Convert Go Abstract Syntax Tree to Static Single Assignment (SSA) Form

This challenge requires you to implement a crucial compiler optimization technique: Static Single Assignment (SSA) form. SSA is a program representation where every variable is assigned exactly once. This property simplifies many compiler analyses and optimizations, such as dead code elimination, constant propagation, and common subexpression elimination. Your task is to transform a given Abstract Syntax Tree (AST) representing a simplified Go-like language into its SSA equivalent.

Problem Description

You will be given an Abstract Syntax Tree (AST) representing a simplified procedural programming language (similar to Go, but with some simplifications). Your goal is to transform this AST into SSA form.

In SSA form:

1. Each variable is assigned exactly once. If a variable is assigned multiple times in the original code, new versions of the variable are introduced (e.g., x_1, x_2, x_3).
2. Control flow merge points require $\phi$-functions. When different control flow paths merge, SSA introduces a $\phi$-function (phi-function) to select the correct version of a variable based on which path was taken.

Key Requirements:

• Parse the input AST: You will be provided with a structured representation of the AST. You do not need to implement a parser itself.
• Identify basic blocks: Decompose the control flow graph (CFG) of the program into basic blocks. A basic block is a sequence of instructions with a single entry point and a single exit point.
• Identify control flow: Determine the branches, jumps, and conditional statements that define the control flow.
• Perform variable renaming: For each variable, track its definitions and uses. Introduce new versions of variables as needed to ensure each is assigned only once.
• Insert $\phi$-functions: At the entry of basic blocks that have multiple predecessors (i.e., merge points), insert $\phi$-functions to resolve the values of variables that may have been defined on different incoming paths.
• Output the SSA form: The output should be a new AST or equivalent representation representing the SSA-transformed code.

Expected Behavior: The transformation should preserve the semantics of the original program. The output SSA representation should accurately reflect the data flow and control flow of the input.

Edge Cases:

• Programs with no control flow (straight-line code).
• Programs with simple conditional statements (if/else).
• Programs with loops (for).
• Variables that are only used but never assigned.
• Variables assigned on all paths leading to a merge point.
• Variables assigned on some paths but not others leading to a merge point.

Examples

Let's assume a simplified AST structure. We'll represent statements as structs. For simplicity, we'll use integers for variable IDs.

Example 1: Simple Assignment and Usage

// Original AST (Conceptual)
Block 1:
  Assign Var 1 = Const 5
  Print Var 1

// Input (Conceptual AST Representation)
{
  "Blocks": [
    {
      "ID": 1,
      "Instructions": [
        {"Type": "Assign", "Target": {"Type": "Var", "ID": 1}, "Value": {"Type": "Const", "Value": 5}},
        {"Type": "Print", "Value": {"Type": "Var", "ID": 1}}
      ],
      "Successors": [] // End of program
    }
  ]
}

// Output SSA (Conceptual AST Representation)
{
  "Blocks": [
    {
      "ID": 1,
      "Instructions": [
        {"Type": "Assign", "Target": {"Type": "Var", "ID": 1, "Version": 0}, "Value": {"Type": "Const", "Value": 5}},
        {"Type": "Print", "Value": {"Type": "Var", "ID": 1, "Version": 0}}
      ],
      "Successors": []
    }
  ]
}

Explanation: In this simple case, Var 1 is assigned once. No $\phi$-functions are needed. We've introduced versioning Version 0 to signify the first (and only) assignment.

Example 2: Conditional Branching

// Original AST (Conceptual)
Block 1:
  Assign Var 1 = Const 10
  If Var 1 > 5 GoTo Block 3
  GoTo Block 2

