INTRODUCTION

Languages and Compilers

Outline

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Programming Languages

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Syntax

Describe correct forms of language constructs. In English, a sentence is composed of the

subject part and the verb part, as shown below.

In a programming language, the syntax describes what a program, a statement, an expression, etc. are composed of.

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Semantics

Operational semantics Describe the meaning of a program by telling how

a computer executes the program. Based on the model of computers.

Axiomatic semantics Describe the meaning of a program by telling the

“condition” before and after the execution of the program.

Conditions are expressed in predicates or assertions.

Denotational semantics Meaning of a program is a function from a

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Operational Semantics

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Describe the meaning by the sequence of operations executing for programs.

Example: A=B+C; move r1, mem[addr B] add r3, r1, r2move r2, mem[addr C] load mem[addr A], r3

Operations are based on some machine. Good for programmers to understand

programs. Difficult to define in detail, due to machine

dependency.

Axiomatic Semantics

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Pre-post form: {P} statement {Q} An example: a = b + 1 {a > 1}

One possible precondition: {b > 10}

Weakest precondition: {b > 0} An axiom for assignment statements (x

= E): {QxE} x = E {Q}

Example: {y*y-9>0} x=y*y-9 {x>0}

{y>3 or y<-3} x=y*y-9 {x>0}

Axiomatic Semantics

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Inference rule:

{P} S {Q} and P’=> P and Q => Q’

Then, {P’} S {Q’}.

Example:

Let {y > 3 or y < -3} x=y*y-9 {x > 0}.

Then, {y < -3} x=y*y-9 {x> -9} (because y < -3 implies y>3 or y < -3 and x> 0 implies x>-9).

Axiomatic Semantics

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An inference rule for sequencesFor a sequence S1;S2:

{P1} S1 {P2}

{P2} S2 {P3}

the inference rule is:

Axiomatic Semantics

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An inference rule for logical pretest loopsFor the loop construct:

{P} while B do S end {Q} the inference rule is:

where I is the loop invariant (the inductive hypothesis)

Characteristics of the loop invariant

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Loop invariant I must meet the following conditions: P => I (the loop invariant must be true initially) {I} B {I}

Evaluation of Boolean must not change the validity of I

{I and B} S {I}

I is not changed by executing the body of the loop (I and (not B)) => Q

If I is true and B is false, Q is implied. The loop terminates (this can be difficult to

prove)

Denotational Semantics

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The state of a program is the values of all its current variables

s = {<i1, v1>, <i2, v2>, …, <in, vn>} Let VARMAP be a function that, when given

a variable name and a state, returns the current value of the variable

VARMAP(ij, s) = vj

The meaning of a program is a function mapping the program construct to the state of the program.

Denotational Semantics

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<dec_num> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | <dec_num> (0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9)

Mdec('0') = 0,

Mdec ('1') = 1, …,

Mdec ('9') = 9

Mdec (<dec_num> '0') = 10 * Mdec (<dec_num>)

Mdec (<dec_num> '1’) = 10 * Mdec (<dec_num>) + 1…

Mdec (<dec_num> '9') = 10 * Mdec (<dec_num>) + 9

Denotational Semantics

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Me(<expr>, s) : case <expr> of <dec_num> => Mdec(<dec_num>, s) <var> => if VARMAP(<var>, s) == undef then error else VARMAP(<var>, s) <binary_expr> => if (Me(<binary>.<left_expr>, s)==undef OR Me(<binary_expr>.<right_expr>, s)==undef) then error

else if (<binary_expr>.<operator> == ‘+’) then Me(<binary_expr>.<left_expr>, s) + Me(<binary_expr>.<right_expr>, s) else Me(<binary_expr>.<left_expr>, s) * Me(<binary_expr>.<right_expr>, s)...

Paradigms in Programming languages

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Imperative Languages

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Programs specify steps of what to do. Major concepts are

Variables Control flows

Examples: FORTRAN Pascal C

Object-oriented Languages

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Major concepts are Objects Control flows

Objects have Attributes Methods Inheritance

Logic Programs

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Programs are definitions of what “things” are.

Running the program is to infer from the definitions what the answer are.

Example of Logic Programs

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sort([],[]).sort(A,B) :- half(A,X,Y), sort(X,M), sort(Y,N),

merge(M,N,B).half([],[],[]).half([A], [A],[]).half([A,B|R], [A|R1], [B|R2]) :- half(R, R1, R2).merge(A, [], A).merge([], A, A).merge([X|A], [Y|B], [X|Z]) :- X<Y, merge(A, [Y|B], Z).merge([X|A], [Y|B], [Y|Z]) :- X>=Y, merge([X|A], B, Z).

Functional Languages

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A program is a collection of mathematical functions.

A function is a composition of functions. The execution of a program is the application

of a function (mostly) on some data. Functions produce results which are used by

other functions. There is no variable in pure functional

languages. No side effect.

Functional Languages

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Functions are a basic data type. Functions can be passed as parameters. Examples:

LISP: a functional language with list as a basic data type

Scheme: a variation of LISP ML Haskell

Example of Functional Program

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sort [] = []sort (h : t) = sort [b | b<-t, b<=h] ++ h ++ sort[b | b <-t, b>h].

Language Processors

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Phases of Compilers

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Compiler Process

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