I'm very new to haskell, and functional programming in general, I'm switching back and fourth between two different books on haskell, but I can't seem to find an answer to my question. Say I have a custom datatype like the one below
data Expr
= Let String Expr Expr
| Binary BinOp Expr Expr
| Unary UnOp Expr
| Literal Literal
| Var String
and I have an instance of this data type that is in the form of the first constructor Let String Expr Expr, is it possible to access a specific piece of that Expr? For example if I wanted to access the String within that specific instance.
Pattern matching is your answer.
Something like this should do the trick:
myfunction :: Expr -> SomeReturnType
myfunction (Let str _ _) = doSomethingWith str -- "str" here is your string
You'll want to handle the other cases as well though, so you don't cause a runtime error:
myfunction :: Expr -> SomeReturnType
myfunction (Let str _ _) = doSomethingElse str
myfunction (Binary _ _ _) = somethingEvenDifferent
myfunction (Unary _ _) = etc
--- etc...
the _ just says to ignore the value at that position in the constructor.
Also, as #Bergi mentioned, there are many other places you can use pattern matching, like let or case statements, just always be sure to handle all the cases that your value could potentially be at that point in your program.
Related
At first, I have a original AST definition like this:
data Expr = LitI Int | LitB Bool | Add Expr Expr
And I want to generalize it so that each AST node can contains some extra attributes:
data Expr a = LitI Int a | LitB Bool a | Add (Expr a) (Expr a) a
In this way, we can easily attach attribute into each node of the AST:
type ExprWithType = Expr TypeRep
type ExprWithSize = Expr Int
But this solution makes it hard to visit the attribute field, we must use pattern matching and process it case by case:
attribute :: Expr a -> a
attribute e = case e of
LitI _ a -> a
LitB _ a -> a
Add _ _ a -> a
We can image that if we can define our AST via a product type of the original AST and the type variable indicating attribute:
type ExprWithType = (Expr, TypeRep)
type ExprWithSize = (Expr, Int)
Then we can simplify the attribute visiting function like this:
attribute = snd
But we know that, the attribute from the outmost product type will not recursively appears in the subtrees.
So, is there a better solution for this problem?
Generally speaking, When we want to extract common field of different cases of a recursive sum type, we met this problem.
You could "lift" the type of the Expr for example like:
data Expr e = LitI Int | LitB Bool | Add e e
Now we can define a data type like:
data ExprAttr a = ExprAttr {
expression :: Expr (ExprAttr a),
attribute :: a
}
So here the ExprAttr has two parameters, the expression, which is thus an Expression that has ExprAttr as in the tree, and attribute which is an a.
You can thus process ExprAttrs, which is an AST of ExprAttrs. If you want to use a "simple" AST, you can define a type like:
newtype SimExpr = SimExpr (Expr SimExpr)
You might want to take a look at Cofree where f will be your recursive data type after abstracting the concept of recursion as an f-algebra and a will be the type of your annotation.
Nate Faubion gave a very accesible talk about this and similar approaches and you can watch it here: https://www.youtube.com/watch?v=eKkxmVFcd74
I'm going through Write Yourself a Scheme in 48 Hours, and in it I've come across some seemingly redundant code; they use #-patterns and then return the value itself, let me explain.
Here's the relevant code:
data LispVal = Atom String
| List [LispVal]
| DottedList [LispVal] LispVal
| Number Integer
| String String
| Bool Bool
eval :: LispVal -> LispVal -- code in question starts here
eval val#(String _) = val
eval val#(Number _) = val
eval val#(Bool _) = val
eval (List [Atom "quote", val]) = val
It seems to me that the entire eval function could just as easily be re-written as
eval :: LispVal -> LispVal
eval (List [Atom "quote", val]) = val
eval val = val
And have the bottom case account for all the #-patterns in the original code.
Am I mistaken in thinking this, and is there an actual benefit of doing it the way they did? Or is the other way more concise?
One difference is that the original code is undefined for values constructed with Atom, i.e. there is no line
eval val#(Atom _) = val
And whether this is a copy’n’paste error or not, it highlights the important difference in style:
The first style encourages you to think about each value individually, making an explicit assertion “this is the right equation for this”. If you later add more constructors t othe LispVal type, you get runtime errors (or compiler warnings with -fwarn-incomplete-patterns, which is good practice).
