    temp2 = id2 + temp1
    temp3 = realtoint(temp2)
    id1 = temp3

We see that three-address code can include instructions with fewer than 3 operands.

Sometimes three-address code is called quadruples because one can view the previous code sequence as

    inttoreal temp1 3     --
    add       temp2 id2   temp1
    realtoint temp3 temp2 --
    assign    id1   temp3 --
Each quad has the form
    operation  target source1 source2

1.2.5: Code optimization

This is a very serious subject, one that we will not really do justice to in this introductory course. Some optimizations are fairly easy to see.

  1. Since 3 is a constant, the compiler can perform the int to real conversion and replace the first two quads with
    	add       temp2 id2  3.0
  2. The last two quads can be combined into
    	realtoint id1   temp2

In addition to optimizations performed on the intermediate code, further optimizations can be performed on the machine code by the machine-dependent back end.

1.2.6: Code generation

Modern processors have only a limited number of register. Although some processors, such as the x86, can perform operations directly on memory locations, we will for now assume only register operations. Some processors (e.g., the MIPS architecture) use three-address instructions. We follow this model. Other processors permit only two addresses; the result overwrites one of the sources. Using three-address instructions restricted to registers (except for load and store instructions, which naturally must also reference memory), code something like the following would be produced for our example, after first assigning memory locations to id1 and id2.

    LD   R1,  id2
    ADDF R1,  R1, #3.0    // add float
    RTOI R2,  R1          // real to int
    ST   id1, R2

1.2.7: Symbol-Table Management

The symbol table stores information about program variables that will be used across phases. Typically, this includes type information and storage locations.

A possible point of confusion: the storage location does not give the location where the compiler has stored the variable. Instead, it gives the location where the compiled program will store the variable.

1.2.8: The Grouping of Phases into Passes

Logically each phase is viewed as a separate pass, i.e., a program that reads input and produces output for the next phase. The phases thus form a pipeline. In practice some phases are combined into a pass.

For example one could have the entire front end as one pass.

The term pass is used to indicate that the entire input is read during this activity. So two passes, means that the input is read twice. A grayed out (optional) portion of the notes above discusses 2-pass approaches for both assemblers and linkers. If we implement each phase separately and possibly use multiple passes for some of them, the compiler will perform a large number of I/O operations, an expensive undertaking.

As a result, techniques have been developed to reduce the number of passes. We will see in the next chapter how to combine the scanner, parser, and semantic analyzer into one phase. Consider the parser. When it needs to input the next token, rather than reading the input file (presumably produced by the scanner), the parser calls the scanner instead. At selected points during the production of the syntax tree, the parser calls the intermediate-code generator which performs semantic analysis as well as generating a portion of the intermediate code.

For pedagogical reasons, we will not be employing this technique. That is to ease the programming and understanding, we will use a compiler design that performs more I/O than necessary. Naturally, production compilers do not do this. Thus your compiler will consist of separate programs for the scanner, parser, and semantic analyzer / intermediate code generator. Indeed, these will likely be labs 2, 3, and 4.

Reducing the number of passes

One problem with combining phases, or with implementing a single phase in one pass, is that it appears that an internal form of the entire program being compiled will need to be stored in memory. This problem arises because the downstream phase may need, early in its execution, information that the upstream phase produces only late in its execution. This motivates the use of symbol tables and a two pass approach in which the symbol table is produced during the first pass and used during the second pass. However, a clever one-pass approach is often possible.

Consider an assembler (or linker). The good case is when a symbol definition precedes all its uses so that the symbol table contains the value of the symbol prior to that value being needed. Now consider the harder case of one or more uses preceding the definition. When a not-yet-defined symbol is first used, an entry is placed in the symbol table, pointing to this use and indicating that the definition has not yet appeared. Further uses of the same symbol attach their addresses to a linked list of undefined uses of this symbol. When the definition is finally seen, the value is placed in the symbol table, and the linked list is traversed inserting the value in all previously encountered uses. Subsequent uses of the symbol will find its definition in the table.

