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r-irber-irbe/proof-skills/skills/itp-cross-porting/SKILL.md

itp-cross-porting

Skill3 starsChanged 24 days agoApache-2.0View on GitHub

USE FOR: porting proofs across Lean 4, Rocq, Isabelle, HOL Light, Agda, and Metamath (CONC-01..20). DO NOT USE FOR: single-prover Lean 4 proving (@lean-proof) or Mathlib PRs (@lean-upstream-porting). TRIGGERS: cross-ITP port, translate proof, Agda to Lean, concordance, CONC-01.

The file

We split this skill into the rules it gives an agent

2 rules. About 0 are common, 0 are distinctive, and 2 are very specific to this project.

  • ≈0

    Common · estimate

    Many files like this have a rule of this kind.

  • ≈0

    Distinctive · estimate

    This author's own choices. Worth a look.

  • 2

    Very specific

    Tied to their project's names, files or tools. Probably skip.

  • Common
  • Distinctive
  • Very specific
  1. Very specific:

    STOP: if a foreign proof relies on untyped partiality or set-theoretic junk values that falsify the naïve Lean 4 translation.

    line 58
  2. Very specific:

    STOP: if porting from Agda/Coq introduces a custom axiom in Lean 4.

    line 62

≈ “Common” is an estimate: at least 1 in 5 of the 350,495 skill files we read have a rule of the same kind, not the same words. “Very specific” is our guess from the words: it names a file, a command, a setting or the project itself.

Keep what fits and drop the rest. Your version, ready for your agents.
Files
SKILL.md

Cross-ITP Proof Porting & Concordance Router (CONC-01..20)

Coordinate proof and specification translation across the 6 supported Interactive Theorem Prover (ITP) families (lean4, coq_mathcomp, isabelle_hol, hol_light, agda, metamath) using vendor/itp-ontology/cross-itp-concordance.v1.json and references/dialects/*.json.

Routing

  • USE FOR: end-to-end cross-prover translation planning, Agda <-> Lean 4 ports, multi-prover concordance queries (lean_search(source: "concordance")), and routing dialect-specific translations to @rocq-proof-adapter, @isabelle-isar-adapter, or @hol-metamath-adapter.
  • DO NOT USE FOR: standard Lean 4 proof authoring without a foreign source proof (delegate to @lean-proof); porting existing Lean 4 corpus lemmas into Mathlib4 PRs (delegate to @lean-upstream-porting).
  • TRIGGERS: cross-ITP port, translate proof, Agda to Lean, Coq to Lean, Isabelle to Lean, HOL Light to Lean, Metamath to Lean, CONC-01..CONC-20.

Workflow

  1. Identify Source Prover & Foundation Delta: Classify the source artifact (coq_mathcomp, isabelle_hol, hol_light, agda, metamath) and load its dialect table from references/dialects/<dialect>.json.
  2. Query Concordance (lean_search(source: "concordance")): Map each foreign proof mechanism (CONC-01 through CONC-20) to its idiomatic Lean 4 counterpart rather than translating line-by-line tactical plumbing.
  3. Dispatch Dialect Adapter when Specialized:
    • Rocq / Coq / SSReflect / MathComp -> @rocq-proof-adapter
    • Isabelle/HOL / Isar / locales -> @isabelle-isar-adapter
    • HOL Light / Metamath (set.mm) -> @hol-metamath-adapter

Recovery & STOP

  • STOP if a foreign proof relies on untyped partiality or set-theoretic junk values that falsify the naïve Lean 4 translation; add explicit domain preconditions via @lean-specification.
  • STOP if porting from Agda/Coq introduces a custom axiom in Lean 4; map classical/extensional postulates to Lean's standard [propext, Classical.choice, Quot.sound].

Handoffs

  • Predecessors: skill:lean-gateway, skill:lean-research, skill:lean-specification.
  • Successors: skill:rocq-proof-adapter, skill:isabelle-isar-adapter, skill:hol-metamath-adapter, skill:lean-proof, skill:lean-proof-review.

Detailed reference

Full encyclopedic reference, decision trees, and lookup tables live in references/itp-cross-porting-handbook.md .

See also

  • ../../references/itp-cross-porting-handbook.md -- Complete itp-cross-porting Handbook
  • ../lean-gateway/SKILL.md -- Top-level skill router

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