CS240A- Winter 98 Project1

CS240A, Winter 98.

Project 1, Part 1

The first objective of this project is to add a time domain to Datalog. Although we will assume the Gregorian Calendar, and a very simplified temporal domain, the task is hardly trivial.

In Part 2 of this project, we use this representation for defining an extension of Datalog akin to TSQL2

Dates

Basic Data Type: date(Year, Month, Day)
This (i) will be stored using complex terms, (ii) corresponds to SQL2 DATE, and (iii) satisfies the constraints of the same.
SQL2 TIME and TIMESTAMP will not be supported.
Casting to coarser granularity:
- month_cast($Date1, Date2)
  If Date1 had granularity of days, Date2 is set equal to Date1 but for the field Day which is set to zero. Zero denotes here a non-existing field, since date was set to a coarser granularity.
- year_cast($Date1, Date2)
  The Day and Month fields of Date1 are set to zero.
- day_cast($Date1, Date2)
  When Date1 has granularity of days then Date2 is identical to Date1. Morevover:
Casting to finer granularity resets the appropiate zero fields to 1 (same as TSQL2). For instance:
month_cast(date(1987,0,0), X) yields X= date(1987,1,0)
day_cast(date(1987,8,0), X) yields X= date(1987,8,1)
day_cast(date(1987,0,0), X) yields X= date(1987,1,1)

Comparisons

Equality: same_date(Date1, Date2)
Inequality: before($DATE1, $DATE2)
This is true when Date1 strictly precedes Date2.

When the dates being compared have different granularities, an implicit conversion to the coarser granularity is performed.

Intervals

These are represented by the following two terms:


months(Months)

and days(Days)

Thus we have two types of intervals, as in SQL2 (but we do not allow things such as YEAR TO MONTH)

Equality and inequality between intervals will simply be expressed as equality and inequality between their arguments
Arithmetic on intervals will also be expressed as arithmetic on their arguments (i.e., the user is free to do as he/she pleases and is responsible for semantics).

Mixing Dates and Intervals in Computations

months_btwn($Date1, $Date2, Interval)
This returns the month-interval between the two dates after these were month-cast. The resulting interval could be negative.
days_btwn ($Date1, $Date2, Interval)
This returns the exact day-interval between the two dates after these were day-cast. The exact number of days is computed using the calendar.
The resulting interval could be negative.
time_add ($DATE1, $Interval, NewDate)
Adding a date and an interval yields a new date. The interval can be expressed in either days or months and can also be negative. If Date1 and Interval have the same granularity then NewDate is also expressed in the same granularity. When Date1 and Interval have different granularities, then return date(0,0,0) which denotes an invalid date.

When the first two arguments have different granularities, an implicit conversion to the coarser granularity is performed.

Queries to be Implemented

You must implement the Gregorian Calendar (you can assume that the year is after 1800 AD) to support the following Queries:

Given a year, and a month, print the calendar for that month: i.e., list the month, day, year, and day of the week.
A bank keeps a database of CDs (certificates of deposit) as follows:
cd(CD#, Deposit_Date, Duration, Interest_to_Maturity)
(Duration is a time interval expressed in days)
You must implement the following query which computes the actual interest paid at a given date.
pay($CD, $Withd_date, Interest_paid)
The rules to compute the interest are as follows:
1. zero interest is paid if the CD is redeemed before half of its Duration days have elapsed,
2. if the CD is redeemed after half of its Duration days have elapsed, but before maturity, then pay 0.01 % interest for each day between deposit and withdrawl,
3. if the CD is redeemed at maturity, then pay the Interest_to_Maturity,
4. if the CD is redeemed after maturity, then pay the Interest_to_Maturity plus 0.01 % interest for each day after maturity.
5. Use simple interest (no interest on interest).
Project 1, Part 2
Example 6.2 in the textbook is modified as follows:
- drop the transaction time,
- use a point-based representation of valid time (with granularities days).
Thus short sample of the database might be as follows:
```
prescript('Melanie', 'Beren', 'Prozac', 100mg, 360, date(1996,12,31)).
prescript('Melanie', 'Beren', 'Prozac', 100mg, 360, date(1997,01,01)).
prescript('Melanie', 'Beren', 'Prozac', 100mg, 360, date(1997,01,02)).

prescript('Melanie', 'Beren', 'Prozac', 100mg, 360, date(1997,01,02)).
prescript('Melanie', 'Beren', 'Prozac', 100mg, 360, date(1997,01,03)).

prescript('Melanie', 'Beren', 'Prozac', 100mg, 360, date(1997,01,06)).

prescript('Sally', 'Beren', 'Prozac', 100mg, 360, date(1997,01,03)).
prescript('Sally', 'Beren', 'Prozac', 100mg, 360, date(1997,01,04)).
prescript('Sally', 'Beren', 'Prozac', 100mg, 360, date(1997,01,0)).
```
Define a LDL++ schema for this fact base, and then express the following queries: