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Agent skill

Refinement Step Generator

by ArabelaTso in ArabelaTso/Skills-4-SE

Generate systematic refinement steps from high-level specifications to concrete implementations in Isabelle/HOL or Coq, preserving correctness obligations at each step.

Apache-2.0Auto-check passedWriting & Content

Install Refinement Step Generator

skills CLI
$ npx skills add ArabelaTso/Skills-4-SE --skill refinement-step-generator -a claude-code

Project install by default; add -g for ~/.claude/skills/.

GitHub CLI
$ gh skill install ArabelaTso/Skills-4-SE refinement-step-generator --agent claude-code

Project scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).

Manual copy
$ git clone --depth 1 https://github.com/ArabelaTso/Skills-4-SE.git skills-src && mkdir -p .claude/skills && cp -r skills-src/skills/refinement-step-generator .claude/skills/refinement-step-generator && rm -rf skills-src

Use ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.

Claude Code skills documentation · loads skills from .claude/skills/

Facts

Skill name
refinement-step-generator
GitHub stars
253
Token cost
~2.3k tokens
SKILL.md length
514 words
Files
4 (incl. references)
Skills in repo
151
Repo updated
First seen
Licence
Apache-2.0

At a glance

Generate systematic refinement steps from high-level specifications to concrete implementations in Isabelle/HOL or Coq, preserving correctness obligations at each step.

  • Works in 8 steps: Data Refinement → Algorithmic Refinement → Implementation Refinement → …
  • Working with formal verification
  • SKILL.md covers Overview, Refinement Workflow, Core Refinement Types and Refinement Process, plus 6 more sections
  • Instructions only: no scripts, shell commands, URLs or credentials in SKILL.md

What it does

Refinement Step Generator is an agent skill from ArabelaTso/Skills-4-SE. Generate systematic refinement steps from high-level specifications to concrete implementations in Isabelle/HOL or Coq, preserving correctness obligations at each step. Use when working with formal verification, program refinement, proof development, or when translating abstract specifications into executable code while maintaining formal guarantees. Supports data refinement (abstract types → concrete structures), algorithmic refinement (specifications → algorithms), and stepwise refinement with proof obligations.

Its SKILL.md is about 2.3k tokens, which your agent loads only when the skill is triggered. The skill folder holds 4 other files, including reference files (for example `references/coq_refinement.md`, `references/isabelle_refinement.md` and `references/refinement_patterns.md`).

It sits in Writing & Content, covering Translation. The repository describes itself as: A curated list of 180+ useful Claude Skills for Software Engineering and resources for customizing AI for SE workflows. The licence is Apache-2.0.

When your agent uses it

  • Working with formal verification
  • Program refinement
  • Proof development
  • Translating abstract specifications into executable code while maintaining formal guarantees

Example prompts

  • “/refinement-step-generator”

Workflow steps

8 steps, taken from the step headings in SKILL.md.

  1. Data Refinement
  2. Algorithmic Refinement
  3. Implementation Refinement
  4. Identify Abstraction Gap
  5. Choose Refinement Strategy
  6. Define Abstraction Relation
  7. Generate Proof Obligations
  8. Prove Obligations

What it can do on your machine

Read from SKILL.md and the folder at commit 4f38503. It shows what the files ask for, not the result of running them.

  • Tool permissions

    Pre-approves nothing: there is no allowed-tools line, so your agent's usual permission prompts apply.

    From allowed-tools in the SKILL.md frontmatter.

  • Runs code

    No scripts in the folder and no shell commands in SKILL.md (its code samples are isabelle and coq).

    From the folder's file list and the shell code blocks in SKILL.md.

  • Network

    No URLs in SKILL.md.

    From URLs in SKILL.md, links to its own repository left out.

  • Credentials

    Names no API keys, tokens, secrets or passwords.

    From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.

Context cost

Refinement Step Generator loads about 2.3k tokens when it runs, and up to ~10k if it reads all its reference files. Until then it costs about 136 tokens; SKILL.md has 514 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~136
When it runs · the whole SKILL.md, loaded when a task matches
~2.3k
With references · SKILL.md plus every file in references/, read only if the agent opens them
~10k

Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.

Safety

Auto-check passed

The automated check found no risky patterns in SKILL.md.

Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.

