Write You a Haskell Stephen Diehl

Recommendations

Info

force :: IORef Thunk -> IO Value force ref = do th Expr -> (Thunk -> IO Value) mkThunk env x body = \a -> do a’ Expr -> IO Value eval env ex = case ex of EVar n -> do th do VClosure c eval env b) EBool b -> return $ VBool b EInt n -> return $ VInt n EFix e -> eval env (EApp e (EFix e)) For example, in this model the following program will not diverge since the omega combinator passed into the constant function is not used and therefore the argument is not evaluated. omega = (\x -> x x) (\x -> x x) test1 = (\y -> 42) omega omega :: Expr omega = EApp (ELam ”x” (EApp (EVar ”x”) (EVar ”x”))) (ELam ”x” (EApp (EVar ”x”) (EVar ”x”))) test1 :: IO Value test1 = eval [] $ EApp (ELam ”y” (EInt 42)) omega Higher Order Abstract Syntax (HOAS) GHC Haskell being a rich language has a variety of extensions that, among other things, allow us to map lambda expressions in our defined language directly onto lambda expressions in Haskell. In this 72
case we will use a GADT to embed a Haskell expression inside our expression type. {-# LANGUAGE GADTs #-} data Expr a where Lift :: a -> Expr a Tup :: Expr a -> Expr b -> Expr (a, b) Lam :: (Expr a -> Expr b) -> Expr (a -> b) App :: Expr (a -> b) -> Expr a -> Expr b Fix :: Expr (a -> a) -> Expr a e most notable feature of this encoding is that there is no distinct constructor for variables. Instead they are simply values in the host language. Some example expressions: id :: Expr (a -> a) id = Lam (\x -> x) tr :: Expr (a -> b -> a) tr = Lam (\x -> (Lam (\y -> x))) fl :: Expr (a -> b -> b) fl = Lam (\x -> (Lam (\y -> y))) Our evaluator then simply uses Haskell for evaluation. eval :: Expr a -> a eval (Lift v) = v eval (Tup e1 e2) = (eval e1, eval e2) eval (Lam f) = \x -> eval (f (Lift x)) eval (App e1 e2) = (eval e1) (eval e2) eval (Fix f) = (eval f) (eval (Fix f)) Some examples of use: fact :: Expr (Integer -> Integer) fact = Fix ( Lam (\f -> Lam (\y -> Lift ( if eval y == 0 then 1 else eval y * (eval f) (eval y - 1))))) 73
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 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 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
Page 73: e 1 → e ′ 1 e 1 e 2 → e ′ 1
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 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 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
show all

Write You a Haskell Stephen Diehl

Create successful ePaper yourself

Delete template?

Save as template?