rpn.py - a reverse-Polish notation calculator for Python

Here is rpn.py, a script implementing a reverse-Polish notation (RPN) calculator for Python.

As well as providing for traditional numeric calculator operations, it provides easy access to many Python functions, and you can put Python objects and functions onto the stack and operate on them.

I wrote this for 3 reasons:

1. I absolutely loved the HP-41C programmable calculator series, which used RPN. Although I had taught myself to program on a Casio FX-502P in 1978, the Casio was like a toy compared to the HP-41C. I owned a 41C, a 41CV, and then a 41CX, had a bunch of memory expansion packs, several other add-on packs (e.g., stats), a card reader/writer, and got it overclocked by some hardware hacker friends. It was an amazing machine. I still have one.

2. I have been using the UNIX dc (desk calculator) command on almost a daily basis since 1983. dc is ancient (in UNIX terms), predating even the C programming language. It provides a minimalist RPN calculator. You can even program it, if you have a taste for mystery. Here's a program I wrote in 1984 to factor numbers:

   [[neither]plsx]sn[c2pla2/sallx]se[ladv1+sm0=nla1=ncla2=pla2%0=elfx]sl
   [ldlm<pclald%0=cld2+sdlfx]sf[lap[is prime.]plsx]sp[ldplald/salfx]sc
   [[enter X : ]P?dsa0>n3sdllx]ss[[negative]plsx]snlsx
   

   That code still runs today, 35 years later, totally unchanged. But dc has only a tiny set of operations. So while it's great to be able to easily use it from the command line (e.g., echo 4 5 + p | dc), I frequently find myself reaching for a real calculator or launch an interactive session with a full programming language (Perl, Python, etc), which feels a bit heavyweight and requires more syntax.

3. I was curious what it would be like to have a Python RPN calculator that offered both the minimalist syntax of dc but that also offered a much wider range of operations and made it possible to put Python objects (lists, dicts, functions, etc.) onto the stack and operate on them. I'm curious what use I'll make of it, and what others might do with it too.

Note that this is a work in progress! Everything may change. Suggestions very welcome.

Example rpn.py sessions

Before getting a bit more formal (and boring) in describing how you use rpn.py, here are some example sessions to give you a flavor.

(BTW, I set my shell up to alias pc (Python calculator) for rpn.py to minimize typing and be a bit more like dc. But I'll use rpn.py in the examples below.)

# Add two numbers. The stack is printed after all commands are run.
$ rpn.py 4 5 +
9

# Do the same thing, but read from standard input (all the commands below
# could also be run in this way).
$ echo 4 5 + | rpn.py
9

# Sine of 90 degrees (note that Python's sin function operates on
# radians). The commands are in quotes so the shell doesn't expand the '*'.
$ rpn.py '90 pi 180 / * sin'
1.0

# Same thing, different quoting.
$ rpn.py 90 pi 180 / \* sin
1.0

# Same thing, use 'mul' instead of '*'.
$ rpn.py 90 pi 180 / mul sin
1.0

# Area of a circle radius 10
$ rpn.py 'pi 10 10 * *'
314.1592653589793

# Equivalently, using ':2' to push 10 onto the stack twice.
$ rpn.py 'pi 10:2 * *'
314.1592653589793

# Equivalently, using 'dup' to duplicate the 10 and 'mul' instead of '*'
$ rpn.py pi 10 dup mul mul
314.1592653589793

Function calling argument push order

On a regular RPN calculator you would do what we normally think of as an infix operation such as 5 - 4 by pushing 5 onto the stack, then pushing 4, and finally running the - function. The operator is taken out of middle and given at the end and the original infix order of the arguments is the order you push them onto the stack. Of course this doesn't make any difference for commutative operations like + and *, but is important for / and -.

In Python we have various functions like map, filter, functools.reduce, and the long-ago deprecated Python 2 apply function. These are typically thought of as having a prefix or Polish notation signature, accepting a function followed by an iterable. E.g., map(function, iterable).

To be consistent, with RPN argument pushing just described for the numeric operations, in the case of (what we normally think of as) prefix functions such as map, we should therefore push the function to be run, then push the iterable, then call map (reduce, filter, etc).

Like this:

$ rpn.py 'str:! [6,7,8] map:i'
['6', '7', '8']

Notes

1. Here the :! modifier causes the str function to be pushed onto the stack instead of being run, and the :i modifier causes the result of map to be iterated before being added to the stack.
2. When you run a function (like map or apply) that needs a callable (or a function like join that needs a string) and you don't specify a count (using :3 for example), rpn.py will search the stack for a suitable item and use the first one it finds. It doesn't really have a choice in this case because it doesn't know how many arguments the function (once it is found) will be applied to. This should usually work just fine. You can always use an explicit count (like :3) if not. Note that this situation does not apply if you use the :r modifier (see below) because in that case the callable (or string, in the case of join) will be expected to be on the top of the stack (and its signature can then be examined to know how many arguments to pass it).

You might find it more natural to use map and friends the other way around. I.e., first push the iterable, then push the function to be applied, and then call map. In that case, you can use the :r modifier to tell the calculator to reverse the order of the arguments passed to a function. In the following, we push in the other order and then use map:ir (the i is just to iterate the map result to produce a list).

$ rpn.py '[6,7,8] str:! map:ir'
['6', '7', '8']

Continuing on the map theme, you could instead simply reverse part of the stack before running a function:

$ rpn.py '[6,7,8] str:! reverse map:i'
['6', '7', '8']

The reverse command operates on two stack items by default, but it can take a numeric argument or you can run it with the :* modifier which will cause it to be run on the whole stack:

# Reverse the top 3 stack elements then reverse the whole of the stack.
$ rpn.py '5 6 7 8 reverse:3 reverse:*'
[6, 7, 8, 5]

More examples

# The area of a circle again, but using reduce to do the multiplying.  The
# ':!' modifier tells rpn.py to push the '*' function onto the stack
# instead of immediately running it.
$ rpn.py '*:! [pi,10,10] reduce'
314.1592653589793

# Same thing, but push the numbers individually onto the stack, then the
# ':3' tells reduce to use three stack items. Use 'mul' as an
# alternative to '*'.
$ rpn.py 'mul:! pi 10 dup reduce:3'
314.1592653589793

# Equivalently, using ':*' to tell reduce to use the whole stack.
$ rpn.py '*:! pi 10 dup reduce:*'
314.1592653589793

# If you don't want to push the function for 'reduce' to use onto the stack
# first, use ':r' to tell it to use the top of the stack:
$ rpn.py 'pi 10 dup mul:! reduce:3r'
314.1592653589793

# Push 'True' onto the stack 5 times, turn the whole stack ('*') into a
# list and print it ('p'), then pass that list to 'sum'.
$ rpn.py 'True:5 list:*p sum'
[True, True, True, True, True]
5

# Here's something a bit more long-winded (and totally pointless):
#
# Push 0..9 onto the stack (iterating the result of 'range'.
# call Python's 'reversed' function
# push the 'str' function
# use 'map' to convert the list of digits to strings
# join the string digits with the empty string
# convert the result to an int
# take the square root
# push 3 onto the stack
# call 'round' to round the result to three decimal places
#
# the ':i' modifier (used here twice) causes the value from the command
# to be iterated and the result to be put on the stack as a single list.
# It's a convenient way to iterate over a generator, a range, a map,
# dictionary keys, etc.

$ rpn.py 'range(10):i reversed str:! map:ir "" join:r int sqrt 3 round:2'
99380.799

The :2 on the round call tells it to use two arguments from the stack (round uses one by default in rpn.py).

