To help you understand

1. Use/Creation of function contracts
2. Use/Creation of invariants
3. Use/Implementation of the client/server model for contract use
4. Programming logic with sequences

We have created some automated grading tools to speed the grading of homeworks. To apply those tools, we need to make sure that each student uses a consistent naming for all their solutions file. Therefore, we have created an IntelliJ project with template files for your solution. DONT CHANGE THE NAME OF ANY OF THE FILES that we give you.

SETUP

In this homework, you will run logika in SimExe mode. As a reminder, you set this in Settings/Sireum/Logika. One accesses the Settings through either the File or the Intelij menu.

Getting started

You can find examples of completed Logika programming proofs in the Logika example repository (included in the class examples that you downloaded (as illustrated in the Step #2 videos). Here is a direct link to the predicate logic proofs portion of those examples:https://github.com/sireum/v3-logika-examples/tree/release/src/predicate

Considerations

1. All files must run in the Sireum IVE
2. This SimExe mode, you may get get a program to Logika Check and still be incomplete. Carefully read all requirements for each problem
3. Partial credit may be received part of the requirements are met
4. Correct claims that do not add to solving the problems will not hurt you
5. In general pre/post/invariants will be less than a dozen lines long Figuring them out can be time consuming.

Problems

1. The purpose of this program is to simulate a key-value pair dictionary implemented with parallel arrays. First read entire program to understand the calculation. Second create the post condition for findKey, which ensure that if the key is in the sequent, its index is returned, if not -1 is returned. Next, write the pre and post condition for fetch value. Finally, fix the if condition in the client code so the final assertion is true.
2. Consider an application in which we have a vending machine that holds one flavor of Gatorade only (Glacier Freeze). The contents of the vending machine are replenished by a service man who takes Gatorade from a warehouse and puts it in the vending machine.The application has two global variables : (1) machinecount holds the number of Gatorades currently in the vending machine, and (2) warehousecount holds the number of Gatorades in the warehouse.A company hired a programmer named Gerald Slackster to write the code for the application. Unfortunately, Gerald never learned about program logic or the software contract paradigm. Your task for this question is to take Gerarlds procedure declarations (which includes informal documentation) and add software contracts (including the different conditions plus appropriate invariants for globals) in the space provided in the code below. Note that Geralds documentation doesnt spell everything out in detail. In some cases, you will need to add contract information and global invariants that you believe are appropriate to establish reasonable properties that you would want for this application. Then complete the coding of the procedures declared by Gerald and prove that they satisfy the contracts that you have written. Note that for this question, your contracts should be as precise as possible.Hints for this exercise:in the body of a producedure
   • in the post-condition of a procedure, you can refer to the initial value of a global g by writing g_in.
   • at the beginning of the body of a procedure, one is allowed to deduce g == gin using the premise rule. You can use the above mechanism to define, for a particular procedure, a post-condition that specifies the output value of a global variable g in terms of its input value gin.Give the program + function pre/post conditions and loop invariants necessary to demonstrate that your program is correct.
3. (In this problem you will complete both client and server functions to check if a sequence contains values larger than a certain value and create a second sequence containing only those values. Read the entire program to understand its structure. First write loop code and invariants for someGreaterThan to meet the post-conditions. When seeing the sequent (1, 5, 7, 12) and 8, someGreaterthan should return true, 12 is greater than 8 .. (1, 5, 12, 7) and 12 should return false. Next write the function post conditions and loop invariant for reduces. Seeing (1, 5, 7, 12) and 6 it returns (7,12). Finally, in main(), change the variable assignment to bigenough, and the parameters passed to reduce to ensure the program has no errors (does not crash if reduce returns an empty array). No additional if conditions or assumes may be added to the client.
4. (6 points) In the final problem the function takes a sequence (1,2,3,4,5) and returns a palindrome of it starting from the front (1,2,3,2,1). Your task is to provide Loop invariants which ensure the post conditions are met. Add a post condition proving the size the returned array is the same size as the array passed in.