The second style asserts: eval will only have to look at List values, and all others can be treated individually. In particular, later additions to the data type should work just as well, and you don’t want to be bothered about this function then.
Operationally, they are equivalent.
I have 2 parsers:
nexpr::Parser (Expr Double)
sexpr::Parser (Expr String)
How do I build a parser that tries one and then the other if it doesn't work? I can't figure out what to return. There must be a clever way to do this.
Thanks.
EDIT:
Adding a bit more info...
I'm learning Haskel, so I started with :
data Expr a where
N::Double -> Expr Double
S::String -> Expr String
Add::Expr Double -> Expr Double -> Expr Double
Cat::Expr String -> Expr String -> Expr String
then I read about F-algebra (here) and so I changed it to:
data ExprF :: (* -> *) -> * -> * where
N::Double -> ExprF r Double
S::String -> ExprF r String
Add::r Double -> r Double -> ExprF r Double
Cat::r String -> r String -> ExprF r String
with
type Expr = HFix ExprF
so my parse to:
Parser (Expr Double)
is actually:
Parser (ExprF HFix Double)
Maybe I'm biting off more than I can chew...
As noted in the comments, you can have a parser like this
nOrSexpr :: Parser (Either (Expr Double) (Expr String))
nOrSexpr = (Left <$> nexpr) <|> (Right <$> sexpr)
However, I think the reason that you are having this difficulty is because you are not representing your parse tree as a single type, which is the more usual thing to do. Something like this:
data Expr =
ExprDouble Double
| ExprInt Int
| ExprString String
That way you can have parsers for each kind of expression that are all of type Parser Expr. This is the same as using Either but more flexible and maintainable. So you might have
doubleParser :: Parser Expr
doubleParser = ...
intParser :: Parser Expr
intParser = ...
stringParser :: Parser Expr
stringParser = ...
exprParser :: Parser Expr
exprParser = intParser <|> doubleParser <|> stringParser
Note that the order of the parsers does matter and use can use Parsec's try function if backtracking is needed.
So, for example, if you want to have a sum expression now, you can add to the data type
data Expr =
ExprDouble Double
| ExprInt Int
| ExprString String
| ExprSum Expr Expr
and make the parser
sumParser :: Parser Expr
sumParser = do
a <- exprParser
string " + "
b <- exprParser
return $ ExprSum a b
UPDATE
Well, I take my hat off to you diving straight into GADTs if you are just starting with Haskell. I have been reading through the paper you linked and noticed this immediately in the first paragraph:
The jury is still out on whether the additional type-safety provided by GADTs is worth the added inconvenience of working with them.
There are three points worth taking away here I think. The first is simply that I would have a go with the simpler way of doing things first, to get an idea of how it works and why you might want to add more type safety, before trying to more complicated type theoretical stuff. That comment may not help so feel free to ignore it!
Secondly, and more importantly, your representation...
data ExprF :: (* -> *) -> * -> * where
N :: Double -> ExprF r Double
S :: String -> ExprF r String
Add :: r Double -> r Double -> ExprF r Double
Cat :: r String -> r String -> ExprF r String
...is specifically designed to not allow ill formed type expressions. Contrasted with mine which can, eg ExprSum (ExprDouble 5.0) (ExprString "test"). So the question you really want to ask is what should actually happen when the parser attempts to parse something like "5.0 + \"test\""? Do you want it to just not parse, or do you want it to return a nice message saying that this expression is the wrong type? Compilers are usually designed in multiple stages for this reason. The first pass turns the input into an abstract syntax tree (AST), and further passes annotate this tree with type judgements. This annotated AST can then be transformed into the semantic representation that you really want it in.
So in your case I would recommend two stages. first, parse into a dumb representation like mine, that will give you the correct tree shape but allow ill-typed expressions. Like
data ExprAST =
ExprASTDouble Double
| ExprASTInt Int
| ExprASTString String
| ExprASTAdd Expr Expr
Then have another function that will typecheck the ExprAST. Something like
typecheck :: ExprAST -> Maybe (ExprF HFix a)
(You could also use Either and return either the typechecked GADT or an error string saying what the problem is.) The further problem here is that you don't know what a is statically. The other answer solves this by using type tags and an existential wrapper, which you might find to be the best way to go. I feel like it might be simpler to have a top level expression in your GADT that all expressions must live in, so an entire parse will always have the same type. In the end there is usually only one program type.
