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For a change I’ll start with the output rather than the code. This is a calculator that uses RPN (reverse polish notation), this is where the operator follows the numbers, so instead of 2 + 2, you have 2 2 +.

 

RPN expression:?
RPN Calculator (Simple Forth)
Enter expressions in reverse polish notation with spaces between each token
For example 2+3 in reverse polish is 2 3 +, you have the basic mathematic
operations available, +,-,*,/ in addition to % (modulo) ** (power)
You also have the sin,cos,tan and log. You can store a value in a variable
with var name, and retrieve the value with just using name. e and pi are already
defined for you. There are 2 user defined functions that are also already defined
fahrenheit which converts degrees centigrade to fahrenheit and the reverse.
You can define you own words, with def, so to make a shorter version of
fahrenheit, you can just use def f fahrenheit : . You can see all the words
already defined with words. ? will bring up this help, int will convert a value
to it's integer, exit or quit will end the program. You shouldn't need them, but
dup duplicates the top stack entry, and swap, swaps the top 2 entries around.
You can enter numbers in hexadecimal by prefixing then with $, and binary numbers
by prefixing them with %. You can show a number in binary with bin, or in
hexadecimal with hex.

RPN expression:3 4 -
-1.0
RPN expression:3 4 swap -
1.0
RPN expression:3 4 /
0.75
RPN expression:3 4 5 6 7 + * - /
-0.0491803278689
RPN expression:100 var boiling
RPN expression:boiling fahrenheit
212.0
RPN expression:def & and hex :
RPN expression:3 5 &
$1
RPN expression:255 43 &
$2b
RPN expression:255 bin
%11111111
RPN expression:words
fahrenheit : ['9', '*', '5', '/', '32', '+']
celsius : ['32', '-', '5', '*', '9', '/']
& : ['and', 'hex']
RPN expression:def deg 180 * pi / :
RPN expression:45 deg sin
0.806075491116
RPN expression:def deg pi * 180 / :
RPN expression:45 deg
0.785398163397
RPN expression:45 deg sin
0.707106781187
RPN expression:90 sin
0.893996663601
RPN expression:90 deg sin
1.0

3 4 – = -1 and 3 4 swap – = 1 because it swaps the top 2 values, so it is the same as 4 3 -.

100 var boiling means push 100 to the stack, then define a variable, named boiling. It is then
used in boiling fahrenheit (we could have written this as 100 fahrenheit). def & and hex : is used to
define a function, the def starts a function definition (& is used here), it uses and to and 2 values
together, and then hex to display the value and the : ends the definition. words lists the definitions
of the commands, including the 2 built in ones as well as any user defined ones. Trigonometry functions
use radians, so if want to use degrees a small function such as def deg 180 * pi / : allows you to do
45 deg sin to get the sin of 45 degrees. Ok, now lets get on with the code.

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rpn.py

import re,math

number = re.compile(r"-?[0-9]*\.?[0-9]+$|-?[0-9]+\.?[0-9]*$|\d+\.?\d*e[+-]?\d+",re.IGNORECASE)
hexnumber = re.compile(r"\$[0-9a-f]+$",re.IGNORECASE)
binarynumber = re.compile(r"%[01]+$")

words = {'celsius' : "32 - 5 * 9 /".split(), 'fahrenheit' : "9 * 5 / 32 +".split()}
vars = {'e' : math.e, 'pi' : math.pi}
stack = []

running = True

def pop():
    if len(stack):
        return stack.pop()
    else:
        print "ERROR: stack empty"
        return 0

def push(var):
    stack.append(var)

def quit(tokens):
    global running
    running = False

def add(tokens):
    left = pop()
    right = pop()
    push(left+right)

def subtract(tokens):
    right = pop()
    left = pop()
    push(left-right)

def multiply(tokens):
    left = pop()
    right = pop()
    push(left*right)

def divide(tokens):
    right = pop()
    left = pop()
    if right:
        push(left/right)
    else:
        print "ERROR: Division by zero"

def bit_and(tokens):
    right = pop()
    left = pop()
    push(int(left) & int(right))

def bit_or(tokens):
    right = pop()
    left = pop()
    push(int(left) | int(right))

def bit_xor(tokens):
    right = pop()
    left = pop()
    push(int(left) ^ int(right))

def bit_not(tokens):
    num = pop()
    push(~int(num))

def modulo(tokens):
    right = pop()
    left = pop()
    if right:
        push(left/right)
    else:
        print "ERROR: Modulo by zero"

def power(tokens):
    right = pop()
    left = pop()
    push(left**right)

def show(tokens):
    left = pop()
    print left
    push(left)

def duplicate(tokens):
    left = pop()
    push(left)
    push(left)

def pop_off(tokens):
    left = pop()

def list(tokens):
    print stack

def display_words(tokens):
    for word in words:
        print word,':',words[word]

def define(tokens):
    colon = tokens.index(':')
    if colon <= 0:
        print "ERROR: Invalid word defintion"
        return
    else:
        words[tokens[0]] = tokens[1:colon]
        return colon+1

