An extended arithmetic of ordinal numbers
نویسندگان
چکیده
منابع مشابه
Algorithms for Ordinal Arithmetic
Proofs of termination are essential for establishing the correct behavior of computing systems. There are various ways of establishing termination, but the most general involves the use of ordinals. An example of a theorem proving system in which ordinals are used to prove termination is ACL2. In ACL2, every function defined must be shown to terminate using the ordinals up to 0. We use a compac...
متن کاملSequences of Ordinal Numbers
In the first part of the article we introduce the following operations: On X that yields the set of all ordinals which belong to the set X, Lim X that yields the set of all limit ordinals which belong to X, and inf X and sup X that yield the minimal ordinal belonging to X and the minimal ordinal greater than all ordinals belonging to X, respectively. The second part of the article starts with s...
متن کاملOrdinal Arithmetic in ACL2
Ordinals form the basis for termination proofs in ACL2. Currently, ACL2 uses a rather inefficient representation for the ordinals up to 0 and provides limited support for reasoning about them. We present algorithms for ordinal arithmetic on an exponentially more compact representation than the one used by ACL2. The algorithms have been implemented and numerous properties of the arithmetic opera...
متن کاملInterval Arithmetic, Extended Numbers and Computer Algebra Systems
Many ambitious computer algebra systems were initially designed in a flush of enthusiasm, with the goal of automating any symbolic mathematical manipulation “correctly.” Historically, this approach resulted in programs that implicitly used certain identities to simplify expressions. These identities, which very likely seemed universally true to the programmers in the heat of writing the CAS, (a...
متن کاملDRAFT: Interval arithmetic, Extended numbers and Computer Algebra Systems (CAS)
Many ambitious computer algebra systems were initially designed in a flush of enthusiasm, with the goal of automating any symbolic mathematical manipulation “correctly.” We see this kind of goal in programs like Macsyma, Maple, Mathematica. This approach often resulted in programs that implicitly used certain identities to simplify expressions. These identities, which likely seemed universally ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1969
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-65-1-95-127