My third, and last, point is related to this
The jury is still out on whether the additional type-safety provided by GADTs is worth the added inconvenience of working with them.
The more type safety, generally the more work you have to do to get it. You mention you are new to Haskell, yet this adventure has taken us right to the edge of what it is capable of doing. The type of the parsed expression cannot depend only on the input string in a Haskell function, because it does not allow for dependant types. If you want to go down this path, I might suggest you have a look at a language called Idris. A great introduction to what it is capable of can be found in this video, in which he constructs a typesafe printf.
The problem described looks to be using Parsec to parse into a GADT representation, for which probably the easiest solution would be parse into a monotype representation and then have a (likely partial) type checking phase to produce the well-typed GADT, if it can. The monotype representation could be an existential wrapper over a GADT term, with a type-tag to reify the GADT index.
EDIT: a quick example
Let's define a type for type-tags and an existential wrapper:
data Type :: * -> * where
TDouble :: Type Double
TString :: Type String
data Judgement f = forall ix. Judgement (f ix) (Type ix)
With the example GADT given in the original post, we only have a problem with the outer-most production, which we need to parse to a monotype as we don't know statically which expression type we will get at runtime:
pExpr :: Parser (Judgement Expr)
pExpr = Judgement <$> pDblExpr <*> pure TDouble
<|> Judgement <$> pStrExpr <*> pure TString
We can write a type check phase to produce a GADT or fail, depending on whether the type assertion succeeds or not:
typecheck :: Judgement Expr -> Type ix -> Maybe (Expr ix)
typecheck (Judgement e TDouble) TDouble = Just e
typecheck (Judgement e TString) TString = Just e
typecheck _ _ = Nothing
Hi I'm writing an interpreter of C-like, statically typed language in Haskell. I want to perform typechecking before an execution of code, but I have some problems with it. First of all, below there are some type definitions from my abstract syntax:
newtype Ident = Ident String deriving (Eq,Ord,Show)
data Exp = {-- some other value constructors --} | EFuncWithParams Ident [Exp]
data Type = TInt | TDouble | {-- some other value constructors --} | TFunction [Exp]
type TCM a = ErrorT String (Reader Env) a
TCM is for reporting errors and passing the enviroment, eg:
typeof (EVar v) = do
env <- ask
case M.lookup v env of
Nothing -> throwError $ "undefined variable" ++ v ++ "\n"
Just t - > return t
Now I want to check type of expressions so I have following function that performs checks:
typeof Exp :: Exp -> TCM Type
It is defined for all cases but one:
typeof (EFuncWithParams f l)
I'm stuck here. What I think I should do is to check the type of f (I mean first of all check if it really IS a function) and see whether types of arguments that are recorded in definition of f match types of arguments that are actually passed. Unfortunately I'm a haskell newbie and have no idea on how to express it the right way. Any suggestions will be highly appreciated :)
EDIT:
OK, It may not be implied by what I wrote here previously but EFuncWithParams Ident [Exp] is a function call actually (Yes, I know it is somewhat misleading) and I want to be able to call a function like f(2 + 3, a, b[0]) and this is why I used TFunction [Exp]. Function declaration and definition is a statement and is defined:
data Function_def =
Func Type_specifier Declarator Compound_stm
deriving (Eq,Ord,Show)
where Declarator is:
data Declarator = FuncDec Ident Parameter_declarations
Parameter declarations is a list of Type_specifiers and Idents
What I think I should do is to save function type in a map while checking its declaration, and then fetch it here. I mean I also have:
typeof_stm :: Stm -> TCM Type -- Function_def is a statement
The problem is that I have a separate function for type-checking statements and I am in doubt whether the map that is used by one function (eg. typeof_stm) is passed automatically to another one (eg. typeof). I see no way of this to happen but maybe I'm wrong.
I think your function type is wrong. You have it as TFunction [Exp], it should be TFunction [Type] Type (a list of argument types and a return type).
