// This implementation support evaluation of anonymous recursion through Y Combinator (ex. Y Factorial)

type exp = | Var of string

| Lambda of string * exp

| Apply of exp * exp

let rec subst x v a =

match a with

| Var y ->

if x = y then v else a

| Lambda(y, a') ->

if x = y then a else Lambda(y, subst x v a')

| Apply(a', a'') ->

Apply(subst x v a', subst x v a'')

let rec reduce e =

let rec reduce' e =

match e with

| Var _ -> e

| Lambda (s, e') -> Lambda(s, reduce' e')

| Apply(e1, e2) ->

match e1 with

| Lambda(s, e3) -> subst s e2 e3

| _ -> Apply(reduce' e1, reduce' e2)

reduce' e

let rec loop f x =

let x' = f x

if x = x' then x' else loop f x'

let normalOrderReducer = loop reduce

## Saturday, 8 August 2009

### Lambda Calculus Normal Order Reducer

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