Hello! Thanks for your question.

First of all, there are three layers of abstraction within Caten:

1. caten/apis | High-Level Graph Interface 2. caten/air | Low-Level Graph Interface 3. caten/codegen | AIR Graph => Kernel Generator

The inputs of the compiler are just Common Lisp classes (similar to torch modules). For example, in Common Lisp, we could create a module that does SinCos:

    (defclass SinCos (Func) nil
      (:documentation "The func SinCos computes sin(cos(x))"))

    ;; Forward creates a lazy tensor for the next computation.
    ;; You can skip this process by using the `st` macro.
    (defmethod forward ((op SinCos) &rest tensors)
      (st "A[~] -> A[~]" (tensors)))

    ;; Backward is optional (skipped this time)
    (defmethod backward ((op SinCos) &optional prev-grad)
      (declare (ignore prev-grad))
      nil)

    ;; Lower describes the lowered expression of `SinCos`
    (defmethod lower ((op SinCos) &rest inputs)
      (let ((x (car inputs)))
        (with-context
          (a (%sin (%add x (%fconst (/ pi 2)))))
          (b (%sin a)))))

The `apis` layer is the high-level interface, while the `lower` method is the lower-level step before code generation.

Next, the framework generates an Abstract VM (AVM) representation:

    #S(AVM :GRAPH Graph[seen=NIL, outputs=(STC6466_1)] {
      <ALLOCATE : TID6464 <- (shape=(1), stride=(1)) where :dtype=FLOAT32>
      <Node[BUFFER] ALLOCATE(NID6480) : SID6479* <- ()>
      <Node[BINARYOPS] ADD(NID6484) : BID6483* <- (TID6464, LID6481)>
      <Node[UNARYOPS] SIN(NID6486) : UID6485* <- (BID6483)>
      <Node[UNARYOPS] SIN(NID6488) : UID6487* <- (UID6485)>
      <Node[SPECIAL/VM] PAUSE/BACKWARD(NID6501) : STC6466_1* <- (UID6487)>
    })

Then, the computation graph is translated into schedule items:

    FastGraph[outputs=(val_6)] {
      { Allocate } : [ val_0 <- (1) ]
      { KERNEL } : [ val_5 <- val_1, val_0 :name=FUSED_SIN_SIN_ADD_LOAD6511]
    }

Finally, the code generation step produces the following C code:

    void fused_sin_sin_add_load6511(float* val_5, const float* restrict val_0);
    void fused_sin_sin_add_load6511(float* val_5, const float* restrict val_0) {
        val_5[0] = sin(sin((val_0[0] + 1.5707964)));
    }

This C code is compiled by a C compiler and executed.

So to answer your question: the compiler takes Common Lisp code and generates C functions.

Few compilers generate object code. Most generate an intermediate form, often assembler, which is converted to object code by another tool.