Fer-de-lance

DUE Tuesday 11/29/2016 at 23:59:59

Fer-de-lance, aka FDL, aka Functions Defined by Lambdas, is an egg-eater-like language with anonymous, first-class functions.

Language

Syntax

Fer-de-lance starts with the egg-eater and has two significant syntactic changes.

1. First, it removes the notion of function declarations as a separate step in the beginning of the program.

2. Second, it adds the notion of a lambda expression for defining anonymous functions, and allows expressions rather than just strings (names) in function position. The unicode character λ can also be used instead.

3. Third, to allow for recursive functions, it adds the notion of a named function binders.

data Expr a
  = ...
  | App     !(Expr a) [Expr a]             a    -- calls
  | Lam               [Bind a]   !(Expr a) a    -- anon. funcs
  | Fun     !(Bind a) [Bind a]   !(Expr a) a    -- named funcs

Parentheses are required around lambda expressions in FDL:

expr :=
    ...
  | (lambda <ids> : <expr>)
  | (lambda: <expr>)

ids :=
  | <id> , <ids>
  | <id>

For example

let compose = (lambda(f, g): (lambda (x): f(g(x)))),
    incr    = (lambda(x): x + 1)
in
    compose(incr, incr)(100)

We write recursive functions with def f(...): e in e' for example:

def fac(n):
  let t = print(n) in
  if (n < 1):
    1
  else:
    n * fac(n - 1)
in
fac(5)

For a longer example, see map.fdl

Semantics

Functions should behave just as if they followed a substitution-based semantics. This means that when a function is constructed, the program should store any variables that they reference that aren't part of the argument list, for use when the function is called. This naturally matches the semantics of function values in languages like OCaml, Haskell and Python.

There are several updates to errors as a result of adding first-class functions:

• There is no longer a well-formedness error for an arity mismatch. It is a runtime error.

• The value in function position may not be a function (for example, a user may erroneously apply a number), which should raise a (dynamic) error that reports "non-function".

• There should still be a (well-formedness) check for duplicate argument names, but there is no longer a check for duplicate function declarations (as these should be covered by the "shadow binding" check.)

Implementation

Memory Layout

Functions are stored in memory as a tuple

(arity, code-ptr, var1, var2, ... , varN)

i.e. with the following layout:

-----------------------------------------------------------------
| arity | code-ptr | var1 | var2 | ... | varN | (maybe padding) |
-----------------------------------------------------------------

For example, in this program:

let x = 10 in
let y = 12 in
let f = (lambda z: x + y + z) in
f(5)

The memory layout of the lambda would be:

----------------------------------
|   1  | <address> |  20  |  24  |
----------------------------------

• There is one argument (z), so 1 is stored for arity.

• There are two free variables—x and y—so the corresponding values are stored in contiguous addresses (20 to represent 10 and 24 to represent 12).

If the function stored three variables instead of two, then padding would have been needed to ensure the 8-byte-alignment.

Function Values

Function values are stored in variables and registers as the address of the first word in the function's memory, but with an additional 5 (101 in binary) added to the value to act as a tag.

Hence, the value layout is now:

0xWWWWWWW[www0] - Number
0xFFFFFFF[1111] - True
0x7FFFFFF[1111] - False
0xWWWWWWW[w001] - Pair
0xWWWWWWW[w101] - Function

Computing and Storing Free Variables

An important part of saving function values is figuring out the set of free variables that need to be stored, and storing them on the heap.

Our compiler needs to generate code to store all of the free variables in a function – all the variables that are used but not defined by an argument or let binding inside the function.

So, for example, x is free and y is not in:

(lambda(y): x + y)

In this next expression, z is free, but x and y are not, because x is bound by the let expression.

(lambda(y): let x = 10 in x + y + z)

Note that if these examples were the whole program, well-formedness would signal an error that these variables are unbound. However, these expressions could appear as sub-expressions in other programs, for example:

let x = 10 in
let f = (lambda(y): x + y) in
f(10)

In this program, x is not unbound – it has a binding in the first branch of the let. However, relative to the lambda expression, it is free, since there is no binding for it within the lambda’s arguments or body.

You will write a function freeVars that takes an Expr a and returns the list of free variables (without duplicates):

freeVars :: Expr a -> [Id]

You may need to write one or more helper functions for freeVars, that keep track of an environment. Then freevars can be used when compiling Lam to fetch the values from the surrounding environment, and store them on the heap.

HINT: You really don't want the result of freeVars to contain duplicates; thus it may be valuable to use the Data.Set library

In the example of heap layout above, the freeVars function should return ["x", "y"], and that information can be used in conjunction with env to perform the necessary mov instructions.

This means that the generated code for a Lam will look much like it did in class, but with an extra step to move the stored variables:

  jmp after1
temp_closure_1:
  <code for body of closure>
after1:
  mov [esi], <arity>
  mov [esi + 4], temp_closure_1
  mov [esi + 8], <var1>
  ... and so on for each variable to store
  mov eax, esi
  add eax, 5
  add esi, <heap offset amount>

Restoring Saved Variables

The description above outlines how to store the free variables of a function. They also need to be restored when the function is called, so that each time the function is called, they can be accessed.