The :r on the map call makes it look for the function to run on the top of the stack, rather than searching up the stack to find it. If you think further in advance, you can push the function first:

$ rpn.py 'str:! range(10):i reversed map:i "" join:r int sqrt 3 round:2'
99380.799

The same goes for the string used by join: it could have been pushed first, and then there would be no need for the :r on the join:

$ rpn.py '"" str:! range(10):i reversed map:i join int sqrt 3 round:2'
99380.799

You could (of course!) do this last example in Python with a bunch of parens:

from math import sqrt
print(round(sqrt(int(''.join(map(str, reversed(range(10)))))), 3))

The elimination of parens is the main beauty of RPN (at least aesthetically - the stack model of computation is a pretty awesome idea too). The price is that you have to learn to think in postfix. With the :r modifier, rpn.py tries to be flexible in where it will find things on the stack. There's also the swap command in case you forget to push something and need to flip the top stack items before running some other command.

It might be convenient to do more involved calculations in an interactive REPL session:

# REPL usage, with automatic splitting of whitespace turned off
# (so we give one command per line).
$ rpn.py --noSplit
--> 4
--> 5
--> 6
--> stack
[4, 5, 6]
--> f  # f is an alias for 'stack', as in dc.
[4, 5, 6]
--> clear  # Or just 'c'
--> f
[]
--> from numpy import log2
--> 32
--> log2
--> p
5.0
--> {'a':6, 'b':10, 'c':15}
--> len
--> p
3
--> [6,7,8]
--> str :!
--> f
[[6, 7, 8], <class 'str'>]
--> swap
--> f
[<class 'str'>, [6, 7, 8]]
--> map :i
--> f
['6', '7', '8']

$ rpn.py --noSplit
--> def celcius(f): return (f - 32) / 1.8  # Nothing is added to the stack here.
--> 212
--> celcius :p  # Use :p to print the result immediately
100.0

$ rpn.py --noSplit
--> lambda f: (f - 32) / 1.8
--> 212
--> apply :p
100.0

# Same as above, but push the anonymous function last.
$ rpn.py --noSplit
--> 212
--> lambda f: (f - 32) / 1.8
--> apply :pr
100.0

Usage

The calculator either works interactively from the shell using a read-eval-print loop (REPL) or will read commands either from the command line or from standard input. If you specify file names (including using - to indicate standard input), commands will be read from the file(s). Run rpn.py --help to see command line options.

Command syntax

Input lines are either comments (first non-whitespace character on the line is #) or specify a command (or commands) followed by optional modifiers.

If given, modifiers must follow a :. The modifiers are a set of single letters and may also include a single number. The input + :p= 17 causes the + command to be executed, with modifiers p, =, and 17. The full list of commands and modifiers is given below.

If modifiers are given, they apply to all commands on an input line.

Input line splitting

By default, rpn.py will split lines on whitespace and each field will be taken as a command. Hence:

$ rpn.py 4 5 +
9

will push 4 and then 5 onto the stack and then replace those two values by their sum.

In REPL mode, rpn.py prints --> as a prompt (see the REPL section below).

In many cases it is easy to avoid using spaces and inadvertently having your input interpreted as multiple commands. For example, push a list onto the stack:

$ rpn.py
--> [1,2,3]

but if you try that with embedded spaces, you'll get an error:

$ rpn.py
--> [1, 2, 3]
Could not eval('[1,'): unexpected EOF while parsing (<string>, line 1)
Could not exec('[1,'): unexpected EOF while parsing (<string>, line 1)
Did you accidentally include whitespace in a command line?

this can be avoided with the :n (no split) modifier, but note that the modifier will only affect the next (and subsequent) lines. You can just give an empty command with the :n modifier to toggle to no line splitting:

$ rpn.py
--> :n  # no splitting of subsequent lines
--> [1, 2, 3]

If you want rpn.py not to split lines into multiple commands by default, run with the --noSplit command-line option. You can then use :s (split) if you instead want to switch to writing input lines that should be split. Hence:

$ rpn.py --noSplit
--> [1, 2, 3]
--> :s  # split subsequent lines
--> 4 5

the above will first push the list [1, 2, 3] onto the stack, then toggle to line splitting, and then 4 and 5 will be split (on whitespace), treated as two separate commands, and result in two more values being pushed onto the stack.

