Language Compare F#, Ocaml, Scala, Clojure, Ruby and Haskell - Simple AST example

clojure-match.clj

(use '[clojure.core.match :only [match]])

(defn evaluate [env [sym x y]]
  (match [sym]
    ['Number]   x
    ['Add]      (+ (evaluate env x) (evaluate env y))
    ['Multiply] (* (evaluate env x) (evaluate env y))
    ['Variable] (env x)))
    
(def environment {"a" 3, "b" 4, "c" 5})

(def expression-tree '(Add (Variable "a") (Multiply (Number 2) (Variable "b"))))

(def result (evaluate environment expression-tree)) 

clojure-protocol.clj

(defprotocol Expression
  (evaluate [e env] ))
  
(deftype Number1 [x])
(deftype Add [x y] )
(deftype Multiply [x y])
(deftype Variable [x])

(extend-protocol Expression
  Number1  (evaluate [e env] (.x e ) )
  Add      (evaluate [e env] (+ (evaluate (.x e) env) (evaluate (.y e) env)))
  Multiply (evaluate [e env] (* (evaluate (.x e) env) (evaluate (.y e) env)))
  Variable (evaluate [e env] (env (.x e))))

(def environment {"a" 3, "b" 4, "c" 5})  

(def expression-tree (Add. (Variable. "a") (Multiply. (Number1. 2) (Variable. "b"))))

(def result (evaluate expression-tree environment)) 
  

fsharp.ml

//Here's some F# code...

type Expression = 
    | Number of int
    | Add of Expression * Expression
    | Multiply of Expression * Expression
    | Variable of string

let rec Evaluate (env:Map<string,int>) exp = 
    match exp with
    | Number n -> n
    | Add (x, y) -> Evaluate env x + Evaluate env y
    | Multiply (x, y) -> Evaluate env x * Evaluate env y
    | Variable id    -> env.[id]

let environment = Map.ofList [ "a", 1 ;
                               "b", 2 ;
                               "c", 3 ]

// Create an expression tree that represents
// the expression: a + 2 * b.
let expressionTree1 = Add(Variable "a", Multiply(Number 2, Variable "b"))

// Evaluate the expression a + 2 * b, given the
// table of values for the variables.
let result = Evaluate environment expressionTree1

haskell-case.hs

import Data.Map

data Expression = 
    Number   Int
  | Add      Expression Expression
  | Multiply Expression Expression
  | Variable String
  
evaluate :: Map String Int -> Expression -> Int
evaluate env exp = 
  case exp of
    Number x     -> x
    Add x y      -> evaluate env x + evaluate env y
    Multiply x y -> evaluate env x * evaluate env y
    Variable x   -> findWithDefault 0 x env

environment = fromList([("a",3), ("b",4), ("c",7)])

expressionTree = Add (Variable "a") (Multiply (Number 2) (Variable "b"))

result = evaluate environment expressionTree

haskell-constructor.hs

import Data.Map

data Expression = 
    Number   Int
  | Add      Expression Expression
  | Multiply Expression Expression
  | Variable String
  
evaluate :: Map String Int -> Expression -> Int
evaluate env (Number x) = x
evaluate env (Add x y) = evaluate env x + evaluate env y
evaluate env (Multiply x y) = evaluate env x * evaluate env y
evaluate env (Variable x) = findWithDefault 0 x env

environment = fromList([("a",3), ("b",4), ("c",7)])

expressionTree = Add (Variable "a") (Multiply (Number 2) (Variable "b"))

result = evaluate environment expressionTree

ocaml.ml

type expression = 
    Number of int
  | Add of expression * expression
  | Multiply of expression * expression
  | Variable of string
  
  
let rec evaluate (env: string->int) exp = 
  match exp with
      Number n -> n
    | Add (x, y) -> evaluate env x + evaluate env y
    | Multiply (x, y) -> evaluate env x * evaluate env y
    | Variable id    -> env id

let environment (str: string) : 'a = match str with "a" -> 3 | "b" -> 4 | "c" -> 5

let expressiontree1 = Add(Variable "a", Multiply(Number 2, Variable "b"))

let result = evaluate environment expressiontree1

ruby-jimweirich.rb

def evaluate(env, exp)
  keyword, a, b = exp
  case keyword
  when :number;   a
  when :variable; env[a]
  when :add;      evaluate(env, a) + evaluate(env, b)
  when :multiply; evaluate(env, a) * evaluate(env, b)
  end
end

ExpressionTree = [:add, [:variable, :a], [:multiply, [:number, 2], [:variable, :b]]]
Env = { a: 3, b: 4, c: 5 }

puts evaluate(Env, ExpressionTree)

ruby2-jimweirich.rb

Number   = lambda { |env, num| num }
Variable = lambda { |env, var| env[var] }
Add      = lambda { |env, a, b| evaluate(env, a) + evaluate(env, b) }
Multiply = lambda { |env, a, b| evaluate(env, a) * evaluate(env, b) }

def evaluate(env, exp)
  op, *args = exp
  op.(env, *args)
end

ExpressionTree = [Add, [Variable, :a], [Multiply, [Number, 2], [Variable, :b]]]
Env = { a: 3, b: 4, c: 5 }

puts evaluate(Env, ExpressionTree)

scala.scala

abstract class Expression

case class Number(i: Int) extends Expression
case class Add(x: Expression, y: Expression) extends Expression
case class Multiply(x: Expression, y: Expression) extends Expression
case class Variable(id: Symbol) extends Expression

object Maths extends App {
  val environment = Map('a -> 1,
      'b -> 2,
      'c -> 3)
      
