Write You a Haskell Stephen Diehl

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Type Error Provenance Before our type inference engine would generate somewhat typical type inference error messages. If two terms couldn’t be unified it simply told us this and some information about the toplevel declaration where it occurred. Leaving us with a bit of a riddle about this error came to be. Cannot unify types: Int with Bool in the definition of ’foo’ Effective error reporting in the presence of type inference is a difficult task, effectively our typechecker takes our frontend AST and transforms it into a large constraint problem but effectively destroys position information information in the process. Even if the position information were tracked, the nature of unification is that a cascade of several unifications can give rise to invalid solution and the immediate two syntactic constructs that gave rise to a unification fail are not necessarily the two that map back to human intuition about how the type error arose. Very little research has done on this topic and it remains a open topic with very immediate and applicable results to programming. To do simple provenance tracking we will use a technique of track the “flow” of type information through out typechecker and associate position information associated with the inferred types back to their position information in the source. type Name = String data Expr = Var Loc Name | App Loc Expr Expr | Lam Loc Name Expr | Lit Loc Int data Loc = NoLoc | Located Int deriving (Show, Eq, Ord) So now inside of our parser we simply attach Parsec information on to each AST node. For example for the variable term. variable :: Parser Expr variable = do x
data Type = TVar Loc TVar | TCon Loc Name | TArr Loc Type Type deriving (Show, Eq, Ord) newtype TVar = TV String deriving (Show, Eq, Ord) typeInt :: Type typeInt = TCon NoLoc ”Int” setLoc :: Loc -> Type -> Type setLoc l (TVar _ a) = TVar l a setLoc l (TCon _ a) = TCon l a setLoc l (TArr _ a b) = TArr l a b getLoc :: Type -> Loc getLoc (TVar l _) = l getLoc (TCon l _) = l getLoc (TArr l _ _) = l Our fresh variable supply now also takes a location field which is attached to resulting type variable. fresh :: Loc -> Check Type fresh l = do s Check Type infer expr = case expr of Var l n -> do t do ta
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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
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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
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 and 126: Typeclass Declarations Typeclass de
Page 127 and 128: Syntax Name Kind Description (,) Pa
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: Expr : let VAR ’=’ Expr in Expr
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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