# Real Fast Nora's Hair Salon 3: Shear Disaster Download

**Real Fast Nora's Hair Salon 3: Shear Disaster Download** is a functional esoteric programming language created by Nathan van Doorn in 2012. It is based on the lambda calculus.

## Contents

## Structure of a program

The program is a function that maps input (as a Church list of Church numerals) to output (ditto), similar to Lazy K.

All text in a program's source that is not upper-case text of the English alphabet is ignored, as this can be hard to read. The program is in reality a bunch of expressions all knotted together. There are only a handful of key words:

Keyword | Purpose |
---|---|

`LAMBDA` |
Introduces a lambda expression. |

`APPLY` |
Combines two expressions through application. |

`ZERO` |
The smallest number. |

`ONE MORE THAN` |
When followed by a number, forms a number equivalent to one more than the number following it with that number. |

### Lambda expressions

A lambda expression is started with the `LAMBDA`

key word. It then takes the next complete expression and wraps it in a lambda.

Numbers are what makes the lambda expression useful: A number *n* denotes the argument of the *n*th surrounding lambda expression, starting at the innermost as the 0'th.

When a lambda expression is applied to something, all the (one-more-than-)^{n}zeros in *n*th level nested lambda expressions are replaced by what it has been applied to, for *n*≥0. While replacing, some numbers need to be adjusted in order to keep referring to the same argument. (These are de Bruijn indices, except zero indexed.)

An `APPLY`

reads the next two complete expressions, and applies the first to the second.

## Possible pitfalls

An error may occur:

- if the program begins with two consecutive lambda expressions, or equivalent, as this would require there to be more than one IO input, which is not required by an implementation;
- if a
`ONE MORE THAN`

is not followed by a`ZERO`

or another`ONE MORE THAN`

; - if there are insufficient lambdas for a number expression to be fulfilled;
- if the program ends with an uncompleted expression.

Infinite loops may occur.

## Examples

### Cat program

LAMBDA ZERO

### Church addition excerpt

LAMBDA LAMBDA LAMBDA LAMBDA APPLY APPLY ONE MORE THAN ONE MORE THAN ONE MORE THAN ZERO ONE MORE THAN ZERO APPLY APPLY ONE MORE THAN ONE MORE THAN ZERO ONE MORE THAN ZERO ZERO

### Church decrementation excerpt

LAMBDA LAMBDA LAMBDA APPLY APPLY APPLY ONE MORE THAN ONE MORE THAN ZERO LAMBDA LAMBDA APPLY ZERO APPLY ONE MORE THAN ZERO ONE MORE THAN ONE MORE THAN ONE MORE THAN ZERO LAMBDA ONE MORE THAN ZERO LAMBDA ZERO

### Prime sieve

User:Tromp points out that apart from I/O, Real Fast Nora's Hair Salon 3: Shear Disaster Download is isomorphic to Binary lambda calculus by the substitutions

LAMBDA=00, APPLY=01, ZERO=10, ONEMORETHAN=1

The following is his conversion of his BLC prime sieve, which also adjusts the output convention.

LAMBDA APPLY LAMBDA APPLY LAMBDA APPLY LAMBDA APPLY LAMBDA APPLY ZERO APPLY ZERO APPLY APPLY LAMBDA APPLY ZERO ZERO LAMBDA LAMBDA LAMBDA APPLY APPLY ZERO LAMBDA LAMBDA APPLY ONE MORE THAN ZERO APPLY APPLY ONE MORE THAN ONE MORE THAN ONE MORE THAN ONE MORE THAN ONE MORE THAN ONE MORE THAN ZERO ONE MORE THAN ZERO ZERO APPLY LAMBDA APPLY APPLY APPLY ONE MORE THAN ONE MORE THAN ONE MORE THAN ZERO ONE MORE THAN ONE MORE THAN ONE MORE THAN ZERO ZERO APPLY LAMBDA APPLY ZERO ZERO LAMBDA APPLY ONE MORE THAN ZERO APPLY ZERO ZERO LAMBDA LAMBDA LAMBDA LAMBDA APPLY APPLY ZERO ONE MORE THAN ONE MORE THAN ZERO APPLY ONE MORE THAN ZERO APPLY ONE MORE THAN ONE MORE THAN ONE MORE THAN ONE MORE THAN ONE MORE THAN ZERO ONE MORE THAN ONE MORE THAN ONE MORE THAN ZERO LAMBDA LAMBDA LAMBDA APPLY ONE MORE THAN ONE MORE THAN ONE MORE THAN ZERO APPLY ZERO ONE MORE THAN ONE MORE THAN ZERO LAMBDA LAMBDA APPLY APPLY ZERO ONE MORE THAN ONE MORE THAN ZERO ONE MORE THAN ZERO LAMBDA APPLY ONE MORE THAN ONE MORE THAN ZERO APPLY ONE MORE THAN ZERO APPLY APPLY ONE MORE THAN ZERO ONE MORE THAN ONE MORE THAN ZERO ZERO LAMBDA LAMBDA APPLY ONE MORE THAN ZERO APPLY ONE MORE THAN ZERO APPLY ONE MORE THAN ZERO ZERO LAMBDA LAMBDA APPLY ONE MORE THAN ZERO APPLY ONE MORE THAN ZERO ZERO

