Ok, Fexprs are calls to combiners - combiners are either applicatives or operatives.
Combiners are introduced with _vau_ and take an extra paramter (here called _dynamic_env_, earlier called _de_) which is the dynamic environment.
<pre><codeclass="remark_code">(vau dynamicEnv (normalParam1 normalParam2) (body of combiner))
</code></pre>
--
Lisps, as well as Kraken, have an _eval_ function.
This function takes in code as a data structure, and in R5RS Scheme an "environment specifier", and in Kraken, a full environment (like what is passed as _dynamicEnv_).
- Functions - runtime, evaluate parameters once, return value
--
- Macros - expansion time, do not evaluate parameters, return code to be inlined
--
- Special Forms - look like function or macro calls, but do something special (if, lambda, etc)
--
- **Kraken** (and Kernel)
--
- Combiners
--
- Applicatives (like normal functions, combiners that evaluate all their parameters once in their dynamic environment)
--
- Operatives (combiners that do something unusual with their parameters, do not evaluate them right away)
--
_Operatives can replace macros and special forms, so combiners replace all_
---
# Background: Fexprs - detail
Combiners, like functions in Lisp, are first class.
This means that unlike in Lisp, Kraken's version of macros and special forms are *both* first class.
---
# Background: Fexprs - detail
As we've mentioned, in Scheme _or_ is a macro expanding
<pre><codeclass="remark_code">(or a b)
</code></pre>
to
<pre><codeclass="remark_code">(let ((temp a))
(if temp temp
b))
</code></pre>
So passing it to a higher-order function doesn't work, you have to wrap it in a function:
<pre><codeclass="remark_code">> (fold or #f (list #t #f))
Exception: invalid syntax and
> (fold (lambda (a b) (or a b)) #f (list #t #f))
#t
</code></pre>
---
# Background: Fexprs - detail
But in Kraken, _or_ is a combiner (an operative!), so it's first-class
<pre><codeclass="remark_code">(vau de (a b) (let ((temp (eval a de)))
(if temp temp
(eval b de))))
</code></pre>
So it's pefectly legal to pass to a higher-order combiner:
<pre><codeclass="remark_code">> (foldl or false (array true false))
true
</code></pre>
---
# Background: Fexprs - detail
All special forms in Kaken are combiners too, and are thus also first class.
In this case, we can not only pass the raw _if_ around, but we can make an _inverse_if_ which inverts its condition (kinda macro-like) and pass it around.
What were special forms in Lisp are now just built-in combiners in Kraken.
*if* is not any more special than *+*, and in both cases you can define your own versions that would be indistinguishable, and in both cases they are first-class.
5. Additionally, because it is unclear what code will be evaluated as a parameter to a function call and what code must be passed unevaluated to the combiner, little optimization can be done.
---
# Solution: Partial Eval
1. Partially evaluate a purely functional version of this language in a nearly-single pass over the entire program
2. Environment chains consisting of both "real" environments with every contained symbol mapped to a value and "fake" environments that only have placeholder values.
3. Since the language is purely functional, we know that if a symbol evaluates to a value anywhere, it will always evaluate to that value at runtime, and we can perform inlining and continue partial evaluation.
4. If the resulting partially-evaluated program only contains static references to a subset of built in combiners and functions (combiners that evaluate their parameters exactly once), the program can be compiled just like it was a normal Scheme program
Macros, espicially *define-macro* macros, are essentially functions that runat expansion time and compute new code from old code.
This is essentially partial evaluation / inlining, depending on how you look at it.
It thus makes sense to ask if we can identify and partial evaluate / inline operative combiners to remove and optimize them like macros. Indeed, if we can determine what calls are to applicative combiners we can optimize their parameters, and if we can determine what calls are to macro-like operative combiners, we can try to do the equlivant of macro expansion.
For Kraken, this is exactly what we do, using a specialized form of Partial Evaluation to do so.
---
# Challenges
So what's the hard part? Why hasn't this been done before?
- Detour through Lisp history?
Determining even what code will be evaluated is difficult.