SKILL.md

The full file from ArabelaTso/Skills-4-SE at commit 4f38503, republished under its Apache-2.0 licence (© ArabelaTso). 514 words, ~2,285 tokens.

Download SKILL.mdSave it as .claude/skills/refinement-step-generator/SKILL.md (or your agent's skills folder). This skill also uses 3 other files; get the full folder from GitHub.
name
refinement-step-generator
description
Generate systematic refinement steps from high-level specifications to concrete implementations in Isabelle/HOL or Coq, preserving correctness obligations at each step. Use when working with formal verification, program refinement, proof development, or when translating abstract specifications into executable code while maintaining formal guarantees. Supports data refinement (abstract types → concrete structures), algorithmic refinement (specifications → algorithms), and stepwise refinement with proof obligations.

Refinement Step Generator

Generate systematic refinement steps that transform high-level specifications into concrete, executable implementations while preserving correctness through formal proofs.

Overview

Refinement is the process of transforming abstract specifications into concrete implementations through a series of correctness-preserving steps. Each refinement step:

  1. Makes the specification more concrete (closer to executable code)
  2. Preserves correctness through formal proof obligations
  3. Maintains a clear abstraction relation between levels
  4. Can be verified independently

This skill provides guidance for generating refinement steps in Isabelle/HOL and Coq.

Refinement Workflow

Abstract Specification
    ↓ [Data Refinement]
Refined Data Structures
    ↓ [Algorithmic Refinement]
Concrete Algorithm
    ↓ [Implementation Refinement]
Executable Code

Each arrow represents a refinement step with proof obligations.

Core Refinement Types

1. Data Refinement

Transform abstract data types into concrete data structures.

Example: Set → List

Abstract (Isabelle):

isabelle
definition insert_set :: "'a ⇒ 'a set ⇒ 'a set" where
  "insert_set x S = S ∪ {x}"

definition member_set :: "'a ⇒ 'a set ⇒ bool" where
  "member_set x S = (x ∈ S)"

Concrete (Isabelle):

isabelle
definition insert_list :: "'a ⇒ 'a list ⇒ 'a list" where
  "insert_list x xs = (if x ∈ set xs then xs else x # xs)"

definition member_list :: "'a ⇒ 'a list ⇒ bool" where
  "member_list x xs = (x ∈ set xs)"

Abstraction Relation:

isabelle
definition abs_list :: "'a list ⇒ 'a set" where
  "abs_list xs = set xs"

Proof Obligations:

isabelle
lemma insert_refines:
  "abs_list (insert_list x xs) = insert_set x (abs_list xs)"
  by (simp add: insert_list_def insert_set_def abs_list_def)

lemma member_refines:
  "member_list x xs = member_set x (abs_list xs)"
  by (simp add: member_list_def member_set_def abs_list_def)
2. Algorithmic Refinement

Transform specifications into algorithms.

Example: Sorting Specification → Insertion Sort

Abstract (Coq):

coq
Definition is_sorted (l : list nat) : Prop :=
  forall i j, i < j < length l → nth i l 0 ≤ nth j l 0.

Definition sort_spec (input output : list nat) : Prop :=
  is_sorted output ∧ Permutation input output.

Concrete (Coq):

coq
Fixpoint insert (x : nat) (l : list nat) : list nat :=
  match l with
  | [] => [x]
  | h :: t => if x <=? h then x :: l else h :: insert x t
  end.

Fixpoint insertion_sort (l : list nat) : list nat :=
  match l with
  | [] => []
  | h :: t => insert h (insertion_sort t)
  end.

Proof Obligations:

coq
Theorem insertion_sort_correct : forall l,
  sort_spec l (insertion_sort l).
Proof.
  (* Prove is_sorted and Permutation properties *)
Qed.
3. Implementation Refinement

Transform algorithms into efficient implementations.

