You must complete this program with the same partner you had for "Continuations (Written)". This will be your team for the next few assignments.
In this assignment, you will implement two garbage collectors: mark & sweep, and stop & copy. As we have seen, garbage collection involves starting from a root set of references, which reside in local variables and stack frames, and searching for reachable values on the heap.
Your garbage collectors must be written in the GC Collector Scheme language level. This language defines an interface to a program's stack and heap that you will use to implement garbage collection.
Your garbage collectors must implement the following functions:
init-allocator :: -> void The mutator implicitly calls this
function after initializing the heap and before calling any allocation
routines.  It is essentially a callback into the allocator indicating that the
heap is ready.gc:cons :: first-addr rest-addr -> cons-addr returns the
address of a new cons cell with the given field addresses; the field addresses
are presumed to be already allocatedgc:cons? :: addr -> boolean returns a boolean that indicates
whether the given address refers to a cons cellgc:first :: cons-addr -> first-addr and  gc:rest ::
cons-addr -> rest-addr return the fields of a given consgc:set-first! :: cons-addr first-addr  -> void and
gc:set-rest! :: cons-addr rest-addr  -> void set the addresses of the first and last pointers of a cons cellgc:alloc-flat :: atomic -> number allocates space for a flat value and returns the base address of the allocated blockgc:flat? :: addr -> boolean
returns a boolean that indicates whether the given address refers to
an atomic valuegc:deref :: addr -> atomic returns the atomic value stored at
the given addressTo help you write these functions, the GC Collector Scheme language defines an interface for the heap and the roots:
heap-size :: -> number the size of the heapheap-set! :: addr atomic -> void stores a value at the specified addressheap-ref :: addr -> atomic returns the value at the specified addressget-root-set :: -> listof root returns the roots of the collectionread-root :: root -> addr returns the address the root
referencesset-root! :: root addr -> void updates the root to reference the specified addressNote that get-root-set accepts an arbitrary number of
identifiers that it treats as roots and returns as part of the root set.  That
is, read-root returns the cell address stored in the location
referenced by the identifiers and set-root! mutates the identifier
to reference a new cell address.  You may find this useful when you implement
gc:cons; you may wish to add the first and
last arguments to your root set in lieu of manually updating them if they move during garbage collection.
You may write programs that exercise your garbage collectors using the GC Mutator Scheme language. This language is a subset of Scheme that uses a garbage collector that you specify. The first line of a test program must be:
(allocator-setup "collector.ss" heap-size)
"collector.ss" must be the name of your collector's file.  heap-size is the size of the heap your collector will use.
The remainder of the program is in a subset of Scheme with numbers, symbols, lists, etc. The primitives of the language map directly to the procedures you define in your garbage collector.
To get you started, we've provided a sample mutator and a trivial collector that signals an error when the heap fills up. (In fact, our collector does signal an error with the mutator we've provided, if you don't increase the size of the heap.)
You must store bookkeeping data on the heap provided by GC Collector Scheme. You may store 2-3 atomic values, such as addresses into the heap as variables in your garbage collector. We will assume they represent machine registers. However, all compound data structures must be on the heap.
In particular, in the mark & sweep collector, you should maintain a free list in the heap. That is, you should not use any auxiliary data structure; instead, use the available space in the heap to keep track of the free list. You may use one extra box (“register”) to point to the start of the free list. You may need to adjust your allocation accordingly to have enough space to maintain free list pointers!
Some final words of advice: