Write You a Haskell Stephen Diehl

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e 1 → e 2 succ e 1 → succ e 2 e 1 → e 2 pred e 1 → pred e 2 pred 0 → 0 pred (succ n) → n e 1 → e 2 iszero e 1 → iszero e 2 iszero 0 → true iszero (succ n) → false if True then e 2 else e 3 → e 2 if False then e 2 else e 3 → e 3 (E-Succ) (E-Pred) (E-PredZero) (E-PredSucc) (E-IsZero) (E-IsZeroZero) (E-IsZeroSucc) (E-IfTrue) (E-IfFalse) e evaluation logic for our interpreter simply reduced an expression by the predefined evaluation rules until either it reached a normal form ( a value ) or got stuck. nf :: Expr -> Expr nf t = fromMaybe t (nf eval1 t) eval :: Expr -> Maybe Expr eval t = case isVal (nf t) of True -> Just (nf t) False -> Nothing -- term is ”stuck” Values in our language are defined to be literal numbers or booleans. isVal :: Expr -> Bool isVal Tr = True isVal Fl = True isVal t | isNum t = True isVal _ = False Written in applicative form there is a noticeable correspondence between each of the evaluation rules and our evaluation logic. -- Evaluate a single step. eval1 :: Expr -> Maybe Expr 58
eval1 expr = case expr of Succ t -> Succ (eval1 t) Pred Zero -> Just Zero Pred (Succ t) | isNum t -> Just t Pred t -> Pred (eval1 t) IsZero Zero -> Just Tr IsZero (Succ t) | isNum t -> Just Fl IsZero t -> IsZero (eval1 t) If Tr c _ -> Just c If Fl _ a -> Just a If t c a -> (\t’ -> If t’ c a) eval1 t _ -> Nothing As we noticed before we could construct all sorts of pathological expressions that would become stuck. Looking at the evaluation rules, each of the guarded pattern matches gives us a hint of where things might “go wrong” whenever a boolean is used in the place of a number and vice versa. We’d like to statically enforce this invariant at compile-time instead, and so we’ll introduce a small type system to handle the two syntactic categories of terms that exist. e abstract type of natural numbers and the type of booleans: τ ::= Bool Nat Which is implemented in <strong>Haskell</strong> as the following datatype: data Type = TBool | TNat Now for the typing rules: 59
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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 . . . . . . . . . . .
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 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: In all the languages which we will
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
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
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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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