Example: Naive → Optimized

Abstract:

isabelle
definition naive_reverse :: "'a list ⇒ 'a list" where
  "naive_reverse xs = rev xs"

Concrete (tail-recursive):

isabelle
fun reverse_acc :: "'a list ⇒ 'a list ⇒ 'a list" where
  "reverse_acc [] acc = acc" |
  "reverse_acc (x # xs) acc = reverse_acc xs (x # acc)"

definition efficient_reverse :: "'a list ⇒ 'a list" where
  "efficient_reverse xs = reverse_acc xs []"

Proof Obligation:

isabelle
lemma efficient_reverse_correct:
  "efficient_reverse xs = naive_reverse xs"
  by (simp add: efficient_reverse_def naive_reverse_def reverse_acc_correct)

Refinement Process

Step 1: Identify Abstraction Gap

Analyze the specification and identify what needs refinement:

  • Data structures: Abstract types (sets, maps) → Concrete structures (lists, trees)
  • Operations: Non-deterministic specs → Deterministic algorithms
  • Complexity: Inefficient → Efficient implementations
Step 2: Choose Refinement Strategy

Select appropriate refinement approach:

Data Refinement:

  • Define concrete data type
  • Define abstraction function
  • Prove operations preserve abstraction

Algorithmic Refinement:

  • Provide concrete algorithm
  • Prove algorithm satisfies specification
  • Maintain invariants

Compositional Refinement:

  • Refine components independently
  • Compose refinements
  • Prove composition preserves correctness
Step 3: Define Abstraction Relation

Establish connection between abstract and concrete levels:

Isabelle:

isabelle
definition abs_rel :: "'concrete ⇒ 'abstract ⇒ bool" where
  "abs_rel c a = (abs_fun c = a)"

Coq:

coq
Definition abs_rel (c : concrete) (a : abstract) : Prop :=
  abs_fun c = a.
Step 4: Generate Proof Obligations

For each operation, prove refinement correctness:

Forward Simulation:

If: abs_rel c a
    op_concrete c = c'
Then: ∃a'. op_abstract a = a' ∧ abs_rel c' a'

Backward Simulation:

If: abs_rel c a
    op_abstract a = a'
Then: ∃c'. op_concrete c = c' ∧ abs_rel c' a'
Step 5: Prove Obligations

Use proof tactics to discharge obligations:

Isabelle:

  • auto, simp, blast for automation
  • induction for recursive structures
  • case_tac for case analysis

Coq:

  • auto, simpl, reflexivity for automation
  • induction for recursive proofs
  • destruct for case analysis

Framework-Specific Guidance

Show full SKILL.md (213 more words)Show less
Isabelle/HOL Refinement

For Isabelle-specific patterns and the Autoref framework, see references/isabelle_refinement.md.

Key features:

  • Refinement framework with ⊑ relation
  • Autoref for automatic refinement
  • Sepref for imperative refinement
  • Code generation support
Coq Refinement

For Coq-specific patterns and refinement tactics, see references/coq_refinement.md.

Key features:

  • Program for refinement with obligations
  • Equations for well-founded recursion
  • Refinement types
  • Extraction to OCaml/Haskell

Common Refinement Patterns

For detailed refinement patterns (data structures, algorithms, optimizations), see references/refinement_patterns.md.

Common patterns include:

  • Set → List/Tree refinement
  • Map → Association list/Hash table
  • Non-deterministic choice → Deterministic selection
  • Specification → Divide-and-conquer algorithm
  • Naive → Tail-recursive implementation

Example: Complete Refinement

Abstract Specification (Isabelle):

isabelle
definition find_spec :: "'a list ⇒ ('a ⇒ bool) ⇒ 'a option" where
  "find_spec xs P = (if ∃x ∈ set xs. P x
                     then Some (SOME x. x ∈ set xs ∧ P x)
                     else None)"

Refinement Step 1: Deterministic Algorithm

isabelle
fun find_impl :: "'a list ⇒ ('a ⇒ bool) ⇒ 'a option" where
  "find_impl [] P = None" |
  "find_impl (x # xs) P = (if P x then Some x else find_impl xs P)"

Proof Obligation:

isabelle
lemma find_impl_refines:
  "find_impl xs P = find_spec xs P"
proof (induction xs)
  case Nil
  then show ?case by (simp add: find_spec_def)
next
  case (Cons x xs)
  then show ?case
    by (auto simp add: find_spec_def split: if_splits)
qed

Refinement Step 2: Tail-Recursive Implementation

isabelle
fun find_tail :: "'a list ⇒ ('a ⇒ bool) ⇒ 'a option" where
  "find_tail [] P = None" |
  "find_tail (x # xs) P = (if P x then Some x else find_tail xs P)"

lemma find_tail_correct:
  "find_tail xs P = find_impl xs P"
  by (induction xs) auto