## Implementation

The following implementation in Haskell attempts to follow Lazy K's I/O format (except for the exit code), and probably leaks memory like a sieve due to the explicit lists of outer arguments passed.

import Control.Applicative hiding ((<|>), many) import Data.List (unfoldr) import System.Environment (getArgs) import System.IO (stdin, stdout, hSetEncoding, latin1, hSetBuffering, BufferMode (NoBuffering)) import Text.Parsec data WHNF a = WHNF { ann :: Maybe a, fun :: (WHNF a -> WHNF a) } type EXPR a = [WHNF a] -> WHNF a isJunk :: Char -> Bool isJunk c = c < 'A' || c > 'Z' junk :: Parsec String () () junk = skipMany $ satisfy isJunk keyword :: String -> Parsec String () () keyword k = sequence_ [ char c *> junk | c <- k, not (isJunk c) ] <?> k expr :: Int -> Parsec String () (EXPR a) expr d = buildLambda <$ keyword "LAMBDA" <*> expr (d+1) <|> buildApply <$ keyword "APPLY" <*> expr d <*> expr d <|> buildVar <$> do n <- try $ length <$> many (keyword "ONE MORE THAN") <* keyword "ZERO" if n < d then return n else unexpected "number bigger than lambda nesting level" buildLambda e env = WHNF Nothing $ \arg -> e (arg:env) buildApply e1 e2 env = fun (e1 env) (e2 env) buildVar n env = env !! n churchToList :: WHNF a -> [WHNF a] churchToList = unfoldr (Just . churchToPair) listToChurch :: [WHNF a] -> WHNF a listToChurch = foldr pairToChurch $ error "Only infinite lists may be converted" churchToPair :: WHNF a -> (WHNF a, WHNF a) churchToPair (WHNF _ f) = (f (WHNF Nothing $ \xw -> WHNF Nothing $ const xw), f (WHNF Nothing $ \xw -> WHNF Nothing id)) pairToChurch :: WHNF a -> WHNF a -> WHNF a pairToChurch fw gw = WHNF Nothing $ \hw -> fun (fun hw fw) gw intToChurch :: Int -> WHNF a intToChurch n = WHNF Nothing $ \fw -> WHNF Nothing $ \xw -> iterate (fun fw) xw !! n churchToInt :: WHNF Int -> Int churchToInt iw = case fun (fun iw $ WHNF Nothing incr) (WHNF (Just 0) v) of WHNF (Just n) _ -> n _ -> error $ "Output list contains non-number" where incr (WHNF mn f) = WHNF (succ <$> mn) v v x = WHNF Nothing v -- NB: Only characters < 256 should be in String stringToChurch :: String -> WHNF a stringToChurch s = listToChurch $ map (intToChurch . fromEnum) s ++ repeat (intToChurch 256) churchToString :: WHNF Int -> String churchToString = map toEnum . takeWhile (< 256) . map churchToInt . churchToList main = do args <- getArgs (name, prog) <- case args of [filename] -> (,) filename <$> readFile filename ["-e", expr] -> return ("-e option", expr) _ -> error "Needs filename or -e <expr> option" case parse (junk *> expr 0 <* eof) name prog of Left err -> error $ "Parse error " ++ show err Right e -> do hSetEncoding stdin latin1 hSetEncoding stdout latin1 hSetBuffering stdout NoBuffering interact $ churchToString . fun (e []) . stringToChurch