Homework 0

Due: Monday, 3 Sep.

Step 1: Install Coq.

Step 2: Download and Process Basics.v and Induction.v.

Click the orange down-arrow a few times. Each time you click down-arrow, CoqIDE processes the next command in the Basics.v buffer. Progress through the buffer is marked in green.

The keyboard shortcut for down-arrow is Ctl+Alt+Down. It's often more convenient to change this just to Ctl+Down. You can do so by changing the Navigation Shortcut modifier to Ctl in the Edit->Preferences->Shortcuts menu.

In addition to processing files incrementally, you can also compile them to Coq's object .vo format. Try this out, by doing either

• Compile->Compile Buffer from within CoqIDE, or
• coqc Basics.v at the command-line.

> make Basics.vo

To test whether your compile worked, download and open Induction.v and process it through the line Require Export Basics.

Step 3: Read and complete Basics.v and Induction.v. You may skip exercises marked "Optional".

Following the instructions in the files, fill in the proofs and definitions for all exercises in Basics.v and Induction.v, at every spot marked FILL IN HERE.

To check that you've successfully completed a proof, change the Admitted directly after FILL IN HERE to Qed and process the buffer through the Qed.

You can check your overall progress by running:

> make BasicsTest.vo

> make InductionTest.vo

Once you're done, submit the following four individual files in Blackboard:

• Basics.v
• Induction.v
• the console output of running make BasicsTest.vo, as a file named BasicsTest.txt; and
• the console output of running make InductionTest.vo, as a file named InductionTest.txt.