I found this exercise on equational reasoning and proofs in Haskell. The following code is given:
type Stack = [Int]
type Code = [Op]
data Op = PUSH Int | ADD
deriving (Show)
--
-- Stack machine
--
exec :: Code -> Stack -> Stack
exec [ ] s = s
exec (PUSH n : c) s = exec c (n:s)
exec (ADD:c) (m:n:s) = exec c (n+m : s)
--
-- Interpeter
--
data Expr = Val Int | Add Expr Expr
deriving (Show)
eval :: Expr -> Int
eval (Val n) = n
eval (Add x y) = eval x+eval y
--
-- Compiler
--
comp :: Expr -> Code
comp (Val n) = [PUSH n]
comp (Add x y) = comp x ++ comp y ++ [ADD]
Now I have to prove that exec(comp e) s = eval e : s.
So I found this answer so far:
We have to prove that exec (comp e) s = eval e : s.
First case: Assume e = (Val n). Then comp (Val n) = [PUSH n], so we have to prove that exec ([PUSH n]) s = eval ([PUSH n] : s). We find that exec ([PUSH n]) s = exec [] (n:s) = (n:s) using the function definition of exec.
Now eval (Val n) : s = n : s. The first case is OK!
Second case: Assume e = (Add x y). Then comp (Add x y) = comp x ++ comp y ++ [ADD].
But now I'm struggling with this recursive use of comp. Should I be using some form of trees and induction on these trees to prove this? I'm not completely sure how to do that.
When the first argument to exec is a list, the two possibilities are:
exec (PUSH n: codes) -- #1
exec (ADD : codes) -- #2
In the induction step you get to assume that the proposition holds for codes, i.e. you may assume:
exec codes s = eval codes : s
for any value of s -- Keep this in mind - this is usually the key step in any induction proof.
Start by expanding #1 using the code you've written for exec:
exec (PUSH n: codes) s == exec codes (n:s)
== ...
== ...
== eval (PUSH n: codes) : s
Can you see a place to use the induction hypothesis?
Related
I made the pattern where if you give it only a number it's gonna return the Value. I would just add deriving (Show) to Val as well but that doesn't work because of (Val->Val) (that's what I understood from the error messages). Anyone know what I could do ?
import GHC.Show (Show)
type Var = String
-- Expressions of source code in the form of a Abstract syntax tree
data Exp = Enum Int -- constant
|Evar Var -- variable
|Elet Var Exp Exp -- expr "let x = e1 in e2"
|Ecall Exp Exp -- Function call
deriving (Show)
-- returned values
data Val = Vnum Int -- Whole number
|Vprim (Val->Val) -- A primitive
mkPrim::(Int->Int->Int)->Val
mkPrim f = Vprim(\(Vnum x) -> Vprim (\(Vnum y) -> Vnum (f x y)))
-- Initial environement that contains all primitives
type Env = [(Var, Val)]
pervasive::Env
pervasive = [("+", mkPrim (+)), ("-", mkPrim (-)),("*", mkPrim (*)), ("/", mkPrim div)]
eval::Env->Exp->Val
eval pervasive (Enum n) = Vnum n
sampleExp = Elet "x" (Enum 3) (Ecall (Ecall (Evar "+") (Evar "x")) (Enum 4))
main = do print(eval pervasive (Enum 4))
Consider implementing a custom Show instance:
instance Show Val where
show (Vnum n) = show n
show (Vprim _) = "<prim>"
This however shall make printed primitives indistinguishable. It might be convenient to equip prims with names:
data Val = Vnum Int | Vprim String (Val -> Val)
instance Show Val where
show (Vnum n) = show n
show (Vprim name _) = name
So I'm trying to make a little program that can take in data captured during an experiment, and for the most part I think I've figured out how to recursively take in data until the user signals there is no more, however upon termination of data taking haskell throws Exception: <<loop>> and I can't really figure out why. Here's the code:
readData :: (Num a, Read a) => [Point a] -> IO [Point a]
readData l = do putStr "Enter Point (x,y,<e>) or (d)one: "
entered <- getLine
if (entered == "d" || entered == "done")
then return l
else do let l = addPoint l entered
nl <- readData l
return nl
addPoint :: (Num a, Read a) => [Point a] -> String -> [Point a]
addPoint l s = l ++ [Point (dataList !! 0) (dataList !! 1) (dataList !! 2)]
where dataList = (map read $ checkInputData . splitOn "," $ s) :: (Read a) => [a]
checkInputData :: [String] -> [String]
checkInputData xs
| length xs < 2 = ["0","0","0"]
| length xs < 3 = (xs ++ ["0"])
| length xs == 3 = xs
| length xs > 3 = ["0","0","0"]
As far as I can tell, the exception is indication that there is an infinite loop somewhere, but I can't figure out why this is occurring. As far as I can tell when "done" is entered the current level should simply return l, the list it's given, which should then cascade up the previous iterations of the function.