Block 2:
  Assign Var 1 = Const 20
  GoTo Block 3

Block 3:
  Print Var 1

// Input (Conceptual AST Representation)
{
  "Blocks": [
    {
      "ID": 1,
      "Instructions": [
        {"Type": "Assign", "Target": {"Type": "Var", "ID": 1}, "Value": {"Type": "Const", "Value": 10}},
        {"Type": "Branch", "Condition": {"Op": ">", "Left": {"Type": "Var", "ID": 1}, "Right": {"Type": "Const", "Value": 5}}, "TrueTarget": 3, "FalseTarget": 2}
      ],
      "Successors": [2, 3]
    },
    {
      "ID": 2,
      "Instructions": [
        {"Type": "Assign", "Target": {"Type": "Var", "ID": 1}, "Value": {"Type": "Const", "Value": 20}}
      ],
      "Successors": [3]
    },
    {
      "ID": 3,
      "Instructions": [
        {"Type": "Print", "Value": {"Type": "Var", "ID": 1}}
      ],
      "Successors": []
    }
  ]
}

// Output SSA (Conceptual AST Representation)
{
  "Blocks": [
    {
      "ID": 1,
      "Instructions": [
        {"Type": "Assign", "Target": {"Type": "Var", "ID": 1, "Version": 0}, "Value": {"Type": "Const", "Value": 10}},
        {"Type": "Branch", "Condition": {"Op": ">", "Left": {"Type": "Var", "ID": 1, "Version": 0}, "Right": {"Type": "Const", "Value": 5}}, "TrueTarget": 3, "FalseTarget": 2}
      ],
      "Successors": [2, 3]
    },
    {
      "ID": 2,
      "Instructions": [
        {"Type": "Assign", "Target": {"Type": "Var", "ID": 1, "Version": 1}, "Value": {"Type": "Const", "Value": 20}}
      ],
      "Successors": [3]
    },
    {
      "ID": 3,
      "Instructions": [
        {"Type": "Phi", "Target": {"Type": "Var", "ID": 1, "Version": 2}, "Operands": [
          {"BlockID": 1, "VarVersion": 0}, // Value from Block 1 if control flow came from there
          {"BlockID": 2, "VarVersion": 1}  // Value from Block 2 if control flow came from there
        ]},
        {"Type": "Print", "Value": {"Type": "Var", "ID": 1, "Version": 2}}
      ],
      "Successors": []
    }
  ]
}

Explanation:

• In Block 1, Var 1 is assigned version 0.
• In Block 2, Var 1 is assigned version 1.
• Block 3 is a merge point (predecessors are Block 1 and Block 2).
• A $\phi$-function is inserted in Block 3 for Var 1. It receives version 0 from Block 1 and version 1 from Block 2. This $\phi$-function produces version 2 of Var 1.
• The Print statement in Block 3 now uses version 2 of Var 1.

Example 3: Loop

// Original AST (Conceptual)
Block 1:
  Assign Var 1 = Const 0
  Assign Var 2 = Const 5
  GoTo Block 2

Block 2: // Loop Header
  If Var 1 >= Var 2 GoTo Block 4
  Assign Var 1 = Var 1 + Const 1
  GoTo Block 2

Block 4:
  Print Var 1

// Input (Conceptual AST Representation)
{
  "Blocks": [
    {
      "ID": 1,
      "Instructions": [
        {"Type": "Assign", "Target": {"Type": "Var", "ID": 1}, "Value": {"Type": "Const", "Value": 0}},
        {"Type": "Assign", "Target": {"Type": "Var", "ID": 2}, "Value": {"Type": "Const", "Value": 5}}
      ],
      "Successors": [2]
    },
    {
      "ID": 2,
      "Instructions": [
        {"Type": "Branch", "Condition": {"Op": ">=", "Left": {"Type": "Var", "ID": 1}, "Right": {"Type": "Var", "ID": 2}}, "TrueTarget": 4, "FalseTarget": 3}
      ],
      "Successors": [4, 3]
    },
    {
      "ID": 3, // Body of the loop
      "Instructions": [
        {"Type": "Assign", "Target": {"Type": "Var", "ID": 1}, "Value": {"Op": "+", "Left": {"Type": "Var", "ID": 1}, "Right": {"Type": "Const", "Value": 1}}}
      ],
      "Successors": [2]
    },
    {
      "ID": 4,
      "Instructions": [
        {"Type": "Print", "Value": {"Type": "Var", "ID": 1}}
      ],
      "Successors": []
    }
  ]
}