This technique is called backpatching.

1.2.9: Compiler-construction tools

Originally, compilers were written from scratch, but now the situation is quite different. A number of tools are available to ease the burden.

We will mention tools that generate scanners and parsers. This will involve us in some theory: regular expressions for scanners and context-free grammars for parsers. These techniques are fairly successful. One drawback can be that they do not execute as fast as hand-crafted scanners and parsers.

We will also see tools for syntax-directed translation and automatic code generation. The automation in these cases is not as complete.

Finally, there is the large area of optimization. This is not automated; however, a basic component of optimization is data-flow analysis (how values are transmitted between parts of a program) and there are tools to help with this task.

Pedagogically, a problem with using the tools is that your effort shifts from understanding how a compiler works to how the tool is used. So instead of studying regular expressions and finite state automata, you study the flex man pages and user's guide.

Error detection and reporting

As you have doubtless noticed, not all programming efforts produce correct programs. If the input to the compiler is not a legal source language program, errors must be detected and reported. It is often much easier to detect that the program is not legal (e.g., the parser reaches a point where the next token cannot legally occur) than to deduce what is the actual error (which may have occurred earlier). It is even harder to reliably deduce what the intended correct program should be.

1.3: The Evolution of Programming Languages

1.3.1: The Move to Higher-level Languages

Skipped. Assumed knowledge (only one page).

1.3.2: Impacts on Compilers

High performance compilers (i.e., the code generated performs well) are crucial for the adoption of new language concepts and computer architectures. Also important is the resource utilization of the compiler itself.

Modern compilers are large. On my laptop the compressed source of gcc is 38MB so uncompressed it must be about 100MB.

1.4: The Science of Building a Compiler

1.4.1: Modeling in Compiler Design and Implementation

We will encounter several aspects of computer science during the course. Some, e.g., trees, I'm sure you already know well. Other, more theoretical aspects, such as nondeterministic finite automata, may be new.

1.4.2: The Science of Code Optimization

We will do very little optimization. That topic is typically the subject of a second compiler course. Considerable theory has been developed for optimization, but sadly we will see essentially none of it. We can, however, appreciate the pragmatic requirements.

1.5: Applications of Compiler Technology

1.5.1: Implementation of High-Level Programming Languages

1.5.2: Optimization for Computer Architectures


For 50+ years some computers have had multiple processors internally. The challenge with such multiprocessors is to program them effectively so that all the processors are utilized efficiently.

Recently, multiprocessors have become commodity items, with multiple processors (cores) on a single chip.

Major research efforts have lead to improvements in

Memory Hierarchies

All machines have a limited number of registers, which can be accessed much faster than central memory. All but the simplest compilers devote effort to using this scarce resource effectively. Modern processors have several levels of caches and advanced compilers produce code designed to utilize the caches well.

1.5.3: Design of New Computer Architectures

RISC (Reduced Instruction Set Computer)

RISC computers have comparatively simple instructions, complicated instructions require several RISC instructions. A CISC, Complex Instruction Set Computer, contains both complex and simple instructions. A sequence of CISC instructions would be a larger sequence of RISC instructions. Advanced optimizations are able to find commonality in this larger sequence and lower the total number of instructions. The CISC Intel x86 processor line 8086/80286/80386/... had a major implementation change with the 686 (a.k.a. pentium pro). In this processor, the CISC instructions were decomposed into RISC instructions by the processor itself. Currently, code for x86 processors normally achieves highest performance when the (optimizing) compiler emits primarily simple instructions.

Specialized Architectures

A great variety has emerged. Compilers are produced before the processors are fabricated. Indeed, compilation plus simulated execution of the generated machine code is used to evaluate proposed designs.

1.5.4: Program Translations

Binary Translation

This means translating from one machine language to another. Companies changing processors sometimes use binary translation to execute legacy code on new machines. Apple did this when converting from Motorola CISC processors to the PowerPC.

