Write You a Haskell Stephen Diehl

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e 1 : Nat succ e 1 : Nat e 1 : Nat pred e 1 : Nat e 1 : Nat iszero e 1 : Bool (T-Succ) (T-Pred) (T-IsZero) 0 : Nat (T-Zero) True : Bool False : Bool e 1 : Bool e 2 : τ e 3 : τ if e 1 then e 2 else e 3 : τ (T-True) (T-False) (T-If) ese rules restrict the space of all possible programs. It is more involved to show, but this system has both progress and preservation as well. If a term is now well-typed it will always evaluate to a value and cannot “go wrong” at evaluation. To check the well-formedness of an expression we implement a piece of logic known as type checker which determines whether the term has a well-defined type in terms of typing rules, and if so returns it or fails with an exception in the case where it does not. type Check a = Except TypeError a data TypeError = TypeMismatch Type Type check :: Expr -> Either TypeError Type check = runExcept . typeof typeof :: Expr -> Check Type typeof expr = case expr of Succ a -> do ta return TNat _ -> throwError $ TypeMismatch ta TNat Pred a -> do ta
TNat -> return TNat _ -> throwError $ TypeMismatch ta TNat IsZero a -> do ta return TBool _ -> throwError $ TypeMismatch ta TNat If a b c -> do ta return TNat Observations e pathological stuck terms that we encountered previously in our untyped language are now completely inexpressive and are rejected at compile-time. Arith> succ 0 succ 0 : Nat Arith> succ (succ 0) succ (succ 0) : Nat Arith> if false then true else false false : Bool Arith> iszero (pred (succ (succ 0))) false : Bool Arith> pred (succ 0) 0 : Nat Arith> iszero false 61
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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
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 and 20: length :: [a] -> Int length [] = 0
Page 21 and 22: Higher-Kinded Types e “type of ty
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: eval1 expr = case expr of Succ t ->
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
Page 73 and 74: 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
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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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