The Following While Loop Is Annotated with a Pre- and Post-Condition

question 21

Essay

The following while loop is annotated with a pre- and post-condition and also a loop invariant.
Use the loop invariant theorem to prove the correctness of the loop with respect to the pre- and post-conditions.
$[$ Pre-condition: product $= A [ 1 ]$ and $i = 1 ]$ while $( i \neq m )$
1. $i : = i + 1$
2. product := product. $A [ i ]$
end while
$[$ Post-condition: product $= A [ 1 ] \cdot A [ 2 ] \cdots A [ m ] ]$
loop invariant: $I ( n )$ is $" i = n + 1$ and product $: = A [ 1 ] \cdot A [ 2 ] \cdots A [ n + 1 ] "$

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Definitions:

Work in Process Inventory

Goods that are in various stages of the production process but are not yet completed.

Raw Materials Inventory

The total value of raw materials currently held by a company, which are to be used in manufacturing or production processes.

Labor Costs

The total sum of all wages, benefits, and taxes that a business must pay for its employees, often a significant component of production expenses.

Direct Labor

The labor cost directly attributable to the production of goods or services, distinguishable from indirect labor costs like maintenance.