An alternative to binary translation is to have the new processor execute programs in both the new and old instruction set. Intel had the Itanium processor also execute x86 code. Digital Equipment Corp (DEC) had their VAX processor also execute PDP-11 instructions. Apple, does not produce processors so needed binary translation for the MIPS→PowerPC transition

With the recent dominance of x86 processors, binary translators from x86 have been developed so that other microprocessors can be used to execute x86 software.

Hardware Synthesis

In the old days integrated circuits were designed by hand. For example, the NYU Ultracomputer research group in the 1980s designed a VLSI chip for rapid interprocessor coordination. The design software we used essentially let you paint. You painted blue lines where you wanted metal, green for polysilicon, etc. Where certain colors crossed, a transistor appeared.

Current microprocessors are much too complicated to permit such a low-level approach. Instead, designers write in a high level description language which is compiled down the specific layout.

Database Query Interpreters

The optimization of database queries and transactions is quite a serious subject.

Compiled Simulation

Instead of simulating a processor designs on many inputs, it may be faster to compile the design first into a lower level representation and then execute the compiled version.

1.5.5: Software Productivity Tools

Dataflow techniques developed for optimizing code are also useful for finding errors. Here correctness (finding all errors and only errors) is not a requirement, which is a good thing since that problem is undecidable.

Type Checking

Techniques developed to check for type correctness (we will see some of these) can be extended to find other errors such as using an uninitialized variable.

Bounds Checking

As mentioned above optimizations have been developed to eliminate unnecessary bounds checking for languages like Ada and Java that perform the checks automatically. Similar techniques can help find potential buffer overflow errors that can be a serious security threat.

Memory-Management Tools

Languages (e.g., Java) with garbage collection cannot have memory leaks (failure to free no longer accessible memory). Compilation techniques can help to find these leaks in languages like C that do not have garbage collection.

1.6: Programming Language Basics

Skipped (prerequisite).

Remark: You should be able to do the exercises in this section (but they are not assigned).

Chapter 2: A Simple Syntax-Directed Translator

Homework: Read chapter 2.

The goal of this chapter is to implement a very simple compiler. Really we are just going as far as the intermediate code, i.e., the front end. Nonetheless, the output, i.e. the intermediate code, does look somewhat like assembly language.

How is this possible to do in just one chapter?
What is the rest of the book/course about?

In this chapter there is

  1. A simple source language.
  2. A target close to the source.
  3. No optimization.
  4. No machine-dependent back end.
  5. No tools.
  6. Little theory.

The material will be presented too fast for full understanding: Starting in chapter 3, we slow down and explain everything.

Sometimes in chapter 2, we only show some of the possibilities (typically omitting the hard cases) and don't even mention the omissions. Again, this is corrected in the remainder of the course.

A weakness of my teaching style is that I spend too long on chapters like this. I will try not to make that mistake this semester, but I have said that before.

2.1: Introduction

We will be looking at the front end, i.e., the analysis portion of a compiler.

The syntax describes the form of a program in a given language, while the semantics describes the meaning of that program. We will learn the standard representation for the syntax, namely context-free grammars also called BNF (Backus-Naur Form).

We will learn syntax-directed translation, where the grammar does more than specify the syntax. We augment the grammar with attributes and use this to guide the entire front end.

The front end discussed in this chapter has as source language infix expressions consisting of digits, +, and -. The target language is postfix expressions with the same components.

For example, the compiler will convert 7+4-5 to 74+5-. Actually, our simple compiler will handle a few other operators as well.

We will tokenize the input (i.e., write a scanner), model the syntax of the source, and let this syntax direct the translation all the way to three-address code, our intermediate language.

2.2: Syntax Definition

2.2.1: Definition of Grammars

This will be done right in the next two chapters.

A context-free grammar (CFG) consists of

  1. A set of terminal tokens.
  2. A set of nonterminals.
  3. A set of productions (rules for transforming nonterminals). These are written
        LHS → RHS
    where the LHS is a single nonterminal (that is why this is a context-free) and the RHS is a string containing nonterminals and/or terminals.
  4. A specific nonterminal designated as start symbol.