Whitespace

Leading and trailing whitespace in the command is ignored. Whitespace anywhere in the modifiers is ignored (unless line splitting is on, in which case you will get errors).

Engineering notation

Numbers can be inputted using engineering notation:

$ rpn.py
--> 20k 1.5M +
1.52M

Values on the stack will only be displayed using engineering notation if they were inputted so:

$ rpn.py
--> 2000
--> f
--> [2000]
--> 2k
--> f
--> [2000, 2k]
--> +
--> [4k]

Operation via standard input

When reading from standard input, the lines will be split on whitespace and each field is treated as a separate command. This allows for simple command-line usage such as

$ echo 4 5 + | rpn.py
9

For convenience, modifiers can be preceded by whitespace:

$ echo 100 log10 :! apply | rpn.py
2.0

In the above, the :! modifier applies to the preceding log10 function (causing it to be pushed onto the stack).

If you have a file of commands you want to pipe into rpn.py you might want to turn off this splitting:

$ cat data
4
5
# This is a comment
+

$ rpn.py < data
9

You can change the separator using --separator:

$ echo 4_5_+ | rpn.py --separator _
9

By default, the final calculator stack is printed when standard input is exhausted:

$ echo 4 5 | rpn.py
[4, 5]

You can disable the final printing with --noFinalPrint:

$ echo 4 5 | rpn.py --noFinalPrint

in which case you can print things yourself using the p command (see below).

REPL operation

In REPL mode, the calculator repeatedly prints a prompt, reads a command, and executes it. For example:

$ rpn.py
--> 4 5 +
--> p
9

you can change the prompt using --prompt on the command line.

Commands

There are two kinds of commands: special and normal.

Special commands

• apply: Apply a function to some arguments.
• clear (or c): Clear the stack.
• dup (or d): Duplicate count (default 1) arguments.
• functions: Print a list of all known functions.
• join: Join stack items with a string.
• list: Convert the top stack item to a list by iterating it. With a count > 1 pops that many stack items off the stack and into a list that is pushed.
• pop: Pop count (default 1) stack item.
• print (or p): Print count (default 1) stack item from the top of the stack.
• quit (or q): Quit
• reverse: Reverse the count (default 2) top stack items.
• reduce: Repeatedly apply a function to stack items (see functools.reduce).
• stack (or s or f): Print the whole stack.
• store: Store the value on the top of the stack into a variable (whose name has previously been pushed onto the stack). If given a numeric argument, that number of items from the stack will be stored into the variable as a list.
• swap: Swap the top two stack elements.
• undo: Undo the last stack-changing operation and variable settings.
• variables: Show all known variables and their values.

Normal

Many functions from the builtins, math, and operator modules are available. Often you can just type the function name (e.g., log10 not math.log10). You can call a function with an argument if you want and the result will be pushed onto the stack:

# This works unquoted in bash. You may need quotes in your shell (e.g, in fish).
$ rpn.py abs(-50)
50

or if you just name the function it will be applied to the item (or items) on the top of the stack, using a heuristic guess at the number of arguments the function would normally take (the number of positional or positional-or-keyword arguments). If the guess is wrong, you can always undo and run the function again with an explicit number of arguments.

# Call 'round' (which takes one argument by default) on pi.
$ rpn.py pi round
3

# Round pi to 10 decimal places. :2 tells 'round' to use two stack arguments.
$ rpn.py pi 10 round:2
3.1415926536

You can use the functions command to see a list of all known functions and the number of arguments they'll expect on the stack (assuming you don't pass arguments directly as with abs(-50) above or use a numerical modifier (e.g., :3) to explicitly specify the number of arguments that should be passed. Here's the first part of the output of functions:

$ rpn.py functions
!= Function(ne (calls operator.ne with 2 args))
* Function(mul (calls operator.mul with 2 args))
+ Function(add (calls operator.add with 2 args))
- Function(sub (calls operator.sub with 2 args))
/ Function(truediv (calls operator.truediv with 2 args))
== Function(eq (calls operator.eq with 2 args))
Context Function(Context (calls decimal.Context with 0 args))
Decimal Function(Decimal (calls decimal.Decimal with 1 arg))
DecimalTuple Function(DecimalTuple (calls decimal.DecimalTuple with 3 args))
abs Function(abs (calls operator.abs with 1 arg))
acos Function(acos (calls math.acos with 1 arg))
acosh Function(acosh (calls math.acosh with 1 arg))
add Function(add (calls operator.add with 2 args))
all Function(all (calls builtins.all with 1 arg))
and_ Function(and_ (calls operator.and_ with 2 args))
any Function(any (calls builtins.any with 1 arg))
ascii Function(ascii (calls builtins.ascii with 1 arg))
asin Function(asin (calls math.asin with 1 arg))
asinh Function(asinh (calls math.asinh with 1 arg))
atan Function(atan (calls math.atan with 1 arg))
atan2 Function(atan2 (calls math.atan2 with 2 args))
atanh Function(atanh (calls math.atanh with 1 arg))
attrgetter Function(attrgetter (calls operator.attrgetter with 1 arg))
# 300+ lines deleted

Modifiers

Modifiers for a command are introduced with a colon, :. The modifiers are all single letters and may also include a single non-negative integer. When line splitting is on, the colon and modifier letters and integer cannot contain whitespace. I.e., :pr34. If line splitting is off, whitespace is allowed (and ignored).

The full list of modifiers is:

• !: Push the given thing (either a function or a variable) onto the stack, do not try to run or evaluate it.

• *: Use all arguments from the stack in the command execution.

• =: The command will be run but the stack will not be altered (think: keep the stack equal). This is useful in combination with the p modifier to print the result. It can be used to try an operation and see its result without actually doing it. If you do execute a command and want to undo it, there is also the undo special command.

• c: Force the command line string to be interpreted as a special command. This must be used if you define a variable with a name like quit or pop and you then can't call the special quit command.

• D: Toggle debug output.

• i: Iterate the result of the command and put the values onto the stack in a list. This is useful when you call a function that returns a generator or other special iterable object. It's a convenience for just calling the function (which would put the generator onto the stack) and then running list.

• n: Turn off (think: no) line splitting. Note that this will only go into effect from the next command on.

• p: Print the result (if any). See also the :P modifier and the --print argument to rpn.py.

• P: Toggle automatic printing of all command results.

• r: When applied to a special command, reverses how the function (for map, apply, reduce) or a string (for join) is looked for on the stack. Normally the function or string argument to one of those special functions has to be pushed onto the stack first. If :r is used, the function or string can be given last (i.e., can be on the top of the stack). In other contexts, causes all arguments given to a function to be reversed (i.e., to use a stack order opposite to the normal).

  ```sh
  $ rpn.py '+:! 5 4 apply'
  9
  $ rpn.py '5 4 +:! apply:r'
  9
  $ rpn.py '5 4 -'
  1
  $ rpn.py '5 4 -:r'
  -1
  ```
  

• s: Turn on line splitting on whitespace. Note that this will only go into effect from the next command on.

If a count is given, it is either interpreted as a number of times to push something onto the stack or the number of arguments to act on, depending on context (um, sorry about that - should be clearer).

Variables

You can set variables and push them (or their values) onto the stack:

$ rpn.py --noSplit
--> a = 4
--> a
--> f
[4]
--> a:!
--> f
[4, Variable(a, current value: 4)]
--> a = 10
--> f
[4, Variable(a, current value: 10)]
--> 20
--> +:p
30

Undo

The effect of commands on the stack and variables can be undone with the undo command. There is currently only one level of undo.

History

rpn.py makes use of Python's readline library to allow familiar/comfortable command line editing. Your input history will be saved to ~/.pycalc_history if your version of readline has the append_history_file command (present only in Python >= 3.6)?

Todo

• Add direct access to functionality from numpy.
• Add rotate-right and rotate-left stack modifying functions?

Thanks

To David Pattinson (@davipatti) for various nice ideas, including executing the command line arguments.