-- ----------------------------------------
--
-- Simple expression evaluator
-- for integer arithmetic
--
-- ----------------------------------------

module Expr0 where

import           Data.Maybe

-- ----------------------------------------
-- syntactic domains

data Expr  = Const  Int
           | Binary BinOp Expr Expr
             deriving (Show)

data BinOp = Add | Sub | Mul | Div | Mod
             deriving (Eq, Show)

-- ----------------------------------------
-- semantic domains

type Result = Int

-- ----------------------------------------
-- the meaning of an expression

eval :: Expr -> Result
eval (Const i)
  = i

eval (Binary op l r)
  = let mf = lookupMft op
    in
    mf (eval l) (eval r)

-- ----------------------------------------
-- the meaning of binary operators

type MF = Result -> Result ->
          Result

lookupMft :: BinOp -> MF
lookupMft op
  = case lookup op mft of
    Nothing -> error
               "operation not implemented"
    Just mf -> mf

mft :: [(BinOp, MF)]
mft
  = [ (Add, (+))
    , (Sub, (-))
    , (Mul, (*))
    , (Div, div)
    ]


-- ----------------------------------------
-- sample expressions

e1 = Binary Mul (Binary Add (Const 2)
                            (Const 4)
                )
                (Const 7)
e2 = Binary Div (Const 1) (Const 0)
e3 = Binary Mod (Const 1) (Const 0)

[v1,v2,v3] = map eval [e1, e2, e3]

-- ----------------------------------------