Write You a Haskell Stephen Diehl

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• A thunk, i.e., the application of a function to values that have not been evaluated yet • A thunk that is currently being evaluated, which may induce the evaluation of other thunks in the process • An expression in weak head normal form, which is only evaluated to the outermost constructor or lambda abstraction e runtime has the task of determining which thunks are to be evaluated by the order in which they are connected to the main function node. is is the essence of all evaluation in Haskell and is called graph reduction. Self-referential functions are allowed in Haskell. For example, the following functions generate infinite lists of values. However, they are only evaluated up to the depth that is necessary. -- Infinite stream of 1’s ones = 1 : ones -- Infinite count from n numsFrom n = n : numsFrom (n+1) -- Infinite stream of integer squares squares = map (^2) (numsfrom 0) e function take consumes an infinite stream and only evaluates the values that are needed for the computation. take :: Int -> [a] -> [a] take n _ | n a undefined :: a 18
Higher-Kinded Types e “type of types” in Haskell is the language of kinds. Kinds are either an arrow (k -> k’) or a star (*). e kind of Int is *, while the kind of Maybe is * -> *. Haskell supports higher-kinded types, which are types that take other types and construct a new type. A type constructor in Haskell always has a kind which terminates in a *. -- T1 :: (* -> *) -> * -> * data T1 f a = T1 (f a) e three special types (,), (->), [] have special type-level syntactic sugar: (,) Int Int = (Int, Int) (->) Int Int = Int -> Int [] Int = [Int] Typeclasses A typeclass is a collection of functions which conform to a given interface. An implementation of an interface is called an instance. Typeclasses are effectively syntactic sugar for records of functions and nested records (called dictionaries) of functions parameterized over the instance type. ese dictionaries are implicitly threaded throughout the program whenever an overloaded identifier is used. When a typeclass is used over a concrete type, the implementation is simply spliced in at the call site. When a typeclass is used over a polymorphic type, an implicit dictionary parameter is added to the function so that the implementation of the necessary functionality is passed with the polymorphic value. Typeclasses are “open” and additional instances can always be added, but the defining feature of a typeclass is that the instance search always converges to a single type to make the process of resolving overloaded identifiers globally unambiguous. For instance, the Functor typeclass allows us to “map” a function generically over any type of kind (* -> *) and apply it to its internal structure. class Functor f where fmap :: (a -> b) -> f a -> f b instance Functor [] where fmap f [] = [] fmap f (x:xs) = f x : fmap f xs instance Functor ((,) a) where fmap f (a,b) = (a, f b) 19
Page 1 and 2: Write You a Haskell Building a mode
Page 3 and 4: Contents Introduction 6 Goals . . .
Page 5 and 6: Evaluation . . . . . . . . . . . .
Page 7 and 8: Syntax Errors . . . . . . . . . . .
Page 9 and 10: • containers • unordered-contai
Page 11 and 12: File ””, line 1, in TypeError:
Page 13 and 14: ] TokenSym ”x”, TokenAdd, Token
Page 15 and 16: f: mov res, arg add res, 1 ret defi
Page 17 and 18: Datatypes Constructors for datatype
Page 19: length :: [a] -> Int length [] = 0
Page 23 and 24: eturn a >>= f = f a Law 2 m >>= ret
Page 25 and 26: data PlatonicSolid = Tetrahedron |
Page 27 and 28: foo :: Stack () foo = Stack $ do pu
Page 29 and 30: , bar :: Int } deriving (Show) comp
Page 31 and 32: class IsString a where fromString :
Page 33 and 34: Parsing Parser Combinators For pars
Page 35 and 36: instance Monad Parser where return
Page 37 and 38: natural :: Parser Integer natural =
Page 39 and 40: print $ eval $ run a Now we can try
Page 41 and 42: module Syntax where data Expr = Tr
Page 43 and 44: cannot proceed because the reductio
Page 45 and 46: later into native CPU instructions
Page 47 and 48: λx.e ere are several syntactical c
Page 49 and 50: type Name = String data Expr = Var
Page 51 and 52: Eta-expansion (λx.ex)e ′ β →
Page 53 and 54: Y = SSK(S(K(SS(S(SSK))))K) In a unt
Page 55 and 56: parensIf :: Bool -> Doc -> Doc pare
Page 57 and 58: In this notation, the expression ab
Page 59 and 60: In all the languages which we will
Page 61 and 62: eval1 expr = case expr of Succ t ->
Page 63 and 64: TNat -> return TNat _ -> throwError
Page 65 and 66: • T-Var Variables are simply pull
Page 67 and 68: t1 throwError $ Mismatch t2 a ty -
Page 69 and 70: Full Source • Typed Arithmetic
Page 71 and 72:
1. Evaluate f to λy.e 2. Evaluate
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e 1 → e ′ 1 e 1 e 2 → e ′ 1
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case we will use a GADT to embed a
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AppP (AppP (VarP f) (VarP x)) (AppP
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e prim function will simply perform
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ere is nothing more practical than
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As before let rec expressions will
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Γ, x : τ = (Γ\x) ∪ {x : τ} Op
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where s’ = foldr Map.delete s as
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s2 Type -> Infer Subst bind a t |
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infer :: TypeEnv -> Expr -> Infer (
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App e1 e2 -> do tv
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-- | Unify two types uni :: Type ->
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unifies t (TVar v) = v ‘bind‘ t
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Interpreter Our evaluator will oper
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Our language can be compiled into a
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exec True contents -- :type command
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let rec fib n = if (n == 0) then 0
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• Higher order functions • Para
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• e PHOAS, the type-erased Core i
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If the ProtoHaskell compiler is inv
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infixl 6 + infixl 7 * f = 1 + 2 * 3
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-- Desugared f x = case x of Just _
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data Kind = KStar | KArr Kind Kind
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TypeError) -- | Inference state dat
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e expression or Expr type is the co
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data qname [var] where [tydecl] dat
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Typeclass Declarations Typeclass de
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Syntax Name Kind Description (,) Pa
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So for instance if we have three AS
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-- **Begin Haskell Syntax** { {-# O
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tokens :- -- Whitespace insensitive
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Expr : let VAR ’=’ Expr in Expr
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data Type = TVar Loc TVar | TCon Lo
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-- Start of layout ( Column: 0 ) fi
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Extensible Operators Haskell famous
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fixityspec :: Parser FixitySpec fix
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Write You a Haskell Stephen Diehl

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