First working solution of new task
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Jan-Niclas Loosen
351
Project-02-03-04-05/cfa/live_variables.py
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351
Project-02-03-04-05/cfa/live_variables.py
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"""
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live_variables.py — Live Variables backward dataflow analysis for TRIPLA CFGs.
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A variable v is *live* at the entry of node n if there exists a path
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n → … → use(v) where v is not redefined along the way.
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Data structures
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---------------
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gen dict[int, set[Var]] — GEN(n) = variables *used* at n
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kill dict[int, set[Var]] — KILL(n) = variables *defined* at n
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in_sets dict[int, set[Var]] — live variables at node *entry*
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out_sets dict[int, set[Var]] — live variables at node *exit*
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Transfer equations (backward):
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OUT(n) = ∪ IN(s) for all successors s
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IN(n) = (OUT(n) − KILL(n)) ∪ GEN(n)
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Variables are represented in scoped form ``(scope, name)``, e.g. ``("f","x")``.
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This avoids collisions between equal variable names in different functions.
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This module also exports ``_BackwardAnalysisBase``, the shared base class
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that ``ReachedUsesAnalysis`` in reached_uses.py inherits from. The base
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provides:
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• AST traversal to collect function-nesting and parameter metadata
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• Lexical variable resolution (parameter shadowing handled correctly)
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• BFS-based CFG-node → owning-function assignment
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• Unified uses / defs extraction for all node types
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Var = tuple[str, str]
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"""
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from __future__ import annotations
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from collections import deque
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from typing import TYPE_CHECKING
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import cfg_build
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import syntax
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from cfg.CFG_Node import CFG_START
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if TYPE_CHECKING:
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from cfg.CFG import CFG
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# ---------------------------------------------------------------------------
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# Public type alias (imported by reached_uses.py)
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# ---------------------------------------------------------------------------
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GLOBAL_SCOPE = ""
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Var = tuple[str, str] # (function_name|GLOBAL_SCOPE, variable_name)
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# ============================================================================
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# Shared base: function metadata, scope assignment, uses/defs extraction
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# ============================================================================
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class _BackwardAnalysisBase:
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"""Infrastructure shared by LiveVariablesAnalysis and ReachedUsesAnalysis.
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Calling ``super().__init__(cfg)`` from a subclass:
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1. Snapshots cfg_build.FUNCTIONS.
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2. Collects AST-level function-nesting and parameter metadata.
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3. BFS-assigns every CFG node to its owning function.
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4. Extracts uses and defs for every CFG node.
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After __init__ the following attributes are available to subclasses:
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self.cfg — the CFG object
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self._functions — dict[str, tuple]: snapshot of cfg_build.FUNCTIONS
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self._func_parent — dict[str, str|None]: lexical parent per function
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self._func_params — dict[str, tuple[str,...]]: params per function
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self._func_scope — dict[int, str]: node-id → owning function name
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self.uses — dict[int, set[Var]]: variables used at each node
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self.defs — dict[int, set[Var]]: variables defined at each node
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"""
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def __init__(self, cfg: "CFG") -> None:
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self.cfg = cfg
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# Snapshot FUNCTIONS so later global-state resets do not affect us.
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self._functions: dict[str, tuple] = dict(cfg_build.FUNCTIONS)
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self.uses: dict[int, set[Var]] = {}
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self.defs: dict[int, set[Var]] = {}
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self._func_parent, self._func_params = self._collect_function_metadata()
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self._func_scope: dict[int, str] = self._compute_function_scope()
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self._extract_uses_defs()
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# ------------------------------------------------------------------
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# Step 1a — Walk AST to collect lexical nesting + parameter lists
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# ------------------------------------------------------------------
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def _collect_function_metadata(
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self,
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) -> tuple[dict[str, str | None], dict[str, tuple[str, ...]]]:
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"""Walk the AST and collect function-parent and parameter information.
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Returns
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-------
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func_parent : dict[str, str | None]
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func_parent[f] is the name of the immediately enclosing function
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(or None for top-level functions).
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func_params : dict[str, tuple[str, ...]]
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func_params[f] is the ordered tuple of formal parameter names of f.