Thanks for any help. (And yes, checkInputData will have proper error handling once I figure out how to do that.)
<<loop>> basically means GHC has detected an infinite loop caused by a value which depends immediately on itself (cf. this question, or this one for further technical details if you are curious). In this case, that is triggered by:
else do let l = addPoint l entered
This definition, which shadows the l you passed as an argument, defines l in terms of itself. You meant to write something like...
else do let l' = addPoint l entered
... which defines a new value, l', in terms of the original l.
As Carl points out, turning on -Wall (e.g. by passing it to GHC at the command line, or with :set -Wall in GHCi) would make GHC warn you about the shadowing:
<interactive>:171:33: warning: [-Wname-shadowing]
This binding for ‘l’ shadows the existing binding
bound at <interactive>:167:10
Also, as hightlighted by dfeuer, the whole do-block in the else branch can be replaced by:
readData (addPoint l entered)
As an unrelated suggestion, in this case it is a good idea to replace your uses of length and (!!) with pattern matching. For instance, checkInputData can be written as:
checkInputData :: [String] -> [String]
checkInputData xs = case xs of
[_,_] -> xs ++ ["0"]
[_,_,_] -> xs
_ -> ["0","0","0"]
addPoint, in its turn, might become:
addPoint :: (Num a, Read a) => [Point a] -> String -> [Point a]
addPoint l s = l ++ [Point x y z]
where [x,y,z] = (map read $ checkInputData . splitOn "," $ s) :: (Read a) => [a]
That becomes even neater if you change checkInputData so that it returns a (String, String, String) triple, which would better express the invariant that you are reading exactly three values.
I'm trying to use CPS to simplify control-flow implementation in my Python interpreter. Specifically, when implementing return/break/continue, I have to store state and unwind manually, which is tedious. I've read that it's extraordinarily tricky to implement exception handling in this way. What I want is for each eval function to be able to direct control flow to either the next instruction, or to a different instruction entirely.
Some people with more experience than me suggested looking into CPS as a way to deal with this properly. I really like how it simplifies control flow in the interpreter, but I'm not sure how much I need to actually do in order to accomplish this.
Do I need to run a CPS transform on the AST? Should I lower this AST into a lower-level IR that is smaller and then transform that?
Do I need to update the evaluator to accept the success continuation everywhere? (I'm assuming so).
I think I generally understand the CPS transform: the goal is to thread the continuation through the entire AST, including all expressions.
I'm also a bit confused where the Cont monad fits in here, as the host language is Haskell.
Edit: here's a condensed version of the AST in question. It is a 1-1 mapping of Python statements, expressions, and built-in values.
data Statement
= Assignment Expression Expression
| Expression Expression
| Break
| While Expression [Statement]
data Expression
| Attribute Expression String
| Constant Value
data Value
= String String
| Int Integer
| None
To evaluate statements, I use eval:
eval (Assignment (Variable var) expr) = do
value <- evalExpr expr
updateSymbol var value
eval (Expression e) = do
_ <- evalExpr e
return ()
To evaluate expressions, I use evalExpr:
evalExpr (Attribute target name) = do
receiver <- evalExpr target
attribute <- getAttr name receiver
case attribute of
Just v -> return v
Nothing -> fail $ "No attribute " ++ name
evalExpr (Constant c) = return c
What motivated the whole thing was the shenanigans required for implementing break. The break definition is reasonable, but what it does to the while definition is a bit much:
eval (Break) = do
env <- get
when (loopLevel env <= 0) (fail "Can only break in a loop!")
put env { flow = Breaking }
eval (While condition block) = do
setup
loop
cleanup
where
setup = do
env <- get
let level = loopLevel env
put env { loopLevel = level + 1 }
loop = do
env <- get
result <- evalExpr condition
when (isTruthy result && flow env == Next) $ do
evalBlock block
-- Pretty ugly! Eat continue.
updatedEnv <- get
when (flow updatedEnv == Continuing) $ put updatedEnv { flow = Next }
loop
cleanup = do
env <- get
let level = loopLevel env
put env { loopLevel = level - 1 }
case flow env of
Breaking -> put env { flow = Next }
Continuing -> put env { flow = Next }
_ -> return ()
I am sure there are more simplifications that can be done here, but the core problem is one of stuffing state somewhere and manually winding out. I'm hoping that CPS will let me stuff book-keeping (like loop exit points) into state and just use those when I need them.
