blob: 88fb1c2ff6d97a7190652219114cd972219bb3ab (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
|
module HW
( fv
, subst
, normalstep
, pickFresh
, repeatedly
, printnormal
) where
import AST
import qualified Data.Set as Set
import Parse (parse)
-- | Return the free variables in an expression
fv :: Expr -> Set.Set String
fv _ = Set.singleton "UNIMPLEMENTED" -- Replace with your solution to problem 1
-- | Substitute n for x in e, avoiding name capture
-- subst n x e e[x := n]
subst :: Expr -> String -> Expr -> Expr
subst _ _ _ = Var "UNIMPLEMENTED" -- Replace with your solution to problem 2
-- | Take a single step in normal order reduction or return Nothing
normalstep :: Expr -> Maybe Expr
normalstep _ = Just (Var "UNIMPLEMENTED") -- Replace with your solution to problem 3
-- | Return a "fresh" name not already in the set.
-- Tries x' then x'', etc.
pickFresh :: Set.Set String -> String -> String
pickFresh s = pickFresh'
where pickFresh' n | n `Set.notMember` s = n
pickFresh' n = pickFresh' $ n ++ "'"
-- | Repeatedly apply a function to transform a value, returning the list
-- of steps it took. The result list starts with the given initial value
repeatedly :: (a -> Maybe a) -> a -> [a]
repeatedly f = repeatedly'
where repeatedly' x = x : case f x of Nothing -> []
Just y -> repeatedly' y
-- | Print out the series of normal order reduction steps
printnormal :: String -> IO ()
printnormal = mapM_ print . repeatedly normalstep . parse
|
