# Tex2hs

This tool takes a Latex document, usually intended for consumption with lhs2tex, and attempts to type check it. While literate Haskell is great for writing a document which is a complete piece of code, when writing fragments of code interspersed with alternative definitions it can be tricky. Tex2hs takes a .tex file, and automatically tries to splice the fragments together in a way that type checks.

## An Example

Let's imagine we are writing a paper:

We have developed a method for short-cut fusion using |foldr|/|build|. By introducing the definition:

\begin{code}
build :: ((a -> [a] -> [a]) -> [b] -> c) -> c
build g = g (:) []
\end{code}

The standard definition of |map| is:

\begin{code}
map :: (a -> b) -> [a] -> [b]
map f []      = []
map f (x:xs)  = f x : map f xs
\end{code}

But we redefine it as:

\begin{code}
map :: (a -> b) -> [a] -> [b]
map f = foldr ((:) . f) []
\end{code}

Which now allows us to have the property:

\begin{code}
propEq g k z = foldr k z (build g) == g k z
\end{code}


This code won't actually type check in a literate document -- for a start map has been defined once in the Prelude, and twice in the paper. We also need to link the build into the propEq. If we try running Tex2hs we get:

$tex2hs sample.tex Checking line 1... success Checking line 1... success Checking line 3... success Checking line 8... success Checking line 10... FAILURE ERROR "temp.hs":4 - Ambiguous variable occurrence "map" *** Could refer to: Main.map Hugs.Prelude.map  We can fix this error easily by creating a file Include.hs in the same directory as the paper with the text import Prelude hiding (map). This file is a great place to put definitions and imports which are necessary. Running the checker again, this time specifying to go from line 10: $ tex2hs sample.tex 10..
Checking line 10... success
Checking line 18... FAILURE
ERROR "temp.hs":5 - Type error in explicitly typed binding
*** Term           : map
*** Type           : (([a] -> [a]) -> [b] -> [b]) -> [a] -> [b]
*** Does not match : (([a] -> [a]) -> [b] -> [b]) -> [[a] -> [a]] -> [[b] -> [b]]
*** Because        : unification would give infinite type


We can now spot the bug, it should have been (:) . f, not the other way round. We fix this bug, and now the entire document type checks.