Assignment 3 Solution Background

• Constant Expression : Infix to postfix2 + 3 * 4

( 2 + (3 * 4 ) )

2 3 4 * +

• Evaluating postfix expression using stack| 2 |

| 2 | 3 | 4 |

| 2 | 12 |

|14|

• Evaluating postfix expression using stack| 2 |

| 2 | 3 | 4 |

| 2 | 12 |

|14|

• Compiling constant expression for a stack machine

Push 2

Push 3

Push 4

Mul

Add

• Generalizing to expressions with variables

i + j * k Push i

Push j

Push k

Mul

Add

• Conversion to abstract syntax tree

+

i *

j k

• Generalizing to expressions with variables

i + j * k Push i

Push j

Push k

Mul

Add

• Byte code generation for static f(int i,j,k) iload_0

iload_1

iload_2

imul

iadd

Byte code for i + j + k for static f(int i,j,k)

• Right associative “+”

iload_0

iload_1

iload_2

iadd

iadd

• Left associative “+”

iload_0

iload_1

iadd

iload_2

iadd

• Introducing numeric types with real variables a + b

Push a

Push b

Add

• Byte code generation for static f(double a,b) dload_0

dload_2

dadd

• Mixing int and double variables (requiring coercion code) for static f(double a,int i, j)

i + j * a iload_2

i2d

iload_3

i2d

dload_0

dmul

dadd

• Translation algorithm essence

trans (e1 * e2) =

trans(e1)

[type coercion code?]

trans(e2)

[type coercion code?]

trans(*)

• Map grammar rules to control structures– E.g., alternatives, while-loop, etc