Level grinding

We incrementally improve our compiler over and over again, which is like grinding levels in a computer role-playing game. There is even a skill tree of sorts. Do we want to add language features? Or optimize the generated code? Or improve error reporting? And so on.

We must also prepare for an an upcoming boss battle.

Stringy

Algorithm 4.1 of Kiselyov’s paper; strings and character constants.

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Binary

Lists; binary operators on the right-hand side.

We can now write xs ++ ys in expressions, though the function itself must be defined with (++) xs ys = ....

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Algebraically

Algebraic data types, sections, case expressions, recursive definitions, but not mutually recursive definitions.

Because of the simplistic way we convert case expressions to lambda calculus, our compiler expects case expressions to list out each data constructor in the order they are given in their data declaration.

We pay a heavy price for simplicity. When a case expression is evaluated, we copy the address of each alternative to the stack, only to eventually eliminate all but one. Furthermore, we copy and delete these addresses by evaluating intricate sequences of B and K combinators.

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Parity

Achievement unlocked. GHC accepts our next compiler if we insert the following preamble:

{-# LANGUAGE BlockArguments #-}
{-# LANGUAGE CPP #-}
{-# LANGUAGE TupleSections #-}
{-# LANGUAGE NoMonomorphismRestriction #-}
import Prelude ((+), (-), (*), Char, Int, String, succ)
import Data.Char (chr, ord)
import qualified Prelude
a <= b = if a Prelude.<= b then True else False
(/) = Prelude.div
(%) = Prelude.mod
class Eq a where { (==) :: a -> a -> Bool };
instance Eq Char where { (==) x y = if (x Prelude.== y) then True else False };
instance Eq Int where { (==) x y = if (x Prelude.== y) then True else False };

We can now develop using GHC with its powerful type checking and friendly error messages. Naturally, we switch back to our compiler when it all works, though we must be mindful that in our language, all operators have the same precedence, every identifier in an expression we’re parsing must have already been defined, and case expressions require all data constructors to appear exactly once and in order.

We drop support for the @ prefix. Our language has advanced enough that we no longer need direct access to primitive combinators.

This compiler supports integer constants. We’ve survived without them for so long because the succ function has been enough for our numerical needs so far.

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Fixity

This compiler supports infix, infixl, infixr declarations at the beginning of the source.

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Ben Lynn blynn@cs.stanford.edu 💡