From 776e65149576cb7d8d20c12edc57e6b919c366ee Mon Sep 17 00:00:00 2001
From: Gregor Kleen <gkleen@yggdrasil.li>
Date: Mon, 25 Jan 2016 13:26:29 +0000
Subject: Thermoprint 5

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+---
+title: Building an Extensible Framework for Specifying Compile-Time Configuration using Universal Quantification
+tags: Thermoprint
+published: 2016-01-24
+---
+
+When I write *Universal Quantification* I mean what is commonly referred to as
+[existintial quantification](https://downloads.haskell.org/~ghc/latest/docs/html/users_guide/data-type-extensions.html#existential-quantification),
+which I think is a misnomer.  To wit:
+
+$( \exists x \ldotp f(x) ) \to y$ is isomorphic to $\forall x \ldotp (f(x) \to y)$ (I
+won´t try to back this claim up with actual category theory just now. You might want to
+nag me occasionally if this bothers you -- I really should invest some more time into
+category theory). Since haskell does not support `exists` we´re required to use the
+`forall`-version, which really is universally quantified.
+
+What we want is to have the user provide us with a set of specifications of how to
+interact with one printer each.
+Something like the following:
+
+~~~ {.haskell}
+newtype PrinterMethod = PM { unPM :: Printout -> IO (Maybe PrintingError) }
+
+data Printer = Printer
+  { print :: PrinterMethod
+  , queue :: TVar Queue
+  }
+~~~
+
+The first step in refining this is necessitated by having the user provide the
+[monad-transformer-stack](http://book.realworldhaskell.org/read/monad-transformers.html)
+to use at compile time.
+Thus we introduce our first universal quantification (in conjunction with
+[polymorphic components](https://prime.haskell.org/wiki/PolymorphicComponents)):
+
+~~~ {.haskell}
+newtype PrinterMethod = PM { unPm :: forall m. MonadResource m => Printout -> m (Maybe PrintingError) }
+~~~
+
+Since we don´t want to *burden* the user with the details of setting up `TVar Queue`{.haskell} we
+also introduce function to help with that:
+
+~~~ {.haskell}
+printer :: MonadResource m => PrinterMethod -> m Printer
+printer p = Printer p <$> liftIO (newTVarIO def)
+~~~
+
+We could at this point provide ways to set up `PrinterMethod`{.haskell}s and have the user
+provide us with a list of them.
+
+We, however, have numerous examples of printers which require some setup (such opening a
+file descriptor). The idiomatic way to handle this is to decorate that setup with some
+constraints and construct our list of printers in an
+[`Applicative`{.haskell}](https://hackage.haskell.org/package/base/docs/Control-Applicative.html#t:Applicative)
+fashion:
+
+~~~ {.haskell}
+printer :: MonadResource m => m PrinterMethod -> m Printer
+printer p = Printer <$> p <*> liftIO (newTVarIO def)
+~~~
+
+At this point a toy implementation of a printer we might provide looks like this:
+
+~~~ {.haskell}
+debugPrint :: Applicative m => m PrinterMethod
+debugPrint = pure . PM $ const return Nothing <=< liftIO . putStrLn . toString
+
+toString :: Printout -> String
+toString = undefined
+~~~
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