abstracdtype.html

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<H1>abstract data type</H1>
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(definition)

<P>
<strong>Definition:</strong>
A mathematically specified collection of data-storing entities with operations to create, access, change, etc. instances.
<P><strong>See also</strong>
<a href="dictionary.html" tppabs="http://hissa.nist.gov/dads/HTML/dictionary.html"><em>dictionary</em></a>, <a href="stack.html" tppabs="http://hissa.nist.gov/dads/HTML/stack.html"><em>stack</em></a>, <a href="queue.html" tppabs="http://hissa.nist.gov/dads/HTML/queue.html"><em>queue</em></a>.
<P><em>Note:
Since the collection is defined mathematically, rather than as an implementation in a computer language, we may reason about effects of the operations, relations to other abstract data types, whether a program implements the data type, etc. <P> One of the simplest abstract data types is the <a href="stack.html" tppabs="http://hissa.nist.gov/dads/HTML/stack.html"><em>stack</em></a>.   The operations new(), push(v, S), top(S), and pop(S) may be defined with the following.<BR> new() returns a stack<BR> pop(push(v, S)) = S<BR> top(push(v, S)) = v<BR> where S is a stack and v is a value.   Contrast this with the axiomatic definition of a <a href="dictionary.html" tppabs="http://hissa.nist.gov/dads/HTML/dictionary.html"><em>dictionary</em></a>. <P> From these one may define equality between stacks, define a pop function which returns the top value in a non-empty stack, etc.  The predicate empty(S) may be added and defined with the following two axioms.<BR> empty(new())<BR> ! empty(push(v,S))<BR> <P> From Algorithms and Theory of Computation Handbook, page 4-2, Copyright &copy; 1999 by CRC Press LLC.</em>
<P>Author: <a href="terms.html#authorCRC-A" tppabs="http://hissa.nist.gov/dads/terms.html#authorCRC-A">CRC-A</a>,<a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>

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Entry modified Mon Dec 27 16:28:35 1999.<BR>
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