In this assignment we'll treat the stored variables as if they were a special kind of local variable, and reallocate space for them on the stack at the beginning of each function call.

So each function body will have an additional part of the prelude that restores the variables onto the stack, and their uses will be compiled just as local variables are. This lets us re-use much of our infrastructure of stack offsets and the environment (stackVar).

The outline of work here is:

1. At the top of the function, get a reference to the address at which the function's stored variables are in memory

2. Add instructions to the prelude of each function that restore the stored variables onto the stack, given this address

3. Assuming this stack layout, compile the function's body in an environment that will look up all variables, whether stored, arguments, or let-bound, in the correct location

The second and third points are straightforward applications of ideas we've seen already – copying appropriate values from the heap into the stack, and using the environment to make variable references look at the right locations on the stack.

The first point requires a little more design work.

If we try to fill in the body of temp_closure_1 above, we immediately run into the issue of where we should find the stored values in memory.

We'd like some way to, say, move the address of the function value into eax so we could start copying values onto the stack:

temp_closure_1:
  <usual prelude>
  mov eax, <function value?>

  mov ecx, [eax + 3]
  mov [ebp - 8], ecx
  mov ecx, [eax + 7]
  mov [ebp - 12], ecx
  ... and so on ...

But how do we get access to the function value? The list of instructions for temp_closure_1 may be run for many different instantiations of the function, so they can't all look in the same place.

To solve this, we are going to augment the calling convention in Fer-de-lance to pass along the function value when calling a function. That is, we will push one extra time after pushing all the arguments, and add on the function value itself from the caller.

So, for example, in call like:

f(4, 5)

We would generate code for the caller like:

mov eax, [ebp-4] ;; (or wherever the variable f happens to be)
<code to check that eax is tagged 101, and has arity 2>
push 8
push 10
push eax
mov eax, [eax - 1] ;; the address of the code pointer for the function value
call eax         ;; call the function
add esp, 12        ;; since we pushed two arguments and the function value, adjust esp by 12

Now the function value is available on the stack, accessible just as an argument (e.g. with [ebp+8]), so we can use that in the prelude for restoration:

temp_closure_1:
  <usual prelude>
  mov eax, [ebp+8]

  mov ecx, [eax + 3]
  mov [ebp - 8], ecx
  mov ecx, [eax + 7]
  mov [ebp - 12], ecx
  ... and so on ...

Recursive Functions

With plain lambda expressions you cannot write recursive functions (as you need the "name" of the function so you can call it recursively.)

Recommended TODO List

1. Move over code from past labs and/or lecture code to get the basics going. There is intentionally less support code this time to put less structure on how errors are reported, etc. Feel free to start with code copied from past labs. Note that the initial state of the tests will not run even simple programs until you get things started.

2. Implement ANF for Lam. Hint – it's quite similar to what needed to be done to ANF a declaration.

3. Implement the compilation of Lam and App, ignoring stored variables. You'll deal with storing and checking the arity and code pointer, and generating and jumping over the instructions for a function. Test as you go.

4. Implement freeVars, testing as you go.

5. Implement storing and restoring of variables in the compilation of Lam and App

6. Figure out how to extend your implementation to support recursive functions; it should be a straightforward extension if you play your cards correctly in the implementation of Lam (what should you "bind" the name of the function to, in the body of the function?)

Tests (5-for-5)

• You can test the well-formedness errors using the error tester as usual.

• You must add 10 new tests in yourTests in order to get base credit. Feel free to add more, we'll just take the first 10.

• The creators of the 5 hardest tests get 5% of total points as extra credit

• A test's "score" is the total number of compilers submitted by the entire class on which the test produces the wrong output.

• That is, the harder a test, the higher its score.

Interactive REPL

$ stack ghci

and then you are inside ghci where you can use the function run to rapidly test your code.

λ> :t run
run :: FilePath -> Program -> IO Result

For example to directly compile and run a string do:

λ> run "" (Code "1 + 2")

To run a program whose code is in a file tests/input/file.fdl do:

λ> run "file" File

When you edit your code, instead of having to rebuild, you can more rapidly type :reload in ghci and then re-run the above commands.

Valgrind

If you wish, use valgrind (installed in the lab) to help debug your code, for example thus:

$ make tests/output/file.vresult

Handing In

Before submitting your solutions, make sure you have included a file group.txt containing the PIDs of the people who worked on this assignment. Include this file even if you worked on this assigment alone (in this case the file will only contain one PID). Put the SID of each person in your group on separate lines of the file so the file looks like:

X00000123
X00000456

First, make sure that your code works with the provided test cases by running the command

make test

When you're ready, run the following command to submit your homework:

make turnin

turnin will provide you with a confirmation of the submission process; make sure that the size of the file indicated by turnin matches the size of your file. See the ACS Web page on turnin for more information on the operation of the program.

Also to double check, see if the tarball you're sending contains the files you've changed.

To do this, run

tar tf 06-fdl.tgz

and check whether the output contains the relevant files.

If this is not the first time submitting this assignment, make sure you remove old copies of 06-fdl.tgz left in this directory.