I dislike the split between statements and expressions and worry it might make the CPS transform more work.
This finally gave me a good excuse to try using ContT!
Here's one possible way of doing this: store (in a Reader wrapped in ContT) the continuation of exiting the current (innermost) loop:
newtype M r a = M{ unM :: ContT r (ReaderT (M r ()) (StateT (Map Id Value) IO)) a }
deriving ( Functor, Applicative, Monad
, MonadReader (M r ()), MonadCont, MonadState (Map Id Value)
, MonadIO
)
runM :: M a a -> IO a
runM m = evalStateT (runReaderT (runContT (unM m) return) (error "not in a loop")) M.empty
withBreakHere :: M r () -> M r ()
withBreakHere act = callCC $ \break -> local (const $ break ()) act
break :: M r ()
break = join ask
(I've also added IO for easy printing in my toy interpreter, and State (Map Id Value) for variables).
Using this setup, you can write Break and While as:
eval Break = break
eval (While condition block) = withBreakHere $ fix $ \loop -> do
result <- evalExpr condition
unless (isTruthy result)
break
evalBlock block
loop
Here's the full code for reference:
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
module Interp where
import Prelude hiding (break)
import Control.Applicative
import Control.Monad.Cont
import Control.Monad.State
import Control.Monad.Reader
import Data.Function
import Data.Map (Map)
import qualified Data.Map as M
import Data.Maybe
type Id = String
data Statement
= Print Expression
| Assign Id Expression
| Break
| While Expression [Statement]
| If Expression [Statement]
deriving Show
data Expression
= Var Id
| Constant Value
| Add Expression Expression
| Not Expression
deriving Show
data Value
= String String
| Int Integer
| None
deriving Show
data Env = Env{ loopLevel :: Int
, flow :: Flow
}
data Flow
= Breaking
| Continuing
| Next
deriving Eq
newtype M r a = M{ unM :: ContT r (ReaderT (M r ()) (StateT (Map Id Value) IO)) a }
deriving ( Functor, Applicative, Monad
, MonadReader (M r ()), MonadCont, MonadState (Map Id Value)
, MonadIO
)
runM :: M a a -> IO a
runM m = evalStateT (runReaderT (runContT (unM m) return) (error "not in a loop")) M.empty
withBreakHere :: M r () -> M r ()
withBreakHere act = callCC $ \break -> local (const $ break ()) act
break :: M r ()
break = join ask
evalExpr :: Expression -> M r Value
evalExpr (Constant val) = return val
evalExpr (Var v) = gets $ fromMaybe err . M.lookup v
where
err = error $ unwords ["Variable not in scope:", show v]
evalExpr (Add e1 e2) = do
Int val1 <- evalExpr e1
Int val2 <- evalExpr e2
return $ Int $ val1 + val2
evalExpr (Not e) = do
val <- evalExpr e
return $ if isTruthy val then None else Int 1
isTruthy (String s) = not $ null s
isTruthy (Int n) = n /= 0
isTruthy None = False
evalBlock = mapM_ eval
eval :: Statement -> M r ()
eval (Assign v e) = do
val <- evalExpr e
modify $ M.insert v val
eval (Print e) = do
val <- evalExpr e
liftIO $ print val
eval (If cond block) = do
val <- evalExpr cond
when (isTruthy val) $
evalBlock block
eval Break = break
eval (While condition block) = withBreakHere $ fix $ \loop -> do
result <- evalExpr condition
unless (isTruthy result)
break
evalBlock block
loop
and here's a neat test example:
prog = [ Assign "i" $ Constant $ Int 10
, While (Var "i") [ Print (Var "i")
, Assign "i" (Add (Var "i") (Constant $ Int (-1)))
, Assign "j" $ Constant $ Int 10
, While (Var "j") [ Print (Var "j")
, Assign "j" (Add (Var "j") (Constant $ Int (-1)))
, If (Not (Add (Var "j") (Constant $ Int (-4)))) [ Break ]
]
]
, Print $ Constant $ String "Done"
]
which is
i = 10
while i:
print i
i = i - 1
j = 10
while j:
print j
j = j - 1
if j == 4:
break
so it will print
10 10 9 8 7 6 5
9 10 9 8 7 6 5
8 10 9 8 7 6 5
...
