Write an Imp program [c] that swaps the values of [X] and [Y] and     show that it satisfies the following specification:       {{X <= Y}} c {{Y <= X}}     Your proof should not need to use [unfold valid_hoare_triple].     Hints:        - Remember that Imp commands need to be enclosed in <{...}>          brackets.        - Remember that the assignment rule works best when it's          applied "back to front," from the postcondition to the          precondition.  So your proof will want to start at the end          and work back to the beginning of your program.        - Remember that [eapply] is your friend.)  *) Definition swap_program : com   (* REPLACE THIS LINE WITH ":= _your_definition_ ." *). Admitted. Theorem swap_exercise :   {{X <= Y}}     swap_program   {{Y <= X}}. Proof.   (* FILL IN HERE *) Admitted. (** [] *)

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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** **** Exercise: 3 stars, standard (swap_exercise)

    Write an Imp program [c] that swaps the values of [X] and [Y] and
    show that it satisfies the following specification:

      {{X <= Y}} c {{Y <= X}}

    Your proof should not need to use [unfold valid_hoare_triple].

    Hints:
       - Remember that Imp commands need to be enclosed in <{...}>
         brackets.
       - Remember that the assignment rule works best when it's
         applied "back to front," from the postcondition to the
         precondition.  So your proof will want to start at the end
         and work back to the beginning of your program.
       - Remember that [eapply] is your friend.)  *)

Definition swap_program : com
  (* REPLACE THIS LINE WITH ":= _your_definition_ ." *). Admitted.

Theorem swap_exercise :
  {{X <= Y}}
    swap_program
  {{Y <= X}}.
Proof.
  (* FILL IN HERE *) Admitted.
(** [] *)
From the book software Foundations Volume 2 coq proof

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