  def evaluate(env: Map[Symbol, Int], exp: Expression): Int = exp match {
    case Number(n: Int) => n    
    case Add(x, y) => evaluate(env, x) + evaluate(env, y)
    case Multiply(x, y) => evaluate(env, x) * evaluate(env, y)
    case Variable(id: Symbol) => env(id)
  }
      
  val expressionTree1 = Add(Variable('a), Multiply(Number(2), Variable('b)))
  
  println(evaluate(environment, expressionTree1))
}

ugly.java

import java.util.*;

public class Eval {
	static int evaluate(Map env, Expression exp){ 
		if(exp instanceof Variable){  return (Integer)env.get(((Variable)exp).x); }
		else if(exp instanceof Number){ return ((Number)exp).x; }
		else if(exp instanceof Multiply){ return evaluate(env, ((Multiply)exp).x)*evaluate(env, ((Multiply)exp).y); }
		else if(exp instanceof Add){ return evaluate(env, ((Add)exp).x)+evaluate(env, ((Add)exp).y); }
		return 0;
	}
		
	public static void main(String[] args){
		Map env=new HashMap();
		env.put("a", 3);
		env.put("b", 4);
		env.put("c", 5);
		
		Expression expressionTree=new Add(new Variable("a"), new Multiply(new Number(2), new Variable("b")));
		System.out.println(evaluate(env, expressionTree));
	}
}
abstract class Expression {}

class Number extends Expression{ 
	int x; 
	Number(int x){ this.x=x; }
}

class Add extends Expression{ 
	Expression x; Expression y;
	Add(Expression x, Expression y){ this.x=x;  this.y=y; }
}

class Multiply extends Add{ 
	Multiply(Expression x, Expression y){ super(x, y); }
}

class Variable extends Expression{ 
	String x;
	Variable(String x){ this.x=x; }
}

JavaScript ES2015

let Number   = (n) => (env) => n
let Add      = (e1, e2) => (env) => e1(env) + e2(env)
let Variable = (s) => (env) => env[s]
let Multiply = (e1, e2) => (env) => e1(env) * e2(env)

let environment = {a: 3, b: 4}
let expression  = Add(Variable('a'), Multiply(Number(2), Variable('b')))

console.log(expression(environment))

Question (regarding several implementations I just read):

I would have thought the AST had to be a data expression that can be traversed with different purposes (evaluating, printing, transforming, etc). I don't know if declaring functions/lambdas/etc called Add, Multiply, etc, still qualifies as an Abstract Syntax Tree. I mean, it obviously leads to very compact code (no kidding) but it's no longer a data structure and you can't do anything with it (except evaluating it).

Unrelated to the previous question, here's a slightly shorter F# version using function instead of match (à la OCaml)

type Expression = 
    | Number of int
    | Add of Expression * Expression
    | Multiply of Expression * Expression
    | Variable of string

let rec Evaluate (env:Map<string,int>) = function 
    | Number n -> n
    | Add (x, y) -> Evaluate env x + Evaluate env y
    | Multiply (x, y) -> Evaluate env x * Evaluate env y
    | Variable id    -> env.[id]

let environment = Map.ofList [ "a", 1 ; "b", 2 ; "c", 3 ]

let expressionTree1 = Add(Variable "a", Multiply(Number 2, Variable "b"))

let result = Evaluate environment expressionTree1  

As others have noted: you don't need any type annotations in either the OCaml or the F# and you don't even need a type definition in the OCaml because you can use polymorphic variants.

Reminds me of these OCaml examples I wrote about 12 years ago:

http://www.ffconsultancy.com/ocaml/benefits/examples.html

and this comparison we did a few years back:

http://shenlanguage.org/lambdassociates/htdocs/studies/study10.htm

and this:

http://codereview.stackexchange.com/questions/11804/symbolic-derivative-in-c

Some of the responses have inverted the problem. To help stop that you can pose a problem for which more than one function over the expression type is required. For example, you might multiply out brackets or compute the symbolic derivative before evaluating.

You've also chosen a problem for which dispatch is trivial so pattern matching doesn't help. If you did, for example, symbolic simplification then a big gap would appear between languages without pattern matching and those with. I'd love to see a similar comparison with a fuller interpreter such as the one I linked to above.

FSharp implementation is still the clearest one,
while 1st Ruby & JS implementation are my favorite !

Crystal anyone ?

Funny nobody has mentioned this - but the extension should be fsharp.fs not ml. Gonna guess you did the OCaml one first?

in my own fantasy language :

func Add ( a  b )
push ( a + b )
ret               -- return topmost node on stack

func Mul ( a b )
push ( a * b )
ret

func Var ( env name val )
push [ name val ] -- push an array to stack
local _           -- make local variable
end

local expr = { [a b], Mul, [a 3], Var, [b 4], Var } 

func Eval ( expr )
load expr         -- load all elements in List to stack
Loop : 
  nil?            -- check if stack nil?
  jmp? Exit       -- jump if true     
  call _          -- call whatever on stack
  jmp Loop        -- jump to Loop
Exit : 
  call print      -- print whatever remaining on stack
end

push expr
call Eval

//PHP - arrow functions version:

<?php

$number = fn(int $n) => fn(array $env) => $n;
$variable = fn(string $a) => fn(array $env) => $env[$a] ?? 0;
$add = fn($a, $b) => fn(array $env) => $a($env) + $b($env);
$mul = fn($a, $b) => fn(array $env) => $a($env) * $b($env);

$evaluate = fn(array $env, $tree) => $tree($env);

$environment = ["a" => 3, "b" => 4, "c" => 7];
$tree = $add($variable("a"), $mul($number(2), $variable("b")));

$result = $evaluate($environment, $tree);