Postfix arithmetic

Operators, in postfix arithmetical expressions, follow operands. For example, $34+$ means $3+4.$

The postfix expression $345+*$ is evaluated as follows:

$345+*$

$39*($replace $45+$ with the result of adding $4$ to $5)$

$27($replace $39*$ with $27)$

Postfix expressions are conveniently evaluated using a stack. An expression consisting of

operands and operators $($collectively$,$tokens$),$ is read from left to right. Successive operands are

pushed on a stack until an operator arrives. The appropriate number of operands are then popped

from the stack, combined with the operator, and the result is pushed back on the stack. The result

of a calculation is always to be found at the top of the stack. A stack is notated $[$a b c$...]$ in the

following example; the stack top is the leftmost token.

Postfix with variables

The $++$ refers to an enhanced form of postfix: a postfix with variables. Expressions can contain

variable names; the value of the variable is used for the calculation. The assignment operator $=$

assigns a value to a variable. For example

A $3=$

will set the value of A to $3.$ It is equivalent to the infix assignment statement A $=3$ that is to be

found in many computer languages.

Tokens Stack before Action Stack after

$345+*[]$ Read $3[3]$

$45+*[3]$ Read $4[43]$

$5+*[43]$ Read $5[543]$

$+*[543]$ Pop twice, evaluate, and

push

$[93]$

$*$ Pop two twice, evaluate,

and push

$[27]$

An interactive session might proceed as follows

$>$ A $2=$

$[]$

$>$ B $3=$

$[]$

$>$A B $*$

$[6]$

Symbol Table

A symbol table data structure associates keys with values. For example,

A generic symbol table should support two operations, INSERT and SEARCH. There may also be

a DELETE operation. No assumptions are made on the type and format of keys and values.

You will need a symbol table in your Postfix$++$ interpreter. The table will map variable name $($key$)$

to value.

The target hardware

A Postfix$++$ interpreter might run on a small device with very limited memory. This means that the

variable namespace is small, for example, $$A$-$Z$.$

Work plan

You must consider what data structures and algorithms are required in your Postfix$++$ interpreter.

Phase $1$: Design

Tokens Stack before Action Stack after

A $3=[]$ Read A $[$A$]$

$3=[$A$]$ Read $3[3$ A$]$

$=[3$ A$]$ Pop twice and set the

value of A to $3$

$[]$

Example Key Value

Phone book Name Telephone number

DNS URL IP address

Education Student ID Module grades

Compiler Variable name Memory address

Dictionary Word Definition

Consider first your choice of data structures. Why are they appropriate? How will they be

implemented? Make a list of the data structures and alongside each structure write a few words

of justification.

Then consider the major algorithms. There be will algorithms to access and modify the symbol

table, and an algorithm to perform postfix arithmetic. Your report will contain pseudocode for

each algorithm.

Phase $2$: Implementation

You can use any language you wish. Javascript or C$++$ are good choices.