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## Principal type-schemes for functional programs

**Luis Damas and Robin Milner, POPL '82**

> module W where

> import Data.List
> import Data.Maybe
> import Data.Function

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{-# language FlexibleContexts #-}
{-# language TypeOperators #-}

module DKT where
  
import Control.Monad (guard)
import Control.Monad.Error.Class (throwError)
import Control.Monad.Trans (lift)
import Control.Monad.Trans.State
import Control.Monad.Trans.Writer

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Introduction

At DICOM Grid, we recently made the decision to use Haskell for some of our newer projects, mostly small, independent web services. This isn't the first time I've had the opportunity to use Haskell at work - I had previously used Haskell to write tools to automate some processes like generation of documentation for TypeScript code - but this is the first time we will be deploying Haskell code into production.

Over the past few months, I have been working on two Haskell services:

• A reimplementation of an existing socket.io service, previously written for NodeJS using TypeScript.
• A new service, which would interact with third-party components using standard data formats from the medical industry.

I will write here mostly about the first project, since it is a self-contained project which provides a good example of the power of Haskell. Moreover, the proces

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"use strict";

// module UnderscoreFFI

exports.map = function(f) {
  return function (arr) {
    return require('underscore').map(arr, f);
  };
};

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{-# language TypeInType #-}

-- | Types which have PureScript equivalents
class ToPursTyCon a where
  toPursTyCon :: Tagged a PursTypeConstructor

  -- | The default instance uses 'G.Generic' and pattern matches on the
  -- type's representation to create a PureScript type.
  default toPursTyCon :: (G.Generic a, GenericToPursTyCon (G.Rep a)) => Tagged a PursTypeConstructor
  toPursTyCon = retag $ genericToPursTyConWith @(G.Rep a) defaultPursTypeOptions

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module Main where

main = Debug.Trace.trace ("module Main where\n\n" ++ code ++ "\n  where code = \"\"\"" ++ code ++ "\"\"\"")
  where code = """main = Debug.Trace.trace ("module Main where\n\n" ++ code ++ "\n  where code = \"\"\"" ++ code ++ "\"\"\"")"""

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FreeAp f is a Comonad

While thinking about comonads as spaces and Day convolution, I realized an interesting thing. The free applicative functor generated by a comonad f is also a comonad.

The free applicative can be defined in a few different ways, but I like to define it like this:

data FreeApplicative f a = Pure a | Free (Day f (FreeApplicative f) a)

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module Main where
  
import Data.Maybe (fromMaybe)

import Control.Applicative
import Control.Arrow (first)
import Control.Monad (ap) 
    
import Debug.Trace
  

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module Control.Monad.List.Trans where

import Prelude

import Data.List
import Data.Either

import Control.Apply
import Control.Bind
import Control.Monad.Eff