Finds optimal forth code sequences for stack transformations

pip install forthwiz==2.1


The Forth Wizard finds the shortest sequence of forth instructions needed for a given stack manipulation.

In addition to simple stack transforms it allows for partial specification of the final stack state, usage of the return stack, and caching. All common forth instructions are supported.

This was translated from the orignal forth wizard and heavily extended. It is written in C and provides a Python3 module. Tested only on Ubuntu.


Install from pypi with pip3 install forthwiz, or download and run sudo ./ to build and install. Requires package python3-dev to build.


Instantiate a forthwiz.Wizard object and use the setup method to specify the machine state. This can include the initial and ending state of data stack, initial state of return stack, and options for caching, supported ops, and return stack usage. The stack states are specified with lists, the items in those lists may be any hashable type.

$ python3
>>> import forthwiz
>>> wiz = forthwiz.Wizard()
>>> wiz.setup( in_stack=['a', 'b'], out_stack=['b', 'a', 'a'] )
>>> solution = wiz.solve()
>>> solution.code
['swap', 'dup']

Multiple solutions

Wizard.solve may be called multiple times to generate alternative solutions:

>>> wiz.setup( in_stack=['a', 'b'], out_stack=['b', 'a', 'a'] )
>>> solution = wiz.solve(); solution.code
['swap', 'dup']
>>> solution = wiz.solve(); solution.code
['over', 'rot']
>>> solution = wiz.solve(); solution.code
['swap', '2dup', 'nip']

Partial stack usage

The out_vars parameter can be used to specify symbols that must remain in the final machine state. When out_vars is set the out_stack parameter only specifies the top values that are expected on the stack. Symbols in out_vars that are not in out_stack may be included in the bottom portion of the data stack in any order. This may yield shorter solutions when only the top ordering matters. The final data stack value is saved as the Solution.stack attribute.

>>> wiz.setup( in_stack=[1, 2, 3, 4, 5], out_stack=[1],
               out_vars=[1, 2, 3, 5] )
>>> solution = wiz.solve()
>>> solution.code
['nip', '2swap', 'swap']
>>> solution.stack
[3, 5, 2, 1]

Using the return stack

The use_rstack parameter tells the solver that it is ok to leave values on the return stack. When it is set values that appear in out_vars that are not present in out_stack may be left on the return stack in addition to the bottom of the data stack. This is disabled by default. The final state of the return stack is saved as the Solution.rstack attribute.

>>> wiz.setup( in_stack=[1, 2, 3, 4, 5], out_stack=[1],
               out_vars=[1, 2, 3, 5], use_rstack=True )
>>> solution = wiz.solve()
>>> solution.code
['>r', 'drop', 'rot']
>>> solution.stack
[2, 3, 1]
>>> solution.rstack

in_rstack can be used to specify the starting state of the return stack.

Finding all solutions

Use the to find all the solutions of the minimal length.

>>> wiz.setup( in_stack=[1, 2], out_stack=[2, 1, 1] )
>>> solution =
>>> [s.code for s in solution]
[['swap', 'dup'], ['over', 'rot']]

Subsequent calls to gives the collection of the next longest solution length.

Wizard.solve_many can be used to find all solutions under a given length.

Forth ops

The forth ops the solver will use to find the solution can be set with the ops parameter. Specify the op N pick with Npick, currently supported for N=[2,5]. For example, duplicating top of stack without dup:

>>> wiz.setup( in_stack=['A', 'B'], out_stack=['A', 'B', 'B'],
               ops=['swap', 'r>', 'over', '>r', 'r@'] )
>>> solution = wiz.solve(); solution.code
>>> ['>r', 'r@', 'r>']

Predefined collections of ops supported by common forth interpreters can be set using the target parameter. Currently supported targets are gforth and amforth.

>>> wiz.setup( in_stack=['a', 'b','c','d'], out_stack=['a', 'b','c','d','a','b'],
               target='gforth' )
>>> solution = wiz.solve(); solution.code
>>> wiz.setup( in_stack=['a', 'b','c','d'], out_stack=['a', 'b','c','d','a','b'],
               target='amforth' )
>>> solution = wiz.solve(); solution.code
['2>r', '2dup', '2r>', '2swap']


By default calls to solve will cache the solution. To disable caching set the optional setup parameter use_cache to False.

A different cache file is used for each solver version and collection of ops used to find the solution, for example wizard_cache_1_2_7ffff.txt.

Disabling the pick instruction

Use of the pick instruction may be disabled with the use_pick option:

>>> wiz.setup( in_stack=[0, 1, 2], out_stack=[0, 2, 0, 1] )
>>> solution = wiz.solve(); solution
['2', 'pick', 'rot']
>>> wiz.setup( in_stack=[0, 1, 2], out_stack=[0, 2, 0, 1],
               use_pick=False )
>>> solution = wiz.solve(); solution
['swap', '>r', 'over', 'r>']


forthwiz.solve_stacks is a convenience function supporting only basic usage. It takes two lists describing the input and output states of the data stack and a subset of the options available to Wizard.setup

>>> import forthwiz
>>> forthwiz.solve_stacks( ['a', 'b'], ['b', 'a', 'a'] )
['swap', 'dup']