ECA: Type Namespaces For Non-Aliasing Proofs

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ECA: Type Namespaces for Non-Aliasing Proofs

In this article, we'll explore how to implement Equivalence Class Aliasing (ECA) type namespaces to achieve non-aliasing proofs, which can significantly boost optimization. Let's dive in!

Summary

By implementing type-specific label namespaces within the context system, we can mathematically prove that different semantic types don't alias. This opens the door for aggressive optimization techniques, leading to more efficient code execution. In essence, ECA leverages Perl's strong typing to make the compiler's job easier and the code run faster.

Background

Chalk's context-as-closure memory model, as discussed in Issue #130, organizes values using label namespaces:

  • lexical:$x - Variables
  • index:0 - Array elements
  • key:foo - Hash keys

The current setup lumps all variables into the same namespace, regardless of their type. This forces the compiler to be conservative, assuming that any two variables might alias. This conservative approach severely limits optimization opportunities. We need a better way to tell the compiler, "Hey, these two variables are of completely different types, so they can't possibly be aliases!"

The ECA Approach

Equivalence Class Aliasing (ECA) uses Perl's semantic type system to create distinct label namespaces for each type. This allows us to mathematically prove that values of different types cannot alias each other.

Perl's Semantic Type Lattice

Perl determines types based on operational behavior, not just declarations:

my $x = "10";
my $y = 10;

# Are these the same value? Depends on the operation:
$x + 0     # 10 (numeric context)
$y . ""    # "10" (string context)

This leads to a type lattice like this:

Any
├── Scalar
│   ├── Int (pure integers)
│   ├── Num (floating point)
│   ├── Str (pure strings)
│   └── Undef
└── Reference
    ├── ArrayRef
    ├── HashRef
    ├── CodeRef
    └── Object (class-specific)

The type lattice is crucial because it defines the relationships and conversions between different types in Perl. Understanding this hierarchy allows for more precise type inference and, consequently, more effective non-aliasing proofs.

Type-Specific Namespaces

Instead of this (which is too general):

lexical:$x  →  Could be any type, might alias with any variable

We use this (much more precise):

lexical:Int:$x   →  Provably cannot alias with lexical:Str:$y
lexical:Str:$y   →  Different namespace = different memory
lexical:Num:$z   →  Mathematical proof of non-aliasing

By creating these type-specific namespaces, we can essentially tell the compiler, "Trust me, these variables will never point to the same memory location because they are fundamentally different kinds of data."

Benefits

1. Compile-Time Non-Aliasing Proofs

my $count = 0;      # Type: Int
my $name = "foo";   # Type: Str

# Compiler knows:
# - lexical:Int:$count cannot possibly alias with lexical:Str:$name
# - Different namespaces = mathematical proof of separation
# - No runtime alias checks needed

With ECA, the compiler can know that these variables won't alias at compile time. This eliminates the need for runtime alias checks, saving valuable CPU cycles.

2. Aggressive Optimization

Common Subexpression Elimination (CSE):

my $x = expensive_int_calc();
my $y = expensive_str_calc();
my $z = expensive_int_calc();  # Can reuse $x's result!

# Without ECA: Must recompute (might alias)
# With ECA: Safe to reuse (provably different types)

Without ECA, the compiler has to be cautious and recompute expensive_int_calc() for $z, even though it's already computed for $x. With ECA, it knows it's safe to reuse the result.

Dead Store Elimination:

my $count = 0;
$count = 1;  # Can eliminate first store
$count = 2;  # Can eliminate second store

# ECA proves no Str or Ref variables alias with $count

ECA enables dead store elimination by proving that stores to $count don't affect any other variables of different types. This reduces unnecessary memory writes.

3. Reference Type Specialization

my $aref = [1, 2, 3];
my $href = {a => 1};

# Different reference namespaces:
lexical:ArrayRef:$aref  ≠  lexical:HashRef:$href

# Enables devirtualization of method calls

By differentiating between ArrayRef and HashRef, ECA allows for devirtualization of method calls. This means the compiler can directly call the appropriate method for the specific reference type, rather than having to go through a virtual dispatch table.

Implementation Plan

Step 1: Type Inference System

Implement a type inference system to determine semantic types:

sub infer_type($node) {
    return match($node) {
        Constant(Int) => Type::Int,
        Constant(Str) => Type::Str,
        Add($l, $r)   => Type::Num,  # Arithmetic → numeric
        Concat($l, $r) => Type::Str,  # String op → string
        ...
    }
}

The type inference system is the foundation upon which ECA is built. It's responsible for analyzing the code and determining the semantic type of each variable and expression. A robust and accurate type inference system is crucial for the effectiveness of ECA.

