القائمة
A skill for proving contextual equivalence between programs using operational semantics, bisimulation, and related techniques.
التثبيت باستخدام Codex أو Claude انسخ هذا Prompt والصقه في Codex أو Claude أو مساعد آخر ليراجع صفحة Skill ويثبّتها لك.
استنادا إلى تصنيف SOC المهني
Implement abstract machines for defining and executing operational semantics of programming languages.
Implements alias and points-to analysis for pointer programs. Use for: (1) Optimizing compilers, (2) Verifying memory safety, (3) Program understanding, (4) Parallelization.
Define program meaning through logical assertions and proof rules (Hoare logic).
Transforms closures to explicit environments. Use when: (1) Implementing functional languages, (2) Building compilers, (3) Understanding closures.
Implements common subexpression elimination (CSE). Use when: (1) Building compilers, (2) Optimizing code, (3) Program analysis.
Implements general dataflow analysis framework. Use when: (1) Building compilers, (2) Static analysis tools, (3) Program verification.
| name | contextual-equivalence |
| description | A skill for proving contextual equivalence between programs using operational semantics, bisimulation, and related techniques. |
| version | 1.0.0 |
| tags | ["verification","equivalence","bisimulation","operational-semantics"] |
| difficulty | advanced |
| languages | ["ocaml","coq"] |
| dependencies | ["operational-semantics-definer","bisimulation-checker"] |
Domain: Program Verification / Programming Languages
A skill for proving contextual equivalence between programs using operational semantics, bisimulation, and related techniques.
| Reference | Why It Matters |
|---|---|
| Morris, "Lambda Calculus Types and Models" (1968) | Original contextual equivalence formulation |
| Milner, "Operational and Algebraic Semantics" (1997) | Comprehensive overview of contextual equivalence |
| Gunter, "Semantic Foundations for Programming Languages" | Formal treatment of program equivalence |
| Reynolds, "Theories of Programming Languages" | Contextual equivalence in type theory |
See also: ../simply-typed-lambda-calculus, ../bisimulation-checker, ../operational-semantics-definer
Real-world contextual equivalence verification:
| Tool | Why It Matters |
|---|---|
| Coq | Interactive proof of contextual equivalence |
| Twelf | Logical framework for LF |
| Agda | Dependent types for equivalence proofs |
| Nuprl | Constructive verification system |
| HOL | Higher-order logic proofs |
Current contextual equivalence research:
| Direction | Key Papers | Challenge |
|---|---|---|
| Untyped equivalence | "Equivalence in untyped λ-calculus" | Full abstraction |
| Relational | "Relational Reasoning" (2008) | Semantic relations |
| Step-indexed | "Step-indexed Bisimulation" (2005) | Recursive types |
| Logical relations | "Logical Relations" (1998) | Semantics |
| Game semantics | "Game Semantics" (1997) | Full abstraction |
Common equivalence proof bugs:
| Pitfall | Real Example | Prevention |
|---|---|---|
| Incomplete contexts | Missing context forms | Prove completeness |
| Bisimulation too strong | Fails for equivalent programs | Use weak bisimulation |
| Recursive types | Fixed-point handling | Use step-indexing |
| Non-termination | Divergence not handled | Use contextual equivalence |
| State | State in language | Relational reasoning |
