graphical untyped lambda calculus interactive interpreter

Latest on Hackage:0.3

This package is not currently in any snapshots. If you're interested in using it, we recommend adding it to Stackage Nightly. Doing so will make builds more reliable, and allow to host generated Haddocks.

GPL-2 licensed by Claude Heiland-Allen
Maintained by


GULCII is an untyped lambda calculus interpreter supporting interactive modification of a running program with graphical display of graph reduction.


Lambda calculus terms with some sugar coating:

term ::= variable                    -- free or bound
     | '\' var+ strategy term        -- lambda abstraction
     | term+                         -- application
     | '(' term ')'
     | integer
     | list
variable ::= [a-z][A-Za-z0-9]*
strategy = '.' | '!' | '?'           -- lazy | strict | copy
integer ::= [0-9]+                   -- uses Scott-encoding
list ::= '[' (term (, T)*)? ']'      -- uses Scott-encoding

There are three variants of lambda abstraction: lazy, strict, and copy:

\x . f x x    -- x is evaluated lazily with sharing
\x ! f x x    -- x is evaluated strictly and shared
\x ? f x x    -- x is copied before any evaluation

There is additional syntax sugar for natural numbers and lists, using


There is a small standard library based loosely around the Haskell Prelude:

:load prelude

If you define a term using free variables, they can be modified while the program is running, but sharing is lost. If you define a term as a fixed point (perhaps with Y-combinator) then sharing works (to some extent), but you can't modify the code while it is running any more.

Meta Commands

To exit type:


Entering a term evaluates it.

Terms can be bound to names, stored in a global dictionary:

foo = bar

The global dictionary can be listed or wiped clean:


Installed files can be loaded:

:load church

Machine-readable node statistics are output to stdout, as well as when free variables are instantiated by looking up their definitions. These are intended to be used for sonification, for example with Pure-data:

pd extra/gulcii.pd &
sleep 5
gulcii | pdsend 8765

The sonification is controlled by two commands:



There are some runtime adjustable settings:

:get NewsOnTop
:set NewsOnTop
:unset NewsOnTop
:toggle NewsOnTop

Where NewsOnTop is a setting. Settings include:

Depends on 5 packages:
Used by 1 package:
comments powered byDisqus