    Terminals: 0 1 2 3 4 5 6 7 8 9 + -
    Nonterminals: list digit
    Productions: list → list + digit
    list → list - digit
    list → digit
    digit → 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
    Start symbol: list

We use | to indicate that a nonterminal has multiple possible right hand side. So

    A → B | C
is simply shorthand for
    A → B
    A → C

If no start symbol is specifically designated, the LHS of the first production is the start symbol.

2.2.2: Derivations

Watch how we can generate the string 7+4-5 beginning with the start symbol, applying productions, and stopping when no productions can be applied (because only terminals remain).

    list → list - digit
         → list - 5
         → list + digit - 5
         → list + 4 - 5
         → digit + 4 - 5
         → 7 + 4 - 5

This process of applying productions, starting with the start symbol and ending when only terminals are present is called a derivation and we say that the final string has been derived from the initial string (in this case the start symbol).

The set of all strings derivable from the start symbol is the language generated by the CFG

Given a grammar, parsing a string (of terminals) consists of determining if the string is in the language generated by the grammar. If it is in the language, parsing produces a derivation. If it is not, parsing reports an error.

The opposite of derivation is reduction. Given a production, the LHS produces the RHS (a derivation) and the RHS is reduced to the LHS (a reduction).

Ignoring errors for the moment, parsing a string means reducing the string to the start symbol or equivalently deriving the string from the start symbol.

Homework: 1a, 1c, 2a-c (don't worry about justifying your answers).

Remark: Since we are in section 2.2 these questions are in section 2.2.7.

2.2.3: Parse trees


While deriving 7+4-5, one could produce the Parse Tree shown on the right.

You can read off the productions from the tree. For any internal (i.e., non-leaf) tree node, its children give the right hand side (RHS) of a production having the node itself as the LHS.

The leaves of the tree, read from left to right, is called the yield of the tree. We say that this string is derived from the (nonterminal at the) root, or is generated by the root, or can be reduced to the root. The tree on the right shows that 7+4-5 can be derived from list.

Homework: 1b

2.2.4: Ambiguity

An ambiguous grammar is one in which there are two or more parse trees yielding the same final string. We wish to avoid such grammars.

The grammar above is not ambiguous. For example 1+2+3 can be parsed only one way; the arithmetic must be done left to right. Note that I am not giving a rule of arithmetic, just of this grammar. If you reduced 2+3 to list you would be stuck since it is impossible to further reduce 1+list (said another way it is not possible to derive 1+list from the start symbol).

The following is a wrong proof of ambiguity. Consider the grammar
S → A B
A → x
B → x
This grammar is ambiguous because we can derive the string x x in two ways
S → A B → A x → x x
S → A B → x B → x x
There are two derivations, but they have the same parse tree!
End of Remark.

Homework: 3 (applied only to parts a, b, and c of 2)

2.2.5: Associativity of operators

Our grammar gives left associativity. That is, if you traverse the parse tree in postorder and perform the indicated arithmetic you will evaluate the string left to right. Thus 8-8-8 would evaluate to -8. If you wished to generate right associativity (normally exponentiation is right associative, so 2**3**2 gives 512 not 64), you would change the first two productions to

  list → digit + list
  list → digit - list

Draw in class the parse tree for 7+4-5 with this new grammar.

2.2.6: Precedence of operators

We normally want * to have higher precedence than +. We do this by using an additional nonterminal to indicate the items that have been multiplied. The example below gives the four basic arithmetic operations their normal precedence unless overridden by parentheses. Redundant parentheses are permitted. Equal precedence operations are performed left to right.

  expr   → expr + term | expr - term | term
  term   → term * factor | term / factor | factor
  factor → digit | ( expr )
  digit  → 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

Do the examples 1+2/3-4*5 and (1+2)/3-4*5 on the board.

Note how the precedence is enforced by the grammar; slick!