Step 2: Update Context Label Construction

Modify label creation in lib/Chalk/IR/Builder.pm:

Current:

method make_variable_label($var_name) {
    return "lexical:$var_name";
}

With ECA:

method make_variable_label($var_name, $type) {
    return "lexical:${type}:${var_name}";
}

This simple change is key to enabling ECA. By including the type in the variable label, we create separate namespaces for each type.

Step 3: Update Store/Load Operations

Store with type:

method build_store_node($var_name, $value_node, $control = undef) {
    my $type = $self->infer_type($value_node);
    my $label = $self->make_variable_label($var_name, $type);
    $context = $context->extend($label, $value_node);
}

Load with type lookup:

method build_load_node($var_name) {
    # Try each type namespace in priority order
    for my $type (qw(Int Num Str Ref)) {
        my $label = "lexical:${type}:${var_name}";
        my $node = $context->($label);
        return $node if defined $node;
    }
    return undef;
}

The load operation searches through the type namespaces in a specific order to find the correct value. This ensures that the correct type is loaded, even if the variable has been coerced to a different type.

Step 4: Namespace Isolation

Add to lib/Chalk/IR/Context.pm:

sub make_typed_label($class, $type, $name) {
    return "lexical:${type}:${name}";
}

# Prove non-aliasing through namespace separation
sub types_cannot_alias($class, $type1, $type2) {
    return $type1 ne $type2;  # Different types = different namespaces
}

This step explicitly enforces the non-aliasing rule. If two types are different, their corresponding namespaces are considered separate, and therefore, they cannot alias.

Step 5: Optimization Pass

Create an optimizer that leverages type separation:

# If types cannot alias, enable:
- Common subexpression elimination
- Dead store elimination
- Load forwarding
- Register allocation

This is where the real magic happens. The optimizer uses the non-aliasing information provided by ECA to perform aggressive optimizations, resulting in significant performance improvements.

Type Coercion Handling

When types change through coercion:

my $x = 10;        # lexical:Int:$x
$x = $x . "";      # Now lexical:Str:$x

# Implementation:
# 1. Detect type change through operation
# 2. Create binding in new namespace
# 3. Old namespace binding becomes dead

Type coercion is a potential challenge for ECA. When a variable's type changes, the implementation must detect this change, create a new binding in the appropriate namespace, and mark the old binding as dead.

Testing Strategy

Unit Tests

  • [ ] Type inference for all node types
  • [ ] Label construction with type namespaces
  • [ ] Store/load with type-specific labels
  • [ ] Namespace isolation proofs

Integration Tests

  • [ ] Variables of different types don't alias
  • [ ] Type coercion creates new namespace bindings
  • [ ] Reference type separation works
  • [ ] Self-hosting with ECA namespaces

Optimization Tests

  • [ ] CSE across different type variables
  • [ ] Dead store elimination with type isolation
  • [ ] Verify optimizations preserve semantics

Thorough testing is essential to ensure that ECA is implemented correctly and that it delivers the expected performance benefits. The testing strategy should cover a wide range of scenarios, including unit tests, integration tests, and optimization tests.

Edge Cases

1. Dual-Valued Scalars

my $x = "10";
my $y = $x + 0;   # Numeric context
my $z = $x . "";  # String context

# Both Int and Str namespaces may have bindings

2. Reference Blessing

my $obj = bless {}, 'Foo';  # Object type: Object_Foo
my $obj2 = bless $obj, 'Bar';  # Type changes!

3. Undef Type

my $x;  # Type: Undef
$x = 10;  # Type changes to Int

Edge cases require special attention. Dual-valued scalars, reference blessing, and the Undef type can introduce complexities that need to be carefully handled to ensure the correctness of ECA.

Prerequisites

  • [x] Context abstraction (Issue #130 Phase 1-2)
  • [x] Collections-as-contexts (Issue #130 Phase 3)
  • [x] References (Issue #130 Phase 4)
  • [ ] Type inference system
  • [ ] Type lattice implementation

Success Metrics

  1. Correctness: All tests pass with type namespaces
  2. Non-aliasing proofs: Compiler can prove type separation
  3. Optimization: CSE/DSE enabled by type isolation
  4. Self-hosting: Chalk compiles itself with ECA

Future Extensions

  • Symbolic execution using type constraints
  • Dependent types for arrays/hashes
  • Flow-sensitive type refinement
  • Whole-program type analysis

Related Issues

  • #130 - Context abstraction (prerequisite)
  • #143 - Optimization passes (will benefit from ECA)

References