1 10 9 8 7 6 5
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so I have to build a simple compiler for a simple language, I used Haskell's Alex and Happy to build the parser, and it is printing the right AST's already, so next step I haveto do is to translate that data structure to another one, that represents the program in Three Address Code.
I'm yet a bit lost on how to do this, so, using Haskell data structure, how can I translate an AST to it's three Address Code? would really appreciate some help :)
thanks in advance !
Your parser is quite irrelevant to this question - which seems to be, how do I translate one AST to another. To address this I will use a simplified language. Also, the code below is not intended to be simple, but easily extensible and maintainable.
{-# LANGUAGE DeriveFunctor #-}
import Control.Monad.State
import Control.Monad.Reader
import Control.Monad.Free
import Data.Functor.Foldable
import qualified Data.Set as S
data Ident = Ident Int deriving (Eq)
data ExpF a = IntLitF Int
| PlusF a a
| IntVarF Ident deriving (Eq, Functor)
data Exp = IntLit Int
| Plus Exp Exp
| IntVar Ident deriving (Eq)
data Cmd
= CmdAtrib Ident Exp
| CmdSeq Cmd Cmd
| CmdNone deriving (Eq)
data TAC_F r = Assign Ident (ExpF Ident) r deriving (Eq, Show, Functor)
type TAC = Free TAC_F ()
(=:) :: Ident -> ExpF Ident -> TAC
(=:) i e = Free (Assign i e (Pure ()))
Some of the above definitions might seem strange. ExpF and Exp are defined in the recursion schemes style and used the recursion-schemes package. More info. TAC is defined in terms of Free because like the name implies, you get monad syntax for free. The only thing that a >> b does for TAC is creates the ast which contains a followed by b.
You need a way to generate fresh variables:
freshVar :: Monad m => StateT [Ident] m Ident
freshVar = do
s <- get
case s of
[] -> put [Ident (-1)] >> return (Ident (-1))
(Ident x:xs) -> put (Ident (x-1) : xs) >> return (Ident (x-1))
I use a list because it is simple but you may want to attach more information to your identifiers, in which case you should use Data.Set.Set or Data.Map.Map. By convention, fresh variables are negative while quantified variables are positive. Not a very sophisticted method, but it works.
Now this is where the magic happens. Thanks to recursion schemes, recursion over the tree is very simple:
translateExp :: Exp -> State [Ident] (TAC, Ident)
translateExp = cata go where
go (PlusF a b) = do
(ae,av) <- a
(be,bv) <- b
t <- freshVar
return (ae >> be >> t =: PlusF av bv, t)
go (IntLitF i) = do
t <- freshVar
return (t =: IntLitF i, t)
go (IntVarF a) = return (return (), a)
translateCmd :: Cmd -> State [Ident] TAC
translateCmd (CmdAtrib ident exp) = do
(e,v) <- translateExp exp
return (e >> ident =: IntVarF v)
translateCmd (CmdSeq a b) = do
x <- translateCmd a
y <- translateCmd b
return (x >> y)
translateCmd CmdNone = return (return ())
Then an example:
test0 = CmdSeq (CmdAtrib (Ident 1) (IntLit 10 `Plus` IntVar (Ident 2)))
(CmdAtrib (Ident 3) (IntVar (Ident 1) `Plus` IntVar (Ident 1) `Plus` IntVar (Ident 2)))
>putStrLn $ showTAC $ fst $ runState (translateCmd test0) []
t1 =: 10
t2 =: t1 + v2
v1 =: t2
t3 =: v1 + v1
t4 =: t3 + v2
v3 =: t4
Note that variables bound by the LHS of CmdAtrib will never collide with those found in the RHS.
Boilerplate / show instances:
instance Show Ident where
show (Ident i) | i < 0 = "t" ++ show (abs i)
| otherwise = "v" ++ show i
instance Show a => Show (ExpF a) where
show (IntLitF i) = show i
show (PlusF a b) = show a ++ " + " ++ show b
show (IntVarF i) = show i
type instance Base Exp = ExpF
instance Foldable Exp where
project (IntLit i) = IntLitF i
project (Plus a b) = PlusF a b
project (IntVar b) = IntVarF b
instance Show Cmd where
show (CmdAtrib i e) = show i ++ " <- " ++ show e
show (CmdSeq a b) = show a ++ " ;\n " ++ show b
show (CmdNone) = ""
instance Show Exp where
show (IntLit i) = show i
show (Plus a b) = show a ++ " + " ++ show b
show (IntVar i) = show i
showTAC (Free (Assign i exp xs)) = show i ++ " =: " ++ show exp ++ "\n" ++ showTAC xs
showTAC (Pure a) = ""
I want to implement an imperative language interpreter in Haskell (for educational purposes). But it's difficult for me to create right architecture for my interpreter: How should I store variables? How can I implement nested function calls? How should I implement variable scoping? How can I add debugging possibilities in my language? Should I use monads/monad transformers/other techniques? etc.
Does anybody know good articles/papers/tutorials/sources on this subject?
If you are new to writing this kind of processors, I would recommend to put off using monads for a while and first focus on getting a barebones implementation without any bells or whistles.
The following may serve as a minitutorial.
I assume that you have already tackled the issue of parsing the source text of the programs you want to write an interpreter for and that you have some types for capturing the abstract syntax of your language. The language that I use here is very simple and only consists of integer expressions and some basic statements.
Preliminaries
Let us first import some modules that we will use in just a bit.
import Data.Function
import Data.List
The essence of an imperative language is that it has some form of mutable variables. Here, variables simply represented by strings:
type Var = String
Expressions
Next, we define expressions. Expressions are constructed from integer constants, variable references, and arithmetic operations.
infixl 6 :+:, :-:
infixl 7 :*:, :/:
data Exp
= C Int -- constant
| V Var -- variable
| Exp :+: Exp -- addition
| Exp :-: Exp -- subtraction
| Exp :*: Exp -- multiplication
| Exp :/: Exp -- division
For example, the expression that adds the constant 2 to the variable x is represented by V "x" :+: C 2.
Statements
The statement language is rather minimal. We have three forms of statements: variable assignments, while loops, and sequences.
infix 1 :=
data Stmt
= Var := Exp -- assignment
| While Exp Stmt -- loop
| Seq [Stmt] -- sequence
For example, a sequence of statements for "swapping" the values of the variables x and y can be represented by Seq ["tmp" := V "x", "x" := V "y", "y" := V "tmp"].
Programs
A program is just a statement.
type Prog = Stmt
Stores
Now, let us move to the actual interpreter. While running a program, we need to keep track of the values assigned to the different variables in the programs. These values are just integers and as a representation of our "memory" we just use lists of pairs consisting of a variable and a value.
type Val = Int
type Store = [(Var, Val)]
Evaluating expressions
Expressions are evaluated by mapping constants to their value, looking up the values of variables in the store, and mapping arithmetic operations to their Haskell counterparts.
eval :: Exp -> Store -> Val
eval (C n) r = n
eval (V x) r = case lookup x r of
Nothing -> error ("unbound variable `" ++ x ++ "'")
Just v -> v
eval (e1 :+: e2) r = eval e1 r + eval e2 r
eval (e1 :-: e2) r = eval e1 r - eval e2 r
eval (e1 :*: e2) r = eval e1 r * eval e2 r
eval (e1 :/: e2) r = eval e1 r `div` eval e2 r
Note that if the store contains multiple bindings for a variable, lookup selects the bindings that comes first in the store.
Executing statements
While the evaluation of an expression cannot alter the contents of the store, executing a statement may in fact result in an update of the store. Hence, the function for executing a statement takes a store as an argument and produces a possibly updated store.
exec :: Stmt -> Store -> Store
exec (x := e) r = (x, eval e r) : r
exec (While e s) r | eval e r /= 0 = exec (Seq [s, While e s]) r
| otherwise = r
exec (Seq []) r = r
exec (Seq (s : ss)) r = exec (Seq ss) (exec s r)
Note that, in the case of assignments, we simply push a new binding for the updated variable to the store, effectively shadowing any previous bindings for that variable.
Top-level Interpreter
Running a program reduces to executing its top-level statement in the context of an initial store.
run :: Prog -> Store -> Store
run p r = nubBy ((==) `on` fst) (exec p r)
After executing the statement we clean up any shadowed bindings, so that we can easily read off the contents of the final store.
