• Introduction
• 1. 1.Introduction
• 2. 2.A Simple Syntax-Directed Translator
• 3. 3.Lexical Analysis
• 4. 4.Syntax Analysis
• 5. 5.Syntax-Directed Translation
• 6. 6.Intermediate-Code Generation
• 7. 7.Run-Time Environments
• 8. 8.Code Generation
• 9. 12.InterProcedural Analysis
• Published with GitBook

# 2.3 Exercises for Section 2.3

### 2.3.1

Construct a syntax-directed translation scheme that translates arithmetic expressions from infix notation into prefix notation in which an operator appears before its operands; e.g. , -xy is the prefix notation for x - y. Give annotated parse trees for the inputs 9-5+2 and 9-5*2.

productions:

``````expr -> expr + term
| expr - term
| term
term -> term * factor
| term / factor
| factor
factor -> digit | (expr)
``````

translation schemes:

``````expr -> {print("+")} expr + term
| {print("-")} expr - term
| term
term -> {print("*")} term * factor
| {print("/")} term / factor
| factor
factor -> digit {print(digit)}
| (expr)
``````

### 2.3.2

Construct a syntax-directed translation scheme that translates arithmetic expressions from postfix notation into infix notation. Give annotated parse trees for the inputs 95-2 and 952-.

productions:

``````expr -> expr expr +
| expr expr -
| expr expr *
| expr expr /
| digit
``````

translation schemes:

``````expr -> expr {print("+")} expr +
| expr {print("-")} expr -
| {print("(")} expr {print(")*(")} expr {print(")")} *
| {print("(")} expr {print(")/(")} expr {print(")")} /
| digit {print(digit)}
``````

``````E -> {print("(")} E {print(op)} E {print(")"}} op | digit {print(digit)}
``````

### 2.3.3

Construct a syntax-directed translation scheme that translates integers into roman numerals.

assistant function:

``````repeat(sign, times) // repeat('a',2) = 'aa'
``````

translation schemes:

``````num -> thousand hundred ten digit
{ num.roman = thousand.roman || hundred.roman || ten.roman || digit.roman;
print(num.roman)}
thousand -> low {thousand.roman = repeat('M', low.v)}
hundred -> low {hundred.roman = repeat('C', low.v)}
| 4 {hundred.roman = 'CD'}
| high {hundred.roman = 'D' || repeat('X', high.v - 5)}
| 9 {hundred.roman = 'CM'}
ten -> low {ten.roman = repeat('X', low.v)}
| 4 {ten.roman = 'XL'}
| high {ten.roman = 'L' || repeat('X', high.v - 5)}
| 9 {ten.roman = 'XC'}
digit -> low {digit.roman = repeat('I', low.v)}
| 4 {digit.roman = 'IV'}
| high {digit.roman = 'V' || repeat('I', high.v - 5)}
| 9 {digit.roman = 'IX'}
low -> 0 {low.v = 0}
| 1 {low.v = 1}
| 2 {low.v = 2}
| 3 {low.v = 3}
high -> 5 {high.v = 5}
| 6 {high.v = 6}
| 7 {high.v = 7}
| 8 {high.v = 8}
``````

### 2.3.4

Construct a syntax-directed translation scheme that trans­ lates roman numerals into integers.

productions:

``````romanNum -> thousand hundred ten digit
thousand -> M | MM | MMM | ε
hundred -> smallHundred | C D | D smallHundred | C M
smallHundred -> C | CC | CCC | ε
ten -> smallTen | X L | L smallTen | X C
smallTen -> X | XX | XXX  | ε
digit -> smallDigit | I V | V smallDigit | I X
smallDigit -> I | II | III | ε
``````

translation schemes:

``````romanNum -> thousand hundred ten digit {romanNum.v = thousand.v || hundred.v || ten.v || digit.v; print(romanNun.v)}
thousand -> M {thousand.v = 1}
| MM {thousand.v = 2}
| MMM {thousand.v = 3}
| ε {thousand.v = 0}
hundred -> smallHundred {hundred.v = smallHundred.v}
| C D {hundred.v = smallHundred.v}
| D smallHundred {hundred.v = 5 + smallHundred.v}
| C M {hundred.v = 9}
smallHundred -> C {smallHundred.v = 1}
| CC {smallHundred.v = 2}
| CCC {smallHundred.v = 3}
| ε {hundred.v = 0}
ten -> smallTen {ten.v = smallTen.v}
| X L  {ten.v = 4}
| L smallTen  {ten.v = 5 + smallTen.v}
| X C  {ten.v = 9}
smallTen -> X {smallTen.v = 1}
| XX {smallTen.v = 2}
| XXX {smallTen.v = 3}
| ε {smallTen.v = 0}
digit -> smallDigit {digit.v = smallDigit.v}
| I V  {digit.v = 4}
| V smallDigit  {digit.v = 5 + smallDigit.v}
| I X  {digit.v = 9}
smallDigit -> I {smallDigit.v = 1}
| II {smallDigit.v = 2}
| III {smallDigit.v = 3}
| ε {smallDigit.v = 0}
``````

### 2.3.5

Construct a syntax-directed translation scheme that translates postfix arithmetic expressions into equivalent prefix arithmetic expressions.

``````expr -> expr expr op | digit
``````expr -> {print(op)} expr expr op | digit {print(digit)}