Formalize and analyze LLM prompt behavior with a probabilistic evaluation kernel.
npx skills add https://github.com/jbrukh/skills --skill prompt-calculus
Please help me install this Agent Skill. Skill: prompt-calculus Source: https://github.com/jbrukh/skills/tree/main/skills/prompt-calculus Command: npx skills add https://github.com/jbrukh/skills --skill prompt-calculus
This formalism provides a compact framework to reason about LLM prompts, their evaluation semantics, and how prompt functions compose and affect outputs.
Apply a simple prompt function to a sample input and trace the resulting output distribution using the evaluation kernel.
High-intent search queries and answers about installing and using this skill.
You can model LLM prompt evaluation using a probabilistic evaluation kernel that maps prompts to output distributions, allowing you to analyze predictability and context-dependent behavior.
Prompt composition formalizes applying prompts as functions and combining them (G ∘ F) to build complex behaviors, using rules like the Chapman–Kolmogorov equation for evaluation.
Iterated self-application is analyzed by evaluating convergence properties and fixed points, explaining how repeatedly applying a prompt stabilizes outputs or generates quines.
A probability kernel defines how prompts map to output distributions and how context modifies evaluation, serving as the core mechanism for reasoning about prompt behavior.
Output predictability across contexts is evaluated by applying the distributional kernel K with varying contexts and information predicates to trace how output distributions change.
No external frameworks are needed; the formalism defines its own structure including a distributional kernel K, contexts, information predicates, and the Chapman–Kolmogorov composition rule.
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