Most Functional Compiler

Most functional compiler

Ben Lynn

https://crypto.stanford.edu/~blynn/

Twitter: @bmxlynn

Judges' comments:

To use:

make

Try:

(./prog < fib.hs; cat prog.c) > fib.c
cc fib.c -o fib
./fib

Selected Judges Remarks:

A fully functional compiler. The example prints out the 30th Fibonacci number.

Author’s comments:

Remarks

A Haskell compiler. Supports a subset of Haskell more than large enough to self-host. Like GHC with custom language extensions:

  • WeDontServeYourType : Compilation failing because of inscrutable type checking rules? Confused by the ever-growing mire of extensions to the type system? The solution is simple: no type checking. It also means no typeclasses. Just pass dictionaries explicitly.

  • ZeroPauseGarbageCollection : Instead of disruptive stop-the-world garbage collection, we only tidy up when the world stops of its own accord, that is, on program termination.

  • OneHundredPercentPure : Gone is the catch-all lawless IO monad. And no trace of those scary unsafeThisAndThat functions. All functions must be pure.

  • SyntaxForTheMasses : See below.

Demos

Build the compiler:

$ $(CC) -o prog prog.c

Fibonacci numbers

Test the compiler on fib.hs :

$ (./prog < fib.hs ; cat prog.c) > fib.c

Compiling the output produces a binary that prints the 30th Fibonacci number.

The file ghcfib.hs includes fib.hs with some glue code, and shows GHC also accepts our subset of Haskell:

$ ghc ghcfib.hs

Self-hosting compiler

To avoid spoiling this entry by revealing the original Haskell source, we instead provide hint.hs , the output of a certain stage of the compiler when run on itself. This intermediate output is hopefully difficult to understand, yet is accepted by our compiler:

$ (./prog < hint.hs ; cat prog.c) > hint.c

The output program behaves like the compiler itself.

Unlike the original source from which it is derived, GHC fails to compile hint.hs . This is because values have been replaced with their Scott encodings by this stage, which messes up type-checks; we’d need equirecursive types for it to work.

Regexes

The file lol.hs contains an adaptation of Doug McIlroy’s elegant code from “Enumerating the strings of regular languages” . We exercise it by showing the first entries of the length-ordered list of all strings consisting of the characters a and b that contain an even number of a’s.

$ (./prog < lol.hs ; cat prog.c) > lol.c

A GHC wrapper is provided:

$ ghc ghclol.hs

Strongly-connected components

See scc.hs (and its GHC wrapper ghcscc.hs ) for an elegant way to print the strongly-connected components of a graph in reverse topological order.

$ (./prog < scc.hs ; cat prog.c) > scc.c

It expects the input to be in a similar format as a previous entry (2018 vokes). Indeed, obtain the 2018 winners, and run:

$ ./scc < 2018/vokes/example-1.txt
$ ./scc < 2018/vokes/example-2.txt

The output should agree, though our program omits line numbers and does not sort entries within a line. (Also, our program only treats spaces as whitespace, and supports any nonspace character in a vertex name.)

Syntax

Some claim Haskell syntax is frightening because braces and semicolons are optional. Some complain about a zoo of twisty little operators, all alike. Our compiler addresses such concerns by making braces and semicolons compulsory, disabling layout-based rules, making every operator left-associative with same precedence, and only defining 6 primitive functions:

: + - * / <=

The arithmetic operations behave as they do in C on unsigned ints, and (:) is Haskell’s cons function. Like Haskell and unlike C, (<=) returns a Bool (which are Church booleans behind the scenes) and not an Int.

No ifs, ands, or buts. Define them yourself. No tuples. Who needs them when algebraic data types delivers a better product? There is no do. No where. No list comprehensions. No unary operators.

Let expressions and operator sections are supported.

Within global scope or a let expression, each definition can only refer to itself or previous definitions. This implies we can only achieve mutual recursion by having one function pass itself to others.

Caveats

The only primitive type is Int . In particular, they represent characters. To interoperate with GHC, our compiler treats any undefined functions as the identity function, so that we may freely use ord and chr (or fromEnum and toEnum ) to make our code acceptable to both compilers.

The main function is the last function to successfully parse. It should have type [Int] -> [Int] , and our compiler treats this like the function passed into Prelude.interact , that is, the entire standard input is passed to this function, and the result is printed to standard output.

