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Abstract Domain Explorer

Applies abstract interpretation with interval, sign, congruence, octagon, and polyhedra domains to infer variable ranges and loop invariants without running the code.

Dev & CodingAdvanced★ 252⑂ 24AI score 9/10Last updated: Aug 21, 2026

What it does

Guides Claude through abstract interpretation to statically infer value ranges, variable relationships, and loop invariants.

  • Domain selection guide: precision/cost trade-off table for Sign, Interval, Congruence, Octagon, Polyhedra, and Reduced Product domains.
  • Six-step workflow: pick a domain → initialize the abstract state → apply transfer functions (assignment, assume, join) → widen (∇) at loop headers for termination → narrow (△) to regain precision → extract invariants.
  • Safety checks: flags possible division by zero and array out-of-bounds accesses from the inferred abstractions.
  • Soundness rules: MUST/MUST NOT list forbids reporting approximations as exact values and requires stating what the chosen domain cannot express (e.g., octagons cannot represent y = 2x).

Who it's for

  • Students and researchers in static analysis, formal verification, or compiler optimization.
  • Engineers who need rigorous reasoning about variable ranges and loop invariants during review.
  • Anyone working through textbook fixpoint computations step by step.

Example uses

  1. For int x=0; while(x<10){x++; y--;}, the interval domain yields x ∈ [0,9] inside the loop and x=10, y=90 on exit, while noting intervals miss x+y=100.
  2. For y = x*x; z = 100/y;, the sign domain derives y ≥ 0 and reports a potential division by zero at x = 0.
  3. For nested loops, the octagon domain extracts the relational invariant j ≤ i, and the skill explains when to escalate to polyhedra for relations like z = 3x.

· · · Install guide · · ·

Try it now, no install

Paste this into Claude to use the skill without installing anything.

Read the instructions in this file and follow them to help me:
https://raw.githubusercontent.com/ArabelaTso/Skills-4-SE/HEAD/skills/abstract-domain-explorer/SKILL.md

What I want: (describe your task here)

If Claude can't open the link, open it yourself and paste the contents instead.

↓ If it works for you, download the ZIP below and install it. Then it runs on its own — no pasting each time.

Install in the Claude app (no terminal)
  1. Download the ZIP with the button below.
  2. In Claude, open Settings → Capabilities and turn on 'Code execution and file creation'. (one time)
  3. Go to Customize → Skills → + → 'Upload a skill' and upload the ZIP.
↓ Download ZIP
Install in Claude Code

Let Claude do it — paste this into Claude Code

Install the skill I found on Claude Skill Mart.
Copy the skills/abstract-domain-explorer folder from the GitHub repo ArabelaTso/Skills-4-SE into my ~/.claude/skills/abstract-domain-explorer/.
When it's done, tell me in one line what this skill can do.

Install with a command instead

git clone https://github.com/ArabelaTso/Skills-4-SE.git && mkdir -p ~/.claude/skills && cp -r Skills-4-SE/skills/abstract-domain-explorer ~/.claude/skills/

⚠ This is a third-party skill. Check the source repository before installing.

  1. Open a terminal.
  2. Clone the repository: git clone https://github.com/ArabelaTso/Skills-4-SE.git
  3. Create the skills folder if needed: mkdir -p ~/.claude/skills
  4. Copy the skill: cp -r Skills-4-SE/skills/abstract-domain-explorer ~/.claude/skills/
  5. Confirm the bundled references/abstract_domains.md came along.
  6. Restart Claude Code and try a prompt like "Infer this loop's invariant using abstract interpretation" to trigger the skill.
View source on GitHub ↗License: Apache-2.0