Lec6 - CMPSC 461: Programming Language Concepts Lecture 6...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
CMPSC 461: Programming Language Concepts Lecture 6 Instructor: Prof. Swarat Chaudhuri
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Bottom-up inductive definition of data Define a set inductively. That is, give rules to build it. As usual, the base case and inductive case. Let us take the set S of all even natural numbers. First try: the set that satisfies: 0 is in S if n is in S , then (n+2) is in S Doesn’t work. Many such sets. The least such set. That is, the set that is the subset of all sets satisfying these conditions.
Background image of page 2
Growing sets… S 1 S 2 S 3 S 0 = empty Finally, some set S k such that S k = S k+1 . This set is S. We are defining S as a limit of a sequence of sets , f(Ø), f(f(Ø)),… > where f(S) is obtained by adding to S all numbers (n +2), where n is in S.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
f is a (mathematical) function from sets to sets. f : Sets → Sets We want a solution to the equation f(S) = S But there are many possible solutions to this equation. We want the
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 19

Lec6 - CMPSC 461: Programming Language Concepts Lecture 6...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online