AgentSkillsCN

subtyping-verifier

验证类型系统中的子类型关系。适用场景：(1) 实现类型系统；(2) 证明类型安全；(3) 检查多态性。

SKILL.md
--- frontmatter
name: subtyping-verifier
description: 'Verifies subtyping relations in type systems. Use when: (1) Implementing
  type systems, (2) Proving type safety, (3) Checking polymorphism.'
version: 1.0.0
tags:
- type-systems
- subtyping
- inheritance
- polymorphism
difficulty: intermediate
languages:
- python
- ocaml
dependencies:
- type-checker-generator

Subtyping Verifier

Verifies subtyping relations in type systems.

When to Use

  • •Implementing type systems
  • •Proving type safety
  • •Checking polymorphic code
  • •Formal verification

What This Skill Does

  1. •Defines subtyping rules - Structural/nominal subtyping
  2. •Checks relations - Verify τ₁ <: τ₂
  3. •Handles records - Width/depth subtyping
  4. •Proves transitivity - Compose subtyping proofs

Usage Example

python
checker = SubtypingChecker()

# Int <: Int
assert checker.is_subtype(TInt(), TInt()) == True

# {x:Int, y:Int} <: {x:Int}  (width)
sub = TRecord({'x': TInt(), 'y': TInt()})
super_type = TRecord({'x': TInt()})
assert checker.is_subtype(sub, super_type) == True

# {x:Int} <: {x:Int, y:Int}  (NOT - missing field)
assert checker.is_subtype(super_type, sub) == False

# Function contravariance
# (Int → Bool) <: (Bool → Bool)
# Check: Bool <: Int (false), Bool <: Bool (true)
f1 = TFun(TInt(), TBool())
f2 = TFun(TBool(), TBool())
assert checker.is_subtype(f1, f2) == False

# (Bool → Bool) <: (Int → Bool)  
# Check: Int <: Bool (false), Bool <: Bool (true)
assert checker.is_subtype(f2, f1) == False

# Correct contravariance:
# (Bool → Int) <: (Int → Int)
# Check: Int <: Bool (false)3 = TFun - NO
f(TBool(), TInt())
f4 = TFun(TInt(), TInt())

# Correct: (Int → Bool) <: (Bool → Bool)?
# Dom: Bool <: Int? NO

Key Concepts

ConceptDescription
Width subtypingMore fields allowed
Depth subtypingCompatible field types
ContravarianceFunction domain reversed
CovarianceSame direction as hierarchy
BivarianceBoth allowed (function results)

Tips

  • •Start with simple structural subtyping
  • •Add nominal when needed
  • •Handle recursion carefully
  • •Prove soundness alongside implementation

Related Skills

  • •type-checker-generator - Type checking
  • •type-inference-engine - Type inference
  • •hoare-logic-verifier - Soundness proofs

Research Tools & Artifacts

Subtyping in compilers:

ToolWhat to Learn
JavaNominal subtyping
TypeScriptStructural subtyping

Research Frontiers

1. F-Bounded Polymorphism

  • •Approach: Self types

Implementation Pitfalls

PitfallReal ConsequenceSolution
TransitivityUnsoundnessProve lemmas