Towards the Mechanical Verification of Textbook Proofs
نویسنده
چکیده
Our goal is to implement a program for the machine verification of textbook proofs. We study the task from both the linguistics and automated reasoning perspective and give an in-depth analysis for a sample textbook proof. We propose a framework for natural language proof understanding that extends and integrates state-of-the-art technologies from Natural Language Processing (Discourse Representation Theory) and Automated Reasoning (Proof Planning) in a novel and promising way, having the potential to initiate progress in both of these disciplines.
منابع مشابه
Verifying and Invalidating Textbook Proofs Using Scunak
Many textbook proofs are essentially human-readable representations of natural deduction proofs. Terms in dependent type theory provide formally checkable representations of natural deduction proofs. We show how the new mathematical assistant system Scunak can be used to verify a textbook proof by translating the LTEX version into a proof term in a dependent type theory. We also show how Scunak...
متن کاملAutomatic verification of textbook programs
Textbooks on program verification make use of simple programs in mathematical domains as illustrative examples. Mechanical verification tools can give students a quicker way to learn, because the feedback cycle can be reduced from days (waiting for hand-proofs to be graded by the teaching assistant) to seconds or minutes (waiting for the tool’s output). However, the mathematical domains that ar...
متن کاملStructuring textbook proofs
Topic Areas or Theme ID: discourse analysis, discourse segmentation, discourse plans Word Count: 3196 words (excluding gures) Under consideration for other conferences (specify)? No. Abstract We propose a promising research problem, the machine veriication of textbook proofs. It shows that textbook proofs are a suuciently complex and highly struc-tured form of discourse, embedded in a well-deen...
متن کاملIranian EFL Teachers' and Students' Perceptions towards the First Grade High School English Textbook (Vision1)
In countries where textbooks are considered as the main source of teaching/learning process, textbook evaluation seems to be inevitable and necessary. The current study aimed at evaluating the new English textbook entitled “Vision 1”, developed for the Iranian first grade high school students. To achieve this goal, two groups of participants took part in the study. They consisted of 30 teachers...
متن کاملTowards mechanized correctness proofs for cryptographic algorithms: Axiomatization of a probabilistic Hoare style logic
In [5] we build a formal verification technique for game based correctness proofs of cryptograhic algorithms based on a probabilistic Hoare style logic [10]. An important step towards enabling mechanized verification within this technique is an axiomatization of implication between predicates which is purely semantically defined in [10]. In this paper we provide an axiomatization and illustrate...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000