[SOLVED] CS:3820 Programming Language Concepts

CS:3820 Programming Language Concepts
Homework 5: Verification
1 Overview
1.1 Learning objectives
Read theorems written in Agda and re-state them in English
Prove theorems in Agda using techniques like
o Introducingandusingassumptions o Proof by cases
o Proof by induction
o Rewriting
o Callinghelpertheorems
Document the steps you took in your proof
Determine assumptions that can help make a theorem provable
1.2 Getting the code
Source address: https://research-git.uiowa.edu/cs3820-assignments/hw5-fa19.git
If IAL is not on your agda search path, then simply copy the .agda files in hw5-fa19 into your IAL directory.
1.3 Submitting the code Upload your files to ICON
1.3.1 Checklistforsubmission
You are solely responsible for the integrity of your submission. Please use the following checklist.
Myers, 2019

All .agda files can be compiled by Agda
IMPORTANT: your code MUST compile. If you are missing part of the proof, then
leave a hole instead. Example: a file has 4 theorems, if you complete the proofs for 3 of them and leave holes in the 4th youll get credit for the 3 completed ones. But if you complete proofs for 3 theorems and leave the 4th to not compile, then you get credit for none.
IMPORTANT: you must re-state the theorems in English and document your proof steps (see below)
Youve double-checked the correct version of your files is on ICON by downloading them and re-compiling them. (ICON renames the files that is not a problem, just name them back before compiling).
2 Simpletheorems
Prove all the theorems in hw5-simple.agda. See the file for some hints. Remember
To receive more than 0 credit, you must
o Write a comment above the theorem, re-stating the theorem in plain English o Document your proof with comments that show the steps you took to come to
the final proof. That is, one comment about the goal for each time you left a hole and then filled it in. See the Ch 2 reading assignment on Agda for an example.
o Make sure the file still compiles. That means if you need to leave a proof unfinished, then leave holes such that the file still compiles.
3 Bool theorems
Prove all the theorems in hw5-bool-thms.agda. See the file for some hints. Remember To receive more than 0 credit, you must
o Write a comment above the theorem, re-stating the theorem in plain English o Document your proof with comments that show the steps you took to come to
the final proof. That is, one comment about the goal for each time you left a hole and then filled it in. See the Ch 2 reading assignment on Agda for an example.
o Make sure the file still compiles. That means if you need to leave a proof unfinished, then leave holes such that the file still compiles.
Myers, 2019

4 Listtheorems
Prove all the theorems in hw5-list-thms.agda. See the file for some directions and hints. Remember
To receive more than 0 credit, you must
o Write a comment above the theorem, re-stating the theorem in plain English o Document your proof with comments that show the steps you took to come to
the final proof. That is, one comment about the goal for each time you left a hole and then filled it in. See the Ch 2 reading assignment on Agda for an example.
o Make sure the file still compiles. That means if you need to leave a proof unfinished, then leave holes such that the file still compiles.
Myers, 2019