binary number with a decimal point

bindec2.hs

module Bindec2 where
import Debug.Trace
{-
# binary number with a "decimal" point
Compilers 2nd ed. 
  Exercise 5.2.4 (p.317)
  Exercise 5.2.5 (p.317)
  Exercise 5.5.6 (p.352)
Compilers 1st ed.
  Exercise 5.8 (p.337)

https://gist.github.com/yamasushi/70a83af1a4ac8c9f2f6acf22e6dca94a

------

S -> L . L | L
L -> L B | B
B -> 0 | 1

S -> L F { S.val =L.val + F.val }

F -> . L { F.val=L.val/(2^L.k) }
F -> ε { F.val=0 }

L -> B { R.ik =1 , R.ival=B.val }
     R { L.val = R.val , L.k = R.k }

R -> B  { R1.ik = R.ik + 1 , R1.ival = 2*R.ival + B.val }    
     R1 { R.val = R1.val , R.k = R1.k }

R -> ε { R.val = R.ival , R.k=R.ik }

B -> 0       { B.val =0 } 

B -> 1       { B.val =1 } 

-}

bindec2 :: String -> Float
bindec2 xs = snd.s$xs

s :: String -> (String,Float)
s xs = let (xs0,_,val0)= (l xs) in
         let (xs1,val1)=(f xs0) in
           ( xs1 , val0+val1 )

f :: String->(String,Float)
f ('.':xs) = let (xs0,k,val)= (l xs) in
               (xs0,val/(2^k))
f xs = (xs,0) {-ipsilon-}

l :: String->(String,Int,Float)
l xs = let (xs0,bit) = (b xs) in
         (r xs0 1 bit)

r :: String->Int->Float -> (String,Int,Float)
r [] ik ival = ([],ik,ival) {-ipsilon-}
r xs@(bit:_) ik ival
  | bit=='0' || bit=='1' =
      let (xs0,bval)= (b xs) in
        let
          ik0   = ik+1
          ival0 = ival*2 + bval in
          (r xs0 ik0 ival0)
  | otherwise = (xs,ik,ival) {-ipsilon-}

b :: String -> (String,Float)
b ('0':xs) = (xs,0.0)
b ('1':xs) = (xs,1.0)