// Output SSA (Conceptual AST Representation)
{
  "Blocks": [
    {
      "ID": 1,
      "Instructions": [
        {"Type": "Assign", "Target": {"Type": "Var", "ID": 1, "Version": 0}, "Value": {"Type": "Const", "Value": 0}},
        {"Type": "Assign", "Target": {"Type": "Var", "ID": 2, "Version": 0}, "Value": {"Type": "Const", "Value": 5}}
      ],
      "Successors": [2]
    },
    {
      "ID": 2, // Loop Header
      "Instructions": [
        {"Type": "Phi", "Target": {"Type": "Var", "ID": 1, "Version": 1}, "Operands": [
          {"BlockID": 1, "VarVersion": 0}, // Initial value of Var 1
          {"BlockID": 3, "VarVersion": 2}  // Value from the loop body
        ]},
        {"Type": "Branch", "Condition": {"Op": ">=", "Left": {"Type": "Var", "ID": 1, "Version": 1}, "Right": {"Type": "Var", "ID": 2, "Version": 0}}, "TrueTarget": 4, "FalseTarget": 3}
      ],
      "Successors": [4, 3]
    },
    {
      "ID": 3, // Body of the loop
      "Instructions": [
        {"Type": "Assign", "Target": {"Type": "Var", "ID": 1, "Version": 2}, "Value": {"Op": "+", "Left": {"Type": "Var", "ID": 1, "Version": 1}, "Right": {"Type": "Const", "Value": 1}}}
      ],
      "Successors": [2]
    },
    {
      "ID": 4,
      "Instructions": [
        {"Type": "Phi", "Target": {"Type": "Var", "ID": 1, "Version": 3}, "Operands": [
          {"BlockID": 2, "VarVersion": 1} // Value from the loop header (after phi)
        ]},
        {"Type": "Print", "Value": {"Type": "Var", "ID": 1, "Version": 3}}
      ],
      "Successors": []
    }
  ]
}

Explanation:

• Var 1 and Var 2 are initialized in Block 1 with version 0.
• Block 2 is the loop header. It's a merge point for control flow coming from Block 1 (initialization) and Block 3 (loop body).
• A $\phi$-function is inserted in Block 2 for Var 1. It takes version 0 from Block 1 and version 2 (which will be defined in Block 3) and produces Var 1 version 1.
• The Branch condition in Block 2 uses Var 1 version 1 and Var 2 version 0.
• Block 3 (loop body) assigns to Var 1 version 2, using Var 1 version 1.
• Block 4 (exit block) is a merge point from Block 2 (loop termination). A $\phi$-function is inserted for Var 1 version 3, taking version 1 from Block 2. The Print statement uses this version.

Constraints

• The input AST will be represented using a structured format (e.g., JSON or Go structs that you will define or be provided).
• Variable identifiers will be positive integers.
• The number of basic blocks will not exceed 100.
• The total number of instructions across all blocks will not exceed 500.
• The maximum nesting depth of control flow structures (loops, conditionals) will not exceed 10.
• The solution should aim for reasonable efficiency, but the primary focus is on correctness. An $O(N \cdot M)$ approach, where N is the number of basic blocks and M is the number of instructions, is likely acceptable.

Notes

• You will need to implement algorithms for control flow graph construction and dominance analysis to correctly identify $\phi$-function insertion points.
• A common approach for SSA transformation is the "semi-pruned SSA" algorithm or similar techniques.
• Consider using a map to track the current version of each variable as you traverse the basic blocks.
• You'll need to define the AST node structures for your Go implementation. This might include nodes for:
  • Program (containing blocks)
  • Block (containing instructions and successors)
  • Instruction (e.g., Assign, Print, Branch, Phi)
  • Variable (with an ID and potentially a version)
  • Constant
  • Expression (e.g., binary operations)
• The problem statement uses conceptual representations. You should translate these into concrete Go data structures.
• Pay close attention to the definition of "predecessor" and "successor" in the context of control flow graphs.
• The Phi instruction takes a list of operands, each specifying the value from a particular predecessor block.