py-prop-logic-kernel 0.0.4

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prop-logic-kernel

This repo contains:

• Main.lean: a tiny proposition-logic tactic kernel wrapped in a REPL.run loop
• py_prop_logic_kernel/: the Python package you publish; it parses the kernel output into structured steps such as goals_remaining

Lean code spec

The Lean kernel is defined primarily by:

• PropLogicKernel/Basic.lean: proposition syntax, tactics, goals, and state
• PropLogicKernel/Parser.lean: string parser for propositions and tactics
• PropLogicKernel/Resolver.lean: operational semantics for each tactic
• PropLogicKernel/REPL.lean: REPL transition function built on top of the resolver
• Main.lean: executable entrypoint

Core data model

• A proposition P is one of: ⊥, atom, conjunction A ∧ B, disjunction A ∨ B, implication A → B.
• A goal is a pair of:
  • a hypothesis map from natural-number names to propositions
  • a target proposition
• A state is a stack of goals plus a counter used to assign fresh hypothesis names.

Tactic resolution rules

These are the actual rules implemented in PropLogicKernel/Resolver.lean.

• intro:
  • If the goal is A → B, add a fresh hypothesis A and replace the goal with B.
• apply n:
  • If hypothesis n is A → B and the current goal is B, replace the goal with A.
• exact n:
  • If hypothesis n is exactly the current goal A, solve the goal.
• constructor:
  • If the goal is A ∧ B, split it into two goals: A and B.
• left:
  • If the goal is A ∨ B, replace it with A.
• right:
  • If the goal is A ∨ B, replace it with B.
• cases n:
  • If hypothesis n is A ∨ B, branch into two goals: one with fresh hypothesis A, one with fresh hypothesis B.
  • If hypothesis n is A ∧ B, add fresh hypotheses A and B to the current goal.
  • If hypothesis n is ⊥, solve the goal immediately.
• lem P:
  • Available only in classical mode.
  • Adds a fresh hypothesis (P → ⊥) ∨ P.
• refine n:
  • Available only in classical mode.
  • If hypothesis n is A1 → B1 and the current goal is B, replace the current goal with two goals:
    • B1 → B
    • A1
• sorry:
  • Solves the current goal unconditionally.
• new P:
  • Pushes a fresh goal P onto the state, with an empty hypothesis map.

Failure behavior

• If a tactic does not match the current goal or referenced hypothesis shape, resolution fails with an error message.
• lem and refine fail if classical logic is disabled.
• Any tactic other than new fails on an empty goal stack.

REPL protocol spec (REPL.run)

The executable produced by lake build (see .lake/build/bin/Main-lean) implements a simple line-based protocol driven by REPL.run in REPL/REPL.lean.

Each step:

• stderr (error/status stream): write zero or more lines of status/errors.
  • In this repo, status lines are prefixed with -- and include counters, for example:
    • -- new_count 1 sorry_count 0 goals_remaining 2
    • -- all goals accomplished!
• stdout (output stream): write zero or more lines of “main output” (e.g. the rendered goal state).
• stderr (prompt): write the prompt string (default > ) without a trailing newline.
• stdin (input): read exactly one line (newline-terminated). That line is passed to the transition function.

Then the next step repeats forever.

Exit code policy

At EOF (stdin.getLine returns empty), REPL.run returns the previous step's code.

In this repo, PropLogicKernel/REPL.lean sets code = 0 iff all of the following hold:

• newCount ≥ 1 (at least one goal was successfully introduced via new)
• sorrCount = 0 (no sorry was used)
• goal stack is empty (all goals solved)

Otherwise code = 1.

Important nuance: parse/resolve errors do not directly force code 1; they keep the previous state. So if all goals were already solved and a later command fails, final code can still be 0.

Notes for clients

• Do not assume stdout and stderr are synchronized; a robust client should read both streams until it observes the prompt on stderr.
• Flush matters: REPL/REPL.lean flushes stdout/stderr after writes so subprocess-driven clients do not hang on buffered output.

Python package spec

py_prop_logic_kernel is a Python-only wrapper around the built Lean binary.

• py_prop_logic_kernel.Client:
  • starts .lake/build/bin/Main-lean
  • sends lines to the REPL
  • validates tactic surface syntax in Python before sending (including strict proposition parsing for new and lem)
  • parses stderr status lines like -- new_count N sorry_count M goals_remaining K
  • returns structured Step(out, err, new_count, sorry_count, goals_remaining)
• Client.send(line):
  • sends any supported REPL command, including new and sorry
• Client.send_honest(line):
  • like send, but if new or sorry appears in the input line, it does not send the command and returns a Step with the policy message in err
• Client.finish():
  • closes stdin (EOF), allowing the Lean process to return its final code
  • returns graceful exit code (int) when graceful shutdown succeeds, else None on timeout fallback
• Client.init_prompt():
  • returns a human/AI-oriented summary of usage and tactic semantics

AI-generated code disclaimer

The following files were written by Cursor AI:

• README.md
• All Python code in this repo (for example: py_prop_logic_kernel/)
• PropLogicKernel/Parser.lean