- Partial Evaluation
- Can't use a binding time analysis pass with offline partial evaluation, which elminates quite a bit of mainline partial evaluation research
- Online partial evaluation research generally does not have to deal with the same level of partially/fully dynamic and sometimes explicit environments
- woo
---
# Research
- *Practical compilation of fexprs using partial evaluation*
- Currently under review for ICFP '23
- Wrote partial evaluator with compiler
- Heavily specialized to optimize away operative combiners like macros written in a specific way
- Prototype faster than Python and other interpreted Lisps
- Static calls fully optimized like a normal function call in other langauges
- Dynamic calls have a single branch of overhead - if normal applicative combiner function like call, post-branch optimized as usual
- Optimizes away Y Combinator recursion to static recursive jumps (inc tail call opt)
- Bit of an odd language: purely functional, array based, environment values
- \\(\kprim{0}{eval}\\): evaluates its argument in the given environment.
- \\(\kprim{0}{vau}\\): creates a new combiner and is analogous to lambda in other languages, but with a "wrap level" of 0, meaning the created combiner does not evaluate its arguments.
- \\(\kprim{0}{wrap}\\): increments the wrap level of its argument. Specifically, we are "wrapping" a "wrap level" n combiner (possibly "wrap level" 0, created by *vau* to create a "wrap level" n+1 combiner. A wrap level 1 combiner is analogous to regular functions in other languages.
- \\(\kprim{0}{unwrap}\\): decrements the "wrap level" of the passed combiner, the inverse of *wrap*.
- \\(\kprim{0}{if}\\): evaluates only its condition and converts to the \\(\kprim{0}{vif}\\) primitive for the next step. It cannot evaluate both branches due to the risk of non-termination.
- \\(\kprim{0}{vif}\\): evaluates and returns one of the two branches based on if the condition is non-zero.
- \\(\kprim{0}{int-to-symbol}\\): creates a symbol out of an integer.
- \\(\kprim{0}{array}\\): returns an array made out of its parameter list.
- \\(\kcombine{\kprim{0}{type-test?}}{(A)}{E}\\): *array?*, *comb?*, *int?*, and *symbol?*, each return 0 if the single argument is of that type, otherwise they return 1.
- \\(\kcombine{\kprim{0}{len}}{(A)}{E}\\): returns the length of the single array argument.
- \\(\kcombine{\kprim{0}{idx}}{(A~n)}{E}\\): returns the nth item array A.
- \\(\kcombine{\kprim{0}{concat}}{(A~B)}{E}\\): combines both array arguments into a single concatenated array.
- \\(\kcombine{\kprim{0}{+}}{(A~A)}{E}\\): adds its arguments
- \\(\kcombine{\kprim{0}{<=}}{(A~A)}{E}\\): returns 0 if its arguments are in increasing order, and 1 otherwise.
- This base calculus defined above is not only capable of normal lambda-calculus computations with primitives and derived user applicatives, but also supports a superset of macro-like behaviors via its support for operatives.
- All of the advantages listed in the introduction apply to this calculus, as do the performance drawbacks, at least if implemented naively. Our partial evaluation and compilation framework will demonstrate how to compile this base language into reasonably performant binaries (WebAssembly bytecode, for our prototype).
Not only do we ask if *f* evaluate its parameters, but also does it take in an environment containing `{ f: <>, ...}`, etc
---
# Type-Inference-Based Primitive Inlining
For instance, consider the following code:
<pre><codeclass="remark_code">(cond (and (array? a) (= 3 (len a))) (idx a 2)
true nil)
</code></pre>
- Call to *idx* fully inlined without type or bounds checking
- No type information is needed to inline type predicates, as they only need to look at the tag bits.
- Equality checks can be inlined as a simple word/ptr compare if any of its parameters are of a type that can be word/ptr compared (ints, bools, and symbols).
---
# Immediately-Called Closure Inlining
Inlining calls to closure values that are allocated and then immediately used:
This is inlined
<pre><codeclass="remark_code">(let (a (+ 1 2))
(+ a 3))
</code></pre>
to this
<pre><codeclass="remark_code">((wrap (vau (a) (+ a 3))) (+ 1 2))
</code></pre>
and then inlined (plus lazy environment allocation)
---
# Y-Combinator Elimination
- When compiling a combiner, pre-emptive memoization
- Partial-evaluation to normalize
- Eager lang - extra lambda - eta-conversion in the compiler
