An Automated Proof Assistant (APA), also known as an [[interactive theorem prover]] or [[interactive proof assistant]], is a software tool designed to assist in the development of formal proofs. It combines the power of computer automation with human guidance to verify the correctness of mathematical theorems, software programs, and hardware designs. **How APAs work:** 1. **Formalization:** The user expresses the problem to be solved in a formal language understood by the APA. This includes defining axioms, assumptions, and the statement to be proven. 2. **Interaction:** The user guides the proof process by providing hints, strategies, or high-level proof steps. The APA then fills in the gaps by automatically generating low-level proof details. 3. **Verification:** The APA rigorously checks the validity of each step in the proof, ensuring that it follows from the previous steps and the given axioms. If a step is incorrect, the APA alerts the user. **Benefits of using APAs:** - **Increased Confidence:** APAs provide a high degree of confidence in the correctness of proofs, as they eliminate human errors and ensure that all steps are logically sound. - **Scalability:** APAs can handle large and complex proofs that would be impractical to check manually. - **Automation:** APAs automate tedious and error-prone aspects of proof development, freeing the user to focus on the creative aspects. - **Reusability:** Proofs developed with APAs can be easily reused and modified for other purposes. **Popular APAs:** - Coq - Isabelle/HOL - Lean - Agda - ACL2 **Applications of APAs:** - **Mathematics:** Verifying complex mathematical theorems - **Computer Science:** Proving the correctness of algorithms and software programs - **Hardware Design:** Verifying the correctness of hardware circuits - **Cryptography:** Proving the security of cryptographic protocols APAs have become increasingly important in various fields where formal verification is critical. They have the potential to revolutionize the way we approach complex problems by providing rigorous guarantees of correctness and reliability. # References ```dataview Table title as Title, authors as Authors where contains(subject, "Automated Proof Assistants") or contains(subject, "Automated Proof Assistant") sort title, authors, modified, desc ```