Example
As an example, consider the following program that computes the Fibonacci number of the number stored in the variable n and stores its result in the variable x.
fib :: Prog
fib = Seq
[ "x" := C 0
, "y" := C 1
, While (V "n") $ Seq
[ "z" := V "x" :+: V "y"
, "x" := V "y"
, "y" := V "z"
, "n" := V "n" :-: C 1
]
]
For instance, in an interactive environment, we can now use our interpreter to compute the 25th Fibonacci number:
> lookup "x" $ run fib [("n", 25)]
Just 75025
Monadic Interpretation
Of course, here, we are dealing with a very simple and tiny imperative language. As your language gets more complex, so will the implementation of your interpreter. Think for example about what additions you need when you add procedures and need to distinguish between local (stack-based) storage and global (heap-based) storage. Returning to that part of your question, you may then indeed consider the introduction of monads to streamline the implementation of your interpreter a bit.
In the example interpreter above, there are two "effects" that are candidates for being captured by a monadic structure:
The passing around and updating of the store.
Aborting running the program when a run-time error is encountered. (In the implementation above, the interpreter simply crashes when such an error occurs.)
The first effect is typically captured by a state monad, the second by an error monad. Let us briefly investigate how to do this for our interpreter.
We prepare by importing just one more module from the standard libraries.
import Control.Monad
We can use monad transformers to construct a composite monad for our two effects by combining a basic state monad and a basic error monad. Here, however, we simply construct the composite monad in one go.
newtype Interp a = Interp { runInterp :: Store -> Either String (a, Store) }
instance Monad Interp where
return x = Interp $ \r -> Right (x, r)
i >>= k = Interp $ \r -> case runInterp i r of
Left msg -> Left msg
Right (x, r') -> runInterp (k x) r'
fail msg = Interp $ \_ -> Left msg
Edit 2018: The Applicative Monad Proposal
Since the Applicative Monad Proposal (AMP) every Monad must also be an instance of Functor and Applicative. To do this we can add
import Control.Applicative -- Otherwise you can't do the Applicative instance.
to the imports and make Interp an instance of Functor and Applicative like this
instance Functor Interp where
fmap = liftM -- imported from Control.Monad
instance Applicative Interp where
pure = return
(<*>) = ap -- imported from Control.Monad
Edit 2018 end
For reading from and writing to the store, we introduce effectful functions rd and wr:
rd :: Var -> Interp Val
rd x = Interp $ \r -> case lookup x r of
Nothing -> Left ("unbound variable `" ++ x ++ "'")
Just v -> Right (v, r)
wr :: Var -> Val -> Interp ()
wr x v = Interp $ \r -> Right ((), (x, v) : r)
Note that rd produces a Left-wrapped error message if a variable lookup fails.
The monadic version of the expression evaluator now reads
eval :: Exp -> Interp Val
eval (C n) = do return n
eval (V x) = do rd x
eval (e1 :+: e2) = do v1 <- eval e1
v2 <- eval e2
return (v1 + v2)
eval (e1 :-: e2) = do v1 <- eval e1
v2 <- eval e2
return (v1 - v2)
eval (e1 :*: e2) = do v1 <- eval e1
v2 <- eval e2
return (v1 * v2)
eval (e1 :/: e2) = do v1 <- eval e1
v2 <- eval e2
if v2 == 0
then fail "division by zero"
else return (v1 `div` v2)
In the case for :/:, division by zero results in an error message being produced through the Monad-method fail, which, for Interp, reduces to wrapping the message in a Left-value.
For the execution of statements we have
exec :: Stmt -> Interp ()
exec (x := e) = do v <- eval e
wr x v
exec (While e s) = do v <- eval e
when (v /= 0) (exec (Seq [s, While e s]))
exec (Seq []) = do return ()
exec (Seq (s : ss)) = do exec s
exec (Seq ss)
The type of exec conveys that statements do not result in values but are executed only for their effects on the store or the run-time errors they may trigger.
Finally, in the function run we perform a monadic computation and process its effects.
run :: Prog -> Store -> Either String Store
run p r = case runInterp (exec p) r of
Left msg -> Left msg
Right (_, r') -> Right (nubBy ((==) `on` fst) r')
In the interactive environment, we can now revisit the interpretation of our example program:
> lookup "x" `fmap` run fib [("n", 25)]
Right (Just 75025)
> lookup "x" `fmap` run fib []
Left "unbound variable `n'"
A couple of good papers I've finally found:
Building Interpreters by Composing Monads
Monad Transformers Step by Step - how incrementally build tiny interpreter using
monad transformers
How to build a monadic interpreter in one day
Monad Transformers and Modular Interpreters