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"""
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func_parent: dict[str, str | None] = {}
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func_params: dict[str, tuple[str, ...]] = {}
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def visit(expr: syntax.EXPRESSION | None, current_func: str | None) -> None:
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if expr is None:
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return
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if isinstance(expr, syntax.LET):
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decls = expr.decl if isinstance(expr.decl, list) else [expr.decl]
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# Register metadata for each declared function.
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for d in decls:
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if isinstance(d, syntax.DECL):
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# Use assignment (last-seen wins) to stay consistent
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# with cfg_build.FUNCTIONS, which also overwrites on
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# duplicate names. setdefault (first-seen wins) would
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# disagree when a nested function shadows a top-level
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# one with the same name, causing wrong scope resolution.
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func_parent[d.f_name] = current_func
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func_params[d.f_name] = tuple(d.params)
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# Recurse into function bodies and the in-expression.
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for d in decls:
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if isinstance(d, syntax.DECL):
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visit(d.body, d.f_name)
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else:
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visit(d, current_func)
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visit(expr.body, current_func)
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return
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for _, child in expr.children():
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visit(child, current_func)
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visit(self.cfg.ast, None)
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return func_parent, func_params
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# ------------------------------------------------------------------
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# Step 1b — Resolve a variable name through the lexical scope chain
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# ------------------------------------------------------------------
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def _resolve_var(self, func: str | None, name: str) -> Var:
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"""Resolve a variable name via lexical scope chain."""
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if func is None:
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return (GLOBAL_SCOPE, name)
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cur: str | None = func
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seen: set[str] = set()
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while cur is not None and cur not in seen:
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seen.add(cur)
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if name in self._func_params.get(cur, ()):
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return (cur, name)
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cur = self._func_parent.get(cur)
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# Fallback: local variable in current function scope.
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return (func, name)
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# ------------------------------------------------------------------
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# Step 2 — BFS-assign every CFG node to its owning function
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# ------------------------------------------------------------------
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def _compute_function_scope(self) -> dict[int, str]:
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"""BFS from each function's START node; return node-id → function-name.
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Two stopping conditions keep attribution strictly inside each function:
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1. Do not follow into a *different* function's CFG_START (prevents
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attributing callee body nodes to the caller, and vice-versa).
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2. Do not follow *past* the function's own CFG_END (prevents
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following CFG_END → CFG_RETURN → continuation nodes that belong
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to the *caller* context, which caused variables used there to be
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resolved in the wrong scope).
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The first function whose BFS claims a node wins.
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"""
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functions = self._functions
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func_scope: dict[int, str] = {}
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all_f_start_ids: set[int] = {fs.id for _, (fs, _) in functions.items()}
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for f_name, (f_start, f_end) in functions.items():
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queue: deque = deque([f_start])
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while queue:
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node = queue.popleft()
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if node.id in func_scope:
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continue # already claimed by an earlier function
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func_scope[node.id] = f_name
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# Stop here — do not follow CFG_END into caller context.
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if node.id == f_end.id:
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continue
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for child in node.children:
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# Do not follow into a different function's START.
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if (
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isinstance(child, CFG_START)
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and child.id in all_f_start_ids
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and child.id != f_start.id
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):
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continue
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queue.append(child)
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return func_scope
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# ------------------------------------------------------------------
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# Step 3 — Extract uses / defs for every CFG node
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# ------------------------------------------------------------------
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def _extract_uses_defs(self) -> None:
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"""Populate ``self.uses`` and ``self.defs`` for every node in the CFG.
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Extraction rules:
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• CFG_START(DECL f(p1,…,pk)) → defs = {(f,p1), …, (f,pk)}
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• Node wrapping ID(x) → uses = {lexical_resolve(func, x)}
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• Node wrapping ASSIGN(x = e) → defs = {lexical_resolve(func, x)}
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• Everything else → uses = {}, defs = {}
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Sub-expressions already have their own CFG nodes and are not
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re-inspected here; each node is responsible only for its own ast_node.
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"""
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for node in self.cfg.nodes():
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nid = node.id
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func = self._func_scope.get(nid) # None → outer / global scope
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ast = node.ast_node
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uses: set[Var] = set()
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defs: set[Var] = set()
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if isinstance(node, CFG_START) and isinstance(ast, syntax.DECL):
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# Function entry defines each formal parameter.
