Fer-de-lance

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 pairs compiler (not full tuples, just pairs) and has two significant syntactic changes. First, it removes the notion of function declarations as a separate step in the beginning of the program. Second, it adds the notion of a lambda expression for defining anonymous functions, and allows expressions rather than just strings in function position:

type program = expr

type expr =
    ...
  | ELambda of string list * expr
  | EApp of expr * expr list


type cexpr =
    ...
  | CLambda of string list * aexpr
  | CApp of immexpr * immexpr list

Parentheses are required around lambda expressions in FDL:

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

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

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 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

Implementation

Memory Layout and Function Values

Functions are stored in memory 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  | <padding> |
----------------------------------------------

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 be needed).

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.

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 variables that need to be stored, and storing them on the heap. Our compiler needs to generated 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 aexpr and returns the set of free variables (as a list):

let freevars (ae : aexpr) : (string list) = 
  ...

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 CLambda to fetch the values from the surrounding environment, and store them on the heap. 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 lambda 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.

The outline of work here is:

• At the top of the function, get a reference to the address at which the function's stored variables are in memory
• Add instructions to the prelude of each function that restore the stored variables onto the stack, given this address
• 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 ...

Recommended TODO List

• 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 this assignment uses pairs rather than tuples – most of the code for pairs was given along with lecture notes. Note that the initial state of the tests will not run even simple programs until you get things started.
• Implement ANF for ELambda. Hint – it's quite similar to what needed to be done to ANF a declaration.
• Implement the compilation of CLambda and CApp, 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.
• Implement freevars, testing as you go. You can test with the helper tfvs, which takes a name, an expression string, and a list of identifiers, and checks that freevars returns the same list of strings (in any order).
• Implement storing and restoring of variables in the compilation of CLambda and CApp