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name: use-research description: Find relevant research and guide implementation based on it. Use when implementing features, fixing bugs, or exploring techniques where existing research in docs/research/ may provide guidance. Trigger phrases include "apply research", "use research", "based on the research", "implement from paper", or "find relevant research for [task]".

Use Research Knowledge

Apply knowledge from research documents in docs/research/ to guide implementation of current tasks.

Workflow

Phase 1: Discovery

Find research documents relevant to the current task.

1. List available research

   Glob: docs/research/*.md
   

2. Quick scan each document by reading the title (first H1) and overview/abstract section to build an index of available research:

   Document	Topic
   type-inference.md	HM type inference, Algorithm W/J/M, unification
   grokking-the-sequent-calculus.md	λμμ̃-calculus, producers/consumers, IR design
   malgo.md, anma.md	Related language implementations
   thesis_2024.md	Project background and design decisions
   etc.

3. Match to current task by identifying keywords:

   • Type system tasks → type-inference.md, ziku-type-inference-design.md
   • IR/evaluation tasks → grokking-the-sequent-calculus.md
   • Parser/syntax tasks → arrow-syntax-alternatives.md
   • Testing tasks → golden-test.md, lake-test.md

4. If no relevant research exists:

   • Inform user no prior research was found for this task
   • Ask if they want to proceed without research or run /research first
   • If proceeding, consider creating research doc post-implementation

Phase 2: Analysis

Deep-read the relevant research document(s).

1. Read the full document

   Read: docs/research/<relevant-doc>.md
   

2. Extract key sections:

   • Key Contributions / Features - What this research provides
   • Implementation Details - Code patterns, algorithms, data structures
   • Core Concepts - Definitions and terminology
   • Examples - Code snippets showing usage

3. Identify applicable patterns:

   • Translation rules (e.g., Surface → IR mappings)
   • Evaluation rules (e.g., μ/μ̃-reduction)
   • Type rules (e.g., inference algorithms)
   • Design patterns (e.g., data/codata duality)

Phase 3: Application

Apply research patterns to the current task.

1. Map concepts to codebase:

   Research Concept → Ziku Implementation
   ──────────────────────────────────────
   Producer         → Ziku/IR/Syntax.lean (Producer type)
   Consumer         → Ziku/IR/Syntax.lean (Consumer type)
   μ-reduction      → Ziku/IR/Eval.lean (eval function)
   Translation ⟦−⟧  → Ziku/Translate.lean
   Type inference   → Ziku/Infer.lean
   

2. Provide implementation guidance:

   • Reference specific research sections for context
   • Show how patterns translate to Lean 4 code
   • Note any adaptations needed for Ziku's design

3. Cite sources when referencing research:

   • Link to specific sections in research docs
   • Quote relevant rules or definitions

Example Usage

Task: "Implement let-polymorphism"

Discovery: Match "polymorphism" → type-inference.md

Analysis: From docs/research/type-inference.md:

• Section "Let-Polymorphism" explains the restriction
• Section "Key Operations" covers gen() and inst()
• Code pattern:

  W(Γ, let x = e₁ in e₂) =
    let (S₁, τ₁) = W(Γ, e₁)
        σ = gen(S₁(Γ), τ₁)
        (S₂, τ₂) = W(S₁(Γ)[x↦σ], e₂)
    in (S₂ ∘ S₁, τ₂)
  

Application: Apply to Ziku/Infer.lean:

• Implement generalize function
• Add Scheme type for polymorphic types
• Update infer for let_ case

Task: "Add label/goto control flow"

Discovery: Match "label", "goto", "control" → grokking-the-sequent-calculus.md

Analysis: From docs/research/grokking-the-sequent-calculus.md:

• Section "Translation from Fun to Core" shows:

  ⟦label α {t}⟧  = μα.⟨⟦t⟧ | α⟩
  ⟦goto(t; α)⟧   = μβ.⟨⟦t⟧ | α⟩  (β fresh)
  

• Section "Key Insights" explains let/label duality

Application: Apply to Ziku/Translate.lean:

• Add label case using Producer.mu
• Add goto case with fresh continuation

Tips

• Research documents contain both theory and implementation details
• The "Implementation" or "Implementation in Ziku" sections are most directly applicable
• Cross-reference multiple research docs when tasks span areas
• The "Sources" section in each doc links to original papers for deeper understanding
• If implementation diverges from research, note why and consider updating the research doc