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for param in ast.params:
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defs.add((ast.f_name, param))
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elif ast is not None:
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if isinstance(ast, syntax.ID):
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resolved = self._resolve_var(func, ast.name)
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uses.add(resolved)
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elif isinstance(ast, syntax.ASSIGN):
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resolved = self._resolve_var(func, ast.var.name)
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defs.add(resolved)
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self.uses[nid] = uses
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self.defs[nid] = defs
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# ============================================================================
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# Live Variables Analysis
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# ============================================================================
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class LiveVariablesAnalysis(_BackwardAnalysisBase):
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"""Backward dataflow analysis: Live Variables.
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A variable (f, x) is *live* at the entry of node n if there is a path
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from n to some use of (f, x) along which (f, x) is not redefined.
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This is the simpler predecessor to ReachedUsesAnalysis (reached_uses.py):
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it tracks which variables are live, not *where* they are used.
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Attributes
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----------
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gen dict[int, set[Var]] GEN(n) = uses(n) — vars used at n
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kill dict[int, set[Var]] KILL(n) = defs(n) — vars defined at n
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in_sets dict[int, set[Var]] live variables at n's *entry*
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out_sets dict[int, set[Var]] live variables at n's *exit*
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(uses and defs are identical to gen / kill and are inherited from the
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base class.)
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Transfer equations (backward):
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OUT(n) = ∪ IN(s) for all successors s
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IN(n) = (OUT(n) − KILL(n)) ∪ GEN(n)
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"""
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def __init__(self, cfg: "CFG") -> None:
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# Base populates uses, defs, _func_scope, etc.
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super().__init__(cfg)
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self.gen: dict[int, set[Var]] = {}
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self.kill: dict[int, set[Var]] = {}
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self.in_sets: dict[int, set[Var]] = {}
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self.out_sets: dict[int, set[Var]] = {}
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self._build_gen_kill()
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self.solve()
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# ------------------------------------------------------------------
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# Build gen / kill; initialise in / out to ∅
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# ------------------------------------------------------------------
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def _build_gen_kill(self) -> None:
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"""GEN(n) = uses(n), KILL(n) = defs(n); initialise in/out sets."""
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for node in self.cfg.nodes():
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nid = node.id
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self.gen[nid] = set(self.uses[nid])
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self.kill[nid] = set(self.defs[nid])
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self.in_sets[nid] = set()
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self.out_sets[nid] = set()
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# ------------------------------------------------------------------
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# Backward worklist fixpoint
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# ------------------------------------------------------------------
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def solve(self) -> None:
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"""Backward worklist until fixpoint.
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Transfer:
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OUT(n) = ∪ IN(s) for all successors s
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IN(n) = (OUT(n) − KILL(n)) ∪ GEN(n)
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Only nodes reachable from cfg.START are processed (guard against
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propagate=False parent references from CFG.__remove_and_rewire).
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"""
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nodes = list(self.cfg.nodes())
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known: set[int] = set(self.gen.keys())
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id_to_node = {n.id: n for n in nodes}
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worklist: deque = deque(nodes)
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# Build predecessor relation from children edges. This is more reliable
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# than node.parents because CFG rewiring may add edges with
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# propagate=False, leaving parent links stale.
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preds: dict[int, set[int]] = {nid: set() for nid in known}
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for node in nodes:
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for child in node.children:
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if child.id in known:
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preds[child.id].add(node.id)
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while worklist:
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node = worklist.popleft()
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nid = node.id
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new_out: set[Var] = set()
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for child in node.children:
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if child.id in known:
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new_out |= self.in_sets[child.id]
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new_in: set[Var] = (new_out - self.kill[nid]) | self.gen[nid]
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if new_out != self.out_sets[nid] or new_in != self.in_sets[nid]:
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self.out_sets[nid] = new_out
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self.in_sets[nid] = new_in
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for pred_id in preds[nid]:
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worklist.append(id_to_node[pred_id])
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# ------------------------------------------------------------------
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# Result
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# ------------------------------------------------------------------
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def live_vars_by_node(self) -> dict[int, set[Var]]:
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"""Return the live-variable set at the *entry* of each node.
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Returns
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-------
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dict[int, set[Var]]
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Keys: CFG node ids whose in_set is non-empty.
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Values: copy of the live-variable set at that node's entry.
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"""
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return {nid: set(vs) for nid, vs in self.in_sets.items() if vs}
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