Typechecking code for a function call would look something like
case ... of ...
EFuncWithParams ident args -> do
t <- typeof (EVar ident)
ts <- mapM typeof args
case t of
TFunction ps r -> if ts == ps
then return r
else throwError $ "parameter types do not match"
_ -> throwError $ "called id " ++ ident ++ " which is not a function"
This pseudo-code probably goes in and out of the monad improperly, please bear with me, I don't have all of your code so I cannot really typecheck what I have done. But the overall scheme is like this. You probably will want to give more detailed error report if parameter types do not match (which ones don't match, or perhaps there's a wrong number of parameters).
I'm not practical with Haskell, I just did it in OCaml and in C++ but what you are going to do is to call the type checker function recursively on each parameter and check if they do correspond.
What I mean is that you'll have to type check something that is like
FunCall ident, exp list
Now you'll have in the environment an entry for the function with the types of parameters associated so what you need to ensure in order is that:
function named ident does exist in the environment
the number of parameters is equal to the definition (this can be done implicitly by the param checking function, see below)
for every parameter you call typeof (exp1) and you check that the returned TCM Type is the same of the corresponding parameter
This is how it should work. In OCaml (which is somewhat similar to Haskell) I would do something like:
match exp with
| FunCall ident, (param list) ->
(* get fundecl from ident *)
(* call check_params list_of_parameters, list_of_type_of_parameters *)
(* if check params return true then type check value of the function is the return value *)
let check_params list decl_list =
match list, decl_list with
| [], [] -> true
| p :: rp, d :: rd -> typeof(p) = d && check_params rp rd
| _ -> false
EFuncWithParams Ident [Exp]
It is typical for languages like yours to require a type annotation on the input, and possibly also a type annotation on the output. So if you add this info to that constructor
EFuncWithparams { inType, outType :: Type
, funcInput :: Ident
, funcBody :: [Expr] }
Now to typecheck it, you simply:
Add the binding of funcInput to inType to your type environment
Ascertain the type of funcBody with the new type environment
Make sure it matches with outType.
You should also check function applications to make sure that the input matches the function's inType, and that the results are used correctly according to its outType.
data Expr = Var Char | Tall Int | Sum Expr Expr | Mult Expr Expr | Neg Expr | Let Expr Expr Expr
deriving(Eq, Show)
That is the datatype for Expr, I have a few questions. I'm suppose to parse expressions like *(Expr,Expr) as shown in the datatype definition. However I do have some problems with "creating" a valid Expr. I use pattern matching for recognizing the different things Expr can be. Some more code:
parseExpr :: String -> (Expr, String)
parseExpr ('*':'(':x:',':y:')':s) = (Mult (parseExpr [x] parseExpr [y]),s)
This is not working, obviously. The return type of parseExpr is to return the rest of the expression that is to be parsed an a portion of the parsed code as an Expr. The right side of this code is the problem. I can't make a valid Expr. The function is suppose to call it self recursively until the problem is solved.
ANOTHER problem is that I don't know how to do the pattern matching against Var and Tall. How can I check that Var is an uppercase character between A-Z and that Tall is 0-9 and return it as a valid Expr?
Generally I can just look at a few parts of the string to understand what part of Expr I'm dealing with.
Input like: parseProg "let X be 9 in *(X , 2)" Would spit out: Let (Var 'X') (Tall 9) (Mult (Var 'X') (Tall 2))
Your parseExpr function returns a pair, so of course you cannot use its result directly to construct an Expr. The way I would write this would be something like
parseExpr ('*':'(':s) = (Mult x y, s'')
where (x,',':s') = parseExpr s
(y,')':s'') = parseExpr s'
The basic idea is that, since parseExpr returns the leftover string as the second argument of the pair, you need to save that string in each recursive call you make, and when you've handled all the subexpressions, you need to return whatever is left over. And obviously the error handling here sucks, so you may want to think about that a bit more if this is intended to be a robust parser.
Handling Var and Tall I would do by just extracting the first character as is and have an if to construct an Expr of the appropriate type.
And if you want to write more complex parsers in Haskell, you'll want to look at the Parsec library, which lets you write a parser as pretty much the grammar of the language you're parsing.