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POTyped expression parser
 

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    <p>I'm trying to create a typed expression parser in Haskell, which works great so far, but I'm currently struggling to implement higher order functions. I've boiled the problem down to a simple example:</p> <pre class="lang-hs prettyprint-override"><code>{-# LANGUAGE TypeFamilies,GADTs,FlexibleContexts,RankNTypes #-} -- A function has an argument type and a result type class Fun f where type FunArg f type FunRes f -- Expressions are either constants of function applications data Expr a where Const :: a -&gt; Expr a App :: Fun f =&gt; f -&gt; FunArg f -&gt; Expr (FunRes f) -- A very simple function data Plus = Plus -- Which takes two integer expressions and returns an integer expression instance Fun Plus where type FunArg Plus = (Expr Int,Expr Int) type FunRes Plus = Int -- A more complicated function which lifts a function to lists (like in haskell) data Map f r = Map f -- For this we need the concept of lifting function arguments: class Liftable a where type LiftRes a -- A singleton argument is lifted by changing the expression type from a to [a] instance Liftable (Expr a) where type LiftRes (Expr a) = Expr [a] -- Two function arguments are lifted by lifting each argument instance (Liftable a,Liftable b) =&gt; Liftable (a,b) where type LiftRes (a,b) = (LiftRes a,LiftRes b) -- Now we can declare a function instance for Map instance (Fun f,Liftable (FunArg f),r ~ LiftRes (FunArg f)) =&gt; Fun (Map f r) where type FunArg (Map f r) = r type FunRes (Map f r) = [FunRes f] -- Now a parser for functions: parseFun :: [String] -&gt; (forall f. Fun f =&gt; f -&gt; a) -&gt; a -- The parser for the plus function is easy: parseFun ["plus"] f = f Plus -- But the parser for map is not possible: parseFun ("map":sym) f = parseFun sym (\fun -&gt; f (Map fun)) </code></pre> <p>The problem seems to be that there is no way to convince the type checker that every LiftRes is itself Liftable, because recursive class declarations are forbidden.</p> <p>My question is: How do I make this work? Are there other examples of typed expression parsers from which I could take hints?</p> <p><strong>EDIT:</strong> It seems that <a href="https://stackoverflow.com/questions/14133121/can-i-constrain-a-type-family">this discussion about type family constraints</a> seems to be very related. However, I fail to make their solution work in my case, maybe someone can help with that?</p>
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