# HG changeset patch # User Adam Chlipala # Date 1223489915 14400 # Node ID d829cc24faeea2f90ff6885767c4efadbabdc491 # Parent bc12662ae89543cd324e28b2cb90001c01615650 Add a darn newline diff -r bc12662ae895 -r d829cc24faee src/MoreDep.v --- a/src/MoreDep.v Wed Oct 08 13:55:20 2008 -0400 +++ b/src/MoreDep.v Wed Oct 08 14:18:35 2008 -0400 @@ -1087,11 +1087,11 @@ %\item%#
  • # Define a kind of dependently-typed lists, where a list's type index gives a lower bound on how many of its elements satisfy a particular predicate. In particular, for an arbitrary set [A] and a predicate [P] over it: %\begin{enumerate}%#
      # %\item%#
    1. # Define a type [plist : nat -> Set]. Each [plist n] should be a list of [A]s, where it is guaranteed that at least [n] distinct elements satisfy [P]. There is wide latitude in choosing how to encode this. You should try to avoid using subset types or any other mechanism based on annotating non-dependent types with propositions after-the-fact.#
    2. # - %\item%#
    3. # Define a version of list concatenation that works on [plist]s. The type of this new function should express as much information as possible about the outpit [plist].#
    4. # + %\item%#
    5. # Define a version of list concatenation that works on [plist]s. The type of this new function should express as much information as possible about the output [plist].#
    6. # %\item%#
    7. # Define a function [plistOut] for translating [plist]s to normal [list]s.#
    8. # %\item%#
    9. # Define a function [plistIn] for translating [list]s to [plist]s. The type of [plistIn] should make it clear that the best bound on [P]-matching elements is chosen. You may assume that you are given a dependently-typed function for deciding instances of [P].#
    10. # %\item%#
    11. # Prove that, for any list [ls], [plistOut (plistIn ls) = ls]. This should be the only part of the exercise where you use tactic-based proving.#
    12. # %\item%#
    13. # Define a function [grab : forall n (ls : plist (S n)), sig P]. That is, when given a [plist] guaranteed to contain at least one element satisfying [P], [grab] produces such an element. [sig] is the type family of sigma types, and [sig P] is extensionally equivalent to [{x : A | P x}], though the latter form uses an eta-expansion of [P] instead of [P] itself as the predicate.#
    14. # #
    #%\end{enumerate}% #
  • # -##%\end{enumerate}% *) \ No newline at end of file +##%\end{enumerate}% *)