Best Practices

  1. Small Steps: Make incremental refinements rather than large jumps
  2. Clear Abstractions: Define explicit abstraction relations
  3. Modular Proofs: Prove refinement for each operation separately
  4. Reuse Lemmas: Build library of refinement lemmas
  5. Automation: Use tactics and automation where possible
  6. Documentation: Document refinement decisions and invariants

Verification Checklist

Before finalizing refinement:

  • Abstraction relation is well-defined
  • All operations have refinement proofs
  • Invariants are preserved
  • Termination is proven (if applicable)
  • Concrete implementation is executable
  • Code can be extracted/generated
  • Performance characteristics are acceptable

Additional Resources

For detailed guidance on specific aspects:

© ArabelaTso, Apache-2.0. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file

Files

SKILL.md and 3 other files (references) in skills/refinement-step-generator of ArabelaTso/Skills-4-SE.

  • SKILL.md
  • references/coq_refinement.md
  • references/isabelle_refinement.md
  • references/refinement_patterns.md

Open the folder on GitHubat commit 4f38503

Compare with similar skills

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Categories

Questions about Refinement Step Generator

What does Refinement Step Generator do?

Generate systematic refinement steps from high-level specifications to concrete implementations in Isabelle/HOL or Coq, preserving correctness obligations at each step. Refinement Step Generator is an agent skill from ArabelaTso/Skills-4-SE. Generate systematic refinement steps from high-level specifications to concrete implementations in Isabelle/HOL or Coq, preserving correctness obligations at each step.

When should I use Refinement Step Generator?

Refinement Step Generator fits situations like: working with formal verification; program refinement; proof development; translating abstract specifications into executable code while maintaining formal guarantees.

How do I install Refinement Step Generator in Claude Code?

Run `npx skills add ArabelaTso/Skills-4-SE --skill refinement-step-generator -a claude-code`. Or copy the skill folder (skills/refinement-step-generator in ArabelaTso/Skills-4-SE) into .claude/skills/refinement-step-generator in your project. Claude Code loads it when a task matches its description.

How do I install Refinement Step Generator in Codex?

Run `npx skills add ArabelaTso/Skills-4-SE --skill refinement-step-generator -a codex`. Or copy the skill folder (skills/refinement-step-generator in ArabelaTso/Skills-4-SE) into .agents/skills/refinement-step-generator in your project. Codex loads it when a task matches its description.

Can I use Refinement Step Generator in Cursor, Gemini CLI or GitHub Copilot?

Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add ArabelaTso/Skills-4-SE --skill refinement-step-generator -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/refinement-step-generator, .gemini/skills/refinement-step-generator, .github/skills/refinement-step-generator and .opencode/skills/refinement-step-generator in your project.

What does Refinement Step Generator need to run?

SKILL.md names no scripts, command-line tools or credentials: Refinement Step Generator is instructions for the agent only.

Does Refinement Step Generator access the network?

SKILL.md contains no URLs. Any network use would come from the scripts or tools the agent runs. This is read from the text; nothing was executed.

Is Refinement Step Generator safe to install?

Our automated static check of SKILL.md found no risky patterns, such as piping downloads into a shell, reading credential files or hidden Unicode. It is not a guarantee. Review the folder before installing.

What licence does Refinement Step Generator use?

Refinement Step Generator is published under the Apache-2.0 licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.

How many tokens does Refinement Step Generator use?

About 2.3k tokens (SKILL.md is roughly 9.1k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full. Its references folder adds about 7.7k tokens, read only when the agent opens those files.

What are the alternatives to Refinement Step Generator?

Skills that share tags, products or a category with Refinement Step Generator: Translation Diff Export (Devolutions/UniGetUI, 26k stars), Sync Translations (symfony/symfony, 31k stars), Translation Diff Import (Devolutions/UniGetUI, 26k stars) and Translation Diff Translate (Devolutions/UniGetUI, 26k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Refinement Step Generator?

ArabelaTso (a GitHub user) maintains it in ArabelaTso/Skills-4-SE, which has 253 GitHub stars. The repository holds 151 skills in this directory. The repository was last updated on August 21, 2026.

Source: ArabelaTso/Skills-4-SE on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.