Haskell tool to generate expressions from types
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Exference is a Haskell tool for generating expressions from a type, e.g.

Input: (Show b) => (a -> b) -> [a] -> [String]

Output: \ b -> fmap (\ g -> show (b g))

Djinn is a well known tool that does something similar; the main difference is that Exference supports a larger subset of the haskell type system - most prominently type classes. This comes at a cost, however: Exference makes no promise regarding termination. Where Djinn tells you "there are no solutions", exference will keep trying, sometimes stopping with "i could not find any solutions".


Compiling from source

git clone git@github.com:lspitzner/exference.git
cd exference
cabal sandbox init
# note that ghc-7.10 does not work yet;
# i recommend ghc-7.8.4 for now.
cabal install --only-dependencies
cabal configure
cabal build
# and, for example
cabal run -- "(Show b) => (a->b) -> [a] -> [String]"


git clone git@github.com:lspitzner/exference.git
cd exference
stack build

Usage notes

There are certain types of queries where Exference will not be able to find any / the right solution. Some common current limitations are:

  • By default, searches only for solutions where all input is used up, e.g. (a, b) -> a will not find a solution (unless given --allowunused flag). Often this is the desired behaviour, consider queries such as (a->b) -> [a] -> [b] where a trivial solution would be \_ _ -> []. This also means that certain functions are not included in the environment, e.g. length or mapM_, as they "lose information";
  • Type synonyms are not supported, e.g. String -> [Char] will not give solutions. Should be easy to implement, but I have not come around to it yet;
  • Kinds are not checked, e.g. Maybe -> Either (which can be seen as both advantage and disadvantage, see report);
  • The environment is composed by hand currently, and does only include parts of base plus a few other selected modules. Additions welcome!
  • Pattern-matching on multiple-constructor data-types is not supported;
  • See also the detailed feature description in the exference.pdf report.

Experimental features

  • Pattern-matching on multi-constructor data types can be enabled via -c --patternMatchMC, but reduces performance significantly for any non-trivial queries. Core algorithm needs re-write to optimize stuff sufficiently I fear.
  • I recently added support for RankNTypes, but this is largely untested.

Other known (technical) issues

  • Memory consumption is large (even more so when profiling);
  • The tests should be put in a proper test-suite. (initially the executable was created for testing purposes , but now serves as command-line interface; this is why no parameters run tests.)
  • The dependency bounds of the cabal packages should be cleaned up/checked. I postponed this as there is no automated way to do this. stupid tooling..)



If you want to add new elements to the environment, be careful not to add functions that

  • are just synonyms of other functions (including cases such as mapM vs forM);
  • lose information, e.g. void :: Functor f => f a -> f ();

and avoid adding functions that

  • are polymorphic in their return type (as they increase the search space for any query) - if really necessary, they can be added including an appropriate rating entry;
  • are just more specific versions of existing functions.


  • The author did not learn about the term "entailment" until after implementing the respective part of the algorithm.
  • Exference was used at least once to implement some typed hole in its own source code.