Bool must be defined as:

data Bool = True | False;

so that it matches the Scott-encoded booleans internally used by the primitive function (<=) .

The alternatives in a case expressions must list every data constructor in the order they are defined. For example, if we have:

data Foo a b = Bar a | Baz | Qux Int [b]

then a case expression that examines a term of this type must have the form:

case x of
  { Bar a    -> ...
  ; Baz      -> ...
  ; Qux n bs -> ...
  }

We stress braces and semicolons are required. Our fussy parser treats semicolons as separators, not terminators.

The effect of erroneous input is undefined. It may be best to develop with GHC, but even then, be mindful of changes needed because of issues caused by the uniform operator precedence and the touchy format of case alternatives.

Why?

One-letter variable names abound in IOCCC entries, and for good reason. These tiny pieces of confetti are hard to read, and leave room for more code. Then why not go further and use zero-letter variable names? That is, tacit programming or point-free style.

I had been playing with an algorithm devised by Oleg Kiselyov that effortlessly and efficiently eliminates those pesky variables, leaving behind terms composed from a small set of combinators. No need for lambda lifting or supercombinators.

By adding a handful of lines of mostly parsing code, we get a Haskell compiler, or rather, a compiler that accepts a subset of Haskell sufficiently large to self-host. You might say I wrote a tool for this contest, then ran it on itself to make an entry for it.

Obfuscation techniques

Even with Kiselyov’s algorithm and some term rewriting, the compiler only fit after compression, which naturally obfuscates the code. More tricks were needed to fit within the size limits.

  • One-letter variables, until enough is done to banish variables completely.
  • Ipse dixit. Near the end, the code declares itself to be an obfuscated program. (There is also an exhortation intended for the judges in a similar format earlier in the source.)
  • Typical C mischief: pre- and post-increment, commutative array indexing, ternary operators, and so on.
  • Huffman coding.
  • Base-85 because high bits are frowned upon.
  • Mixed radix encoding to game iocccsize. From a past winner (2018 bellard), it seems 9 11 12 32 are the only whitespace octets that may appear verbatim in string literals.
  • Choosing what to encode in Huffman/base-85 and what to encode in mixed radix was a delicate balancing act. In the end, I only had a few bytes to spare, which I spent on gratuitous confusion.
  • The effects of some functions depend on the order their arguments are evaluated, yet the program works either way. Why?
  • Ugly macros for the runtime system’s jump table for lazy reduction. A previous winner (2013 endoh1) has a cuter solution, which I avoid because of originality concerns and also because my combinators are compressed.
  • Relies on the inability of C comments to nest.
  • Cheaper and more complicated to print comma-separated ints (and header and footer) in C.
  • Primitive functions use a trick described in depth by Naylor and Runciman, “The Reduceron reconfigured and re-evaluated” . We represent the integer n with a term equivalent to Y(BT)n ; it works because Y(BT)ne = e(Y(BT)n) .
  • A sentinel in the heap often confused me, so ought to confuse others.

Other obfuscation techniques are better appreciated after decoding the compiler. See hint.hs .

  • Mercilessly point-free. Everything is a combinator.
  • Scott encoding. Everything is a combinator.
  • Sum types are oddly ordered and may even contain unused data constructors to reduce code duplication. (In C terms, unions may have extra fields, and they’re ordered in such a way so we can reuse code to access certain fields.)
  • The undefined function compiles to the (.) function.
  • Replaced the only (&&) with (||) and not using De Morgan’s law, which makes some comparisons less comprehensible.
  • Kiselyov only published “λ to SKI, Semantically” last year .
  • Recursion via the fixpoint (Y) combinator, which is represented by the variable “” during one stage of compilation.
  • Involves theory that may be less familiar to C programmers: maps, folds, parser combinators, lambda calculus, bracket abstraction, denotational semantics, etc.

Warnings

On my system, it compiles cleanly with -Wall with older standards, e.g. -std=c89 , but less cleanly if -pedantic is also supplied.

Compiling the compiler output with -Wall triggers a warning about a strange-looking comment.

Behind-the-scenes commentary

My website reveals how this compiler works.

© Copyright 1984-2019, Leo Broukhis, Simon Cooper, Landon Curt Noll - All rights reserved

This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License .

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