def variable(tokens):
    vars[tokens[0]] = pop()
    return 1

def integer(tokens):
    left = pop()
    push(int(left))

def sin(tokens):
    left = pop()
    push(math.sin(left))

def cos(tokens):
    left = pop()
    push(math.cos(left))

def tan(tokens):
    left = pop()
    push(math.tan(left))

def log(tokens):
    left = pop()
    push(math.log(left))

def pop_off(tokens):
    pop()

def swap(tokens):
    left = pop()
    right = pop()
    push(left)
    push(right)

def hexadecimal(tokens):
    left = pop()
    hexval = hex(int(left))[2:]
    if hexval[-1] == 'L':
        hexval = hexval[:-1]
    print '$' + hexval

def binary(tokens):
    left = pop()
    print '%' + bin(int(left))[2:]

def help(tokens):
    print """RPN Calculator (Simple Forth)
Students who have doubts in Python can avail our online Python help chat.
Students seek assignment code in Python to solve their complex or simple 
assignment problems by contacting us with their python assignment questions. 
Beginners also seek our help saying ‘do my Python homework’ on live chat or 
email and then our experts guide them to solve their problem.

Enter expressions in reverse polish notation with spaces between each token
For example 2+3 in reverse polish is 2 3 +, you have the basic mathematic
operations available, +,-,*,/ in addition to % (modulo) ** (power)
You also have the sin,cos,tan and log. You can store a value in a variable
with var name, and retrieve the value with just using name. e and pi are already
defined for you. There are 2 user defined functions that are also already defined
fahrenheit which converts degrees centigrade to fahrenheit and the reverse.
You can define you own words, with def, so to make a shorter version of
fahrenheit, you can just use def f fahrenheit : . You can see all the words
already defined with words. ? will bring up this help, int will convert a value
to it's integer, exit or quit will end the program. You shouldn't need them, but
dup duplicates the top stack entry, and swap, swaps the top 2 entries around.
You can enter numbers in hexadecimal by prefixing then with $, and binary numbers
by prefixing them with %. You can show a number in binary with bin, or in
hexadecimal with hex.
"""

cmds = {'+' : add, '-' : subtract, '*' : multiply, '/' : divide, '%' : modulo, 'int' : integer, '**' : power,
        'and': bit_and, 'or' : bit_or, 'xor' : bit_xor, 'not' : bit_not,
        'sin' : sin, 'cos' : cos, 'tan' : tan, 'log' : log, 'hex' : hexadecimal, 'bin' : binary,
        '.' : show, 'dup' : duplicate, 'pop' : pop_off, 'list' : list, 'words' : display_words, 'def' : define,
        'var' : variable, '?' : help, 'exit' : quit, 'quit' : quit, 'swap' : swap}

def calc(expr):
    tokens = expr.lower().split()
    i = 0
    while i < len(tokens):
        token = tokens[i]
        i += 1
        if number.match(token):
            push(float(token))
        elif hexnumber.match(token):
            push(int(token[1:],16))
        elif binarynumber.match(token):
            push(int(token[1:],2))
        else:
            if token in cmds:
                if i < len(tokens):
                    tail = tokens[i:]
                else:
                    tail = []
                skip = cmds[token](tokens[i:])
                if skip:
                    i += skip
            elif token in vars:
                push(vars[token])
            elif token in words:
                pos = i
                for word in words[token]:
                    tokens.insert(pos,word)
                    pos += 1
            else:
                print "ERROR. Invalid token:",token

    if stack:
        return pop()

while (running):
    expr = raw_input("RPN expression:")
    expr = calc(expr)
    if expr != None:
        print expr

Global variables

number = re.compile(r"-?[0-9]*\.?[0-9]+$|-?[0-9]+\.?[0-9]*$|\d+\.?\d*e[+-]?\d+",re.IGNORECASE)
hexnumber = re.compile(r"\$[0-9a-f]+$",re.IGNORECASE)
binarynumber = re.compile(r"%[01]+$")

words = {'celsius' : "32 - 5 * 9 /".split(), 'fahrenheit' : "9 * 5 / 32 +".split()}
vars = {'e' : math.e, 'pi' : math.pi}
stack = []

number is a regular expression that allows 123, 123.45, 123.45e67 (so integer or floating point).

hexnumber is a hexadecimal value and binarynumber is for a binary value.

words is a dictionary with a couple of defined functions.

vars are constant numbers.

stack is where the temporary results are stored.

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Push and Pop

def pop():
    if len(stack):
        return stack.pop()
    else:
        print "ERROR: stack empty"
        return 0

def push(var):
    stack.append(var)

pop is used to get a result off the stack, and push, is used to push a number or a result.

