Expression to Intermediate Representation to Abstract Syntax Tree to Instruction Set with an ISA

isa.md

Understanding Key Concepts

An Instruction Set Architecture (ISA) defines the machine-level instructions, registers, and operations available on a target processor (e.g., x86, ARM). Intermediate Representation (IR) is a platform-independent code form used in compilers, sitting between high-level source code and machine code. It's often graph-based (like SSA form) or linear (like three-address code) and facilitates optimizations before targeting a specific ISA.

Generating IR for an expression typically involves parsing the expression and translating it into IR ops. Since no specific ISA or expression is provided, I'll outline a general process using a simple arithmetic expression like a = (b + c) * d - e as an example. If your ISA/expression differs, adapt accordingly or provide details for a tailored walkthrough.

Step-by-Step Process to Generate IR

1. Parse the Expression into an Abstract Syntax Tree (AST)
   Break the expression into a tree structure representing operators and operands. This handles precedence and associativity.

   • Tokenize: Split into tokens (e.g., variables, operators).
   • Parse: Use a grammar (e.g., via recursive descent or tools like yacc) to build the AST.
     Example AST for a = (b + c) * d - e:
     • Root: Assign (left: a, right: Subtract)
     • Subtract: (left: Multiply, right: e)
     • Multiply: (left: Add, right: d)
     • Add: (left: b, right: c)

2. Choose an IR Format
   Select based on your needs (e.g., three-address code for simplicity, LLVM IR for advanced optimizations). Ensure it can be lowered to your ISA's instructions (e.g., if ISA lacks multiply, emulate in IR).

   • Common formats: Three-address code (TAC) uses temps like t1 = b + c.
   • Consider ISA constraints: If ISA has limited registers, IR should model register allocation early.

3. Traverse the AST and Emit IR Instructions
   Walk the tree (post-order for expressions) and generate IR ops. Introduce temporary variables for subexpressions. Map ops to IR equivalents that can target the ISA.

   • For leaves (variables/constants): Load into temps if needed.
   • For operators: Emit binary ops, handling precedence.
   • Assign results back if it's an assignment.
     Example TAC IR for the expression:

     t1 = b + c
     t2 = t1 * d
     t3 = t2 - e
     a = t3
     

   In KaTeX:
   [ t_1 = b + c ]
   [ t_2 = t_1 \times d ]
   [ t_3 = t_2 - e ]
   [ a = t_3 ]

4. Optimize the IR (Optional but Recommended)
   Apply passes like constant folding or dead code elimination. Ensure optimizations preserve semantics and respect ISA limits (e.g., avoid floating-point if ISA lacks it).

5. Validate and Lower to ISA-Specific Code
   Simulate or check IR for correctness. Then, translate IR to assembly for your ISA (e.g., map + to ADD instruction). Tools like LLVM can automate this.

Example with Code

If implementing in Python, use libraries like ast for parsing. Here's a simple script snippet to generate TAC from an expression:

import ast

def generate_tac(node, temps):
    if isinstance(node, ast.BinOp):
        left = generate_tac(node.left, temps)
        right = generate_tac(node.right, temps)
        op = {ast.Add: '+', ast.Mult: '*', ast.Sub: '-'}[type(node.op)]
        temp = f"t{len(temps)}"
        temps.append(f"{temp} = {left} {op} {right}")
        return temp
    elif isinstance(node, ast.Name):
        return node.id
    # Add more cases as needed

expr = "(b + c) * d - e"
tree = ast.parse(expr, mode='eval').body
temps = []
result = generate_tac(tree, temps)
print("\n".join(temps))
print(f"a = {result}")

This outputs the TAC shown earlier. Adapt for your ISA by adding backend translation.

Learn more about Abstract Syntax Trees (ASTs) and other graph forms at graphtech.dev.