Write You a Haskell Stephen Diehl

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instance Num Int where plus = plusInt# InstDecl [] (Name ”Num”) (TCon AlgTyCon { tyId = Name ”Int” }) [ FunDecl BindGroup { _matchName = Name ”plus” , _matchPats = [ Match { _matchPat = [] , _matchBody = EVar (Name ”plusInt”) } ] , _matchType = Nothing , _matchWhere = [ [] ] } ] Wired-in Types While the base <strong>Haskell</strong> is quite small, several portions of the desugaring process require the compiler to be aware about certain types before they otherwise defined in the Prelude. For instance the type of every guarded pattern in the typechecker is Bool. ese are desugared into a case statement that includes the True and False constructors. e Bool type is therefore necessarily baked into the syntax of the language and is inseparable from the implementation. sign x | x > 0 = 1 | x == 0 = 0 | x < 0 = -1 ese are called the wired-in types, and while they are still defined in our Prelude they will have somewhat special status. e primitive types (of kind #) will be very special and are not user extensible, they map directly to implementation details of the code generation backend or <strong>Haskell</strong> functions hard-wired into the interpreter. Syntax Name Kind Description Int# Int# # Machine integer Char# Char# # Machine char Double# Double# # Machine double Addr# Addr# # Heap address Int Int * Boxed integer Char Char * Boxed char Double Double * Boxed double [] List * -> * List 124
Syntax Name Kind Description (,) Pair * -> * -> * 2-Tuple () Unit * Unit type (->) Arrow * -> * -> * Arrow type Bool Bool * Boolean IO IO * -> * IO Monad Traversals Bottom-up traversals and rewrites in a monadic context are so that common that we’d like to automate this process so that we don’t have duplicate the same logic across all our code. So we’ll write several generic traversal functions. descendM :: (Monad m, Applicative m) => (Expr -> m Expr) -> Expr -> m Expr descendM f e = case e of EApp a b -> EApp descendM f a descendM f b EVar a -> EVar pure a ELam a b -> ELam pure a descendM f b ELit n -> ELit pure n ELet n a b -> ELet pure n descendM f a descendM f b EIf a b c -> EIf descendM f a descendM f b descendM f c ECase a xs -> ECase f a traverse (descendCaseM f) xs EAnn a t -> EAnn descendM f a pure t EFail -> pure EFail descendCaseM :: (Monad m, Applicative m) => (Expr -> m Expr) -> Match -> m Match descendCaseM f e = case e of Match ps a -> Match pure ps descendM f a e case where the monad is Identity simply corresponds to a pure expression rewrite. descend :: (Expr -> Expr) -> Expr -> Expr descend f ex = runIdentity (descendM (return . f) ex) For example a transformation for use in this framework of traversals might just use pattern matching to match specific syntactic structure and rewrite it or simply yield the input and traverse to the next element in the bottom-up traversal. A pure trnasformation that rewrites all variables named “a” to “b” might be written concisely as the following higher order function. transform :: Expr -> Expr transform = descend f 125
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Write You a Haskell Building a mode
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Contents Introduction 6 Goals . . .
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Evaluation . . . . . . . . . . . .
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Syntax Errors . . . . . . . . . . .
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• containers • unordered-contai
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File ””, line 1, in TypeError:
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] TokenSym ”x”, TokenAdd, Token
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f: mov res, arg add res, 1 ret defi
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Datatypes Constructors for datatype
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length :: [a] -> Int length [] = 0
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Higher-Kinded Types e “type of ty
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eturn a >>= f = f a Law 2 m >>= ret
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data PlatonicSolid = Tetrahedron |
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foo :: Stack () foo = Stack $ do pu
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, bar :: Int } deriving (Show) comp
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class IsString a where fromString :
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Parsing Parser Combinators For pars
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instance Monad Parser where return
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natural :: Parser Integer natural =
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print $ eval $ run a Now we can try
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module Syntax where data Expr = Tr
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cannot proceed because the reductio
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later into native CPU instructions
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λx.e ere are several syntactical c
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type Name = String data Expr = Var
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Eta-expansion (λx.ex)e ′ β →
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Y = SSK(S(K(SS(S(SSK))))K) In a unt
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parensIf :: Bool -> Doc -> Doc pare
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In this notation, the expression ab
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In all the languages which we will
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eval1 expr = case expr of Succ t ->
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TNat -> return TNat _ -> throwError
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• T-Var Variables are simply pull
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t1 throwError $ Mismatch t2 a ty -
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Full Source • Typed Arithmetic
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1. Evaluate f to λy.e 2. Evaluate
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e 1 → e ′ 1 e 1 e 2 → e ′ 1
Page 75 and 76: case we will use a GADT to embed a
Page 77 and 78: AppP (AppP (VarP f) (VarP x)) (AppP
Page 79 and 80: e prim function will simply perform
Page 81 and 82: ere is nothing more practical than
Page 83 and 84: As before let rec expressions will
Page 85 and 86: Γ, x : τ = (Γ\x) ∪ {x : τ} Op
Page 87 and 88: where s’ = foldr Map.delete s as
Page 89 and 90: s2 Type -> Infer Subst bind a t |
Page 91 and 92: infer :: TypeEnv -> Expr -> Infer (
Page 93 and 94: App e1 e2 -> do tv
Page 95 and 96: -- | Unify two types uni :: Type ->
Page 97 and 98: unifies t (TVar v) = v ‘bind‘ t
Page 99 and 100: Interpreter Our evaluator will oper
Page 101 and 102: Our language can be compiled into a
Page 103 and 104: exec True contents -- :type command
Page 105 and 106: let rec fib n = if (n == 0) then 0
Page 107 and 108: • Higher order functions • Para
Page 109 and 110: • e PHOAS, the type-erased Core i
Page 111 and 112: If the ProtoHaskell compiler is inv
Page 113 and 114: infixl 6 + infixl 7 * f = 1 + 2 * 3
Page 115 and 116: -- Desugared f x = case x of Just _
Page 117 and 118: data Kind = KStar | KArr Kind Kind
Page 119 and 120: TypeError) -- | Inference state dat
Page 121 and 122: e expression or Expr type is the co
Page 123 and 124: data qname [var] where [tydecl] dat
Page 125: Typeclass Declarations Typeclass de
Page 129 and 130: So for instance if we have three AS
Page 131 and 132: -- **Begin Haskell Syntax** { {-# O
Page 133 and 134: tokens :- -- Whitespace insensitive
Page 135 and 136: Expr : let VAR ’=’ Expr in Expr
Page 137 and 138: data Type = TVar Loc TVar | TCon Lo
Page 139 and 140: -- Start of layout ( Column: 0 ) fi
Page 141 and 142: Extensible Operators Haskell famous
Page 143 and 144: fixityspec :: Parser FixitySpec fix
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Write You a Haskell Stephen Diehl

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