Basic Mathematical Functions

def add(tokens):
    left = pop()
    right = pop()
    push(left+right)

def subtract(tokens):
    right = pop()
    left = pop()
    push(left-right)

def multiply(tokens):
    left = pop()
    right = pop()
    push(left*right)

def divide(tokens):
    right = pop()
    left = pop()
    if right:
        push(left/right)
    else:
        print "ERROR: Division by zero"

def bit_and(tokens):
    right = pop()
    left = pop()
    push(int(left) & int(right))

def bit_or(tokens):
    right = pop()
    left = pop()
    push(int(left) | int(right))

def bit_xor(tokens):
    right = pop()
    left = pop()
    push(int(left) ^ int(right))

def bit_not(tokens):
    num = pop()
    push(~int(num))

def modulo(tokens):
    right = pop()
    left = pop()
    if right:
        push(left/right)
    else:
        print "ERROR: Modulo by zero"

def power(tokens):
    right = pop()
    left = pop()
    push(left**right)

As Python is designed as a highly readable scripting language, which uses English keywords frequently, it is easier for students to understand the language and hence usually beginners go for Python programming assignments.

These functions pop 1 or 2 values off the stack and manipulate them and push the result back onto the stack.

def show

def show(tokens):
    left = pop()
    print left
    push(left)

Show the value at the top of the stack (does not pop the value).

def duplicate

def duplicate(tokens):
    left = pop()
    push(left)
    push(left)

Make a copy of the top value on the stack, so if you want to square a number, you could dup then *.

def pop_off

def pop_off(tokens):
    left = pop()

Remove the top value from the stack.

def list

def list(tokens):
    print stack

Show the contents of the stack.

def display_words

def display_words(tokens):
    for word in words:
        print word,':',words[word]

List all the defined functions.

def define

def define(tokens):
    colon = tokens.index(':')
    if colon <= 0:
        print "ERROR: Invalid word defintion"
        return
    else:
        words[tokens[0]] = tokens[1:colon]
        return colon+1

Define a function, the first token is the function name, and ends when a colon is encountered.

def variable

def variable(tokens):
    vars[tokens[0]] = pop()
    return 1

The first token gives the name of the variable.

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def integer

def integer(tokens):
    left = pop()
    push(int(left))

Convert the top value into an integer.

Trigonometry functions

def sin(tokens):
    left = pop()
    push(math.sin(left))

def cos(tokens):
    left = pop()
    push(math.cos(left))

def tan(tokens):
    left = pop()
    push(math.tan(left))

def log(tokens):
    left = pop()
    push(math.log(left))

More math functions.

def swap

def swap(tokens):
    left = pop()
    right = pop()
    push(left)
    push(right)

Swap the top 2 values on the stack.

def hexadecimal

def hexadecimal(tokens):
    left = pop()
    hexval = hex(int(left))[2:]
    if hexval[-1] == 'L':
        hexval = hexval[:-1]
    print '$' + hexval

Display the top value as a hexadecimal number.

def binary

def binary(tokens):
    left = pop()
    print '%' + bin(int(left))[2:]

Display the top value as a binary number.

Command dictionary

cmds = {'+' : add, '-' : subtract, '*' : multiply, '/' : divide, '%' : modulo, 'int' : integer, '**' : power,
        'and': bit_and, 'or' : bit_or, 'xor' : bit_xor, 'not' : bit_not,
        'sin' : sin, 'cos' : cos, 'tan' : tan, 'log' : log, 'hex' : hexadecimal, 'bin' : binary,
        '.' : show, 'dup' : duplicate, 'pop' : pop_off, 'list' : list, 'words' : display_words, 'def' : define,
        'var' : variable, '?' : help, 'exit' : quit, 'quit' : quit, 'swap' : swap}

The command functions for each token.

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def calc

def calc(expr):
    tokens = expr.lower().split()
    i = 0
    while i < len(tokens):
        token = tokens[i]
        i += 1
        if number.match(token):
            push(float(token))
        elif hexnumber.match(token):
            push(int(token[1:],16))
        elif binarynumber.match(token):
            push(int(token[1:],2))
        else:
            if token in cmds:
                if i < len(tokens):
                    tail = tokens[i:]
                else:
                    tail = []
                skip = cmds[token](tokens[i:])
                if skip:
                    i += skip
            elif token in vars:
                push(vars[token])
            elif token in words:
                pos = i
                for word in words[token]:
                    tokens.insert(pos,word)
                    pos += 1
            else:
                print "ERROR. Invalid token:",token

    if stack:
        return pop()

First of it breaks the line into a series of tokens, it loops through each token. It checks if it is a numeric
value, if it is then it pushes the value, then it checks if the token is a built in command, or a variable, and
then finally a user defined function. If it is a command, it calls the function with the remaining tokens on the
line and uses the return value to skip the next n tokens. If the token is a user defined function, then copy the
tokens that make the function up into the current token stream.

Suggested inprovements

You could make it so that if it is used from the command line it exits after performing the calculation, and saves
the state and restores it on each use. That would make a handy calculator replacement.

A more ambitious expansion would be to allow conditional functions and loops, and you could have a useful mini language.

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