what is the difference between triggers, assertions and checks (in database)
Triggers - a trigger is a piece of SQL to execute either before or after an update, insert, or delete in a database. An example of a trigger in plain English might be something like: before updating a customer record, save a copy of the current record. Which would look something like:
CREATE TRIGGER triggerName
AFTER UPDATE
INSERT INTO CustomerLog (blah, blah, blah)
SELECT blah, blah, blah FROM deleted
The difference between assertions and checks is a little more murky, many databases don't even support assertions.
Check Constraint - A check is a piece of SQL which makes sure a condition is satisfied before action can be taken on a record. In plain English this would be something like: All customers must have an account balance of at least $100 in their account. Which would look something like:
ALTER TABLE accounts
ADD CONSTRAINT CK_minimumBalance
CHECK (balance >= 100)
Any attempt to insert a value in the balance column of less than 100 would throw an error.
Assertions - An assertion is a piece of SQL which makes sure a condition is satisfied or it stops action being taken on a database object. It could mean locking out the whole table or even the whole database.
To make matters more confusing - a trigger could be used to enforce a check constraint and in some DBs can take the place of an assertion (by allowing you to run code un-related to the table being modified). A common mistake for beginners is to use a check constraint when a trigger is required or a trigger when a check constraint is required.
An example: All new customers opening an account must have a balance of $100; however, once the account is opened their balance can fall below that amount. In this case you have to use a trigger because you only want the condition evaluated when a new record is inserted.
In the SQL standard, both ASSERTIONS and CHECK CONSTRAINTS are what relational theory calls "constraints" : rules that the data actually contained in the database must comply with.
The difference between the two is that CHECK CONSTRAINTS are, in a sense, much "simpler" : they are rules that relate to one single row only, while ASSERTIONs can involve any number of other tables, or any number of other rows in the same table. That obviously makes it (much !) more complex for the DBMS builders to support it, and that is, in turn, the reason why they don't : they just don't know how to do it.
TRIGGERs are pieces of executable code of which it can be declared to the DBMS that those should be executed every time a certain kind of update operation (insert/delete/update) gets done on a certain table. Because triggers can raise exceptions, they are a MEANS for implementing the same thing as an ASSERTION. However, with triggers, it's still the programmer who has to do all the coding, and not make any mistake.
EDIT
Onedaywhen's comments re. ASSERTION/CHECK cnstr. are correct. The difference is way more subtle (AND confusing). The standard indeed allows subqueries in CHECK constraints. (Most products don't support it though, so my "relate to a single row" is true for most SQL products, but not for the standard.) So is there still a difference ? Yes there still is. More than one even.
First case : TABLE MEN (ID:INTEGER) and TABLE WOMEN(ID:INTEGER). Now imagine a rule to the effect that "no ID value can appear both in the MEN and in the WOMEN table". That's a single rule. The intent of ASSERTION is precisely that the database designer would state this single rule [and be done with it], and the DBMS would know how to deal with this [efficiently, of course] and how to enforce this rule, no matter what particular update gets done to the database. In the example, the DBMS would know that it has to do a check for this rule upon INSERT INTO MEN, and upon INSERT INTO WOMEN, but not upon DELETE FROM MEN/WOMEN, or INSERT INTO <anyothertable>.
But DBMS's aren't smart enough for doing all that. So what needs to be done ? The database designer must add TWO CHECK constraints to his database, one to the MEN table (checking newly inserted MEN ID's against the WOMEN table) and one to the WOMAN table (checking the other way round). There's your first difference : one rule, one ASSERTION, TWO CHECK constraints. CHECK constraints are a lower level of abstraction than ASSERTIONs, because they require the designer to do more thinking himself about (a) all the kinds of update that could potentially cause his ASSERTION to be violated, and (b) what particular check should be carried out for any of the specific "kinds of update" he found in (a). (Although I don't really like making "absolute" statements on what is still "WHAT" and what is "HOW", I'd summarize that CHECK constraints require more "HOW" thinking (procedural) by the database designer, whereas ASSERTIONs allow the database designer to focus exclusively on the "WHAT" (declarative).)
Second case (though I'm not entirely sure of this - so take with a grain of salt) : just your average RI rule. Of course you are used to specify this using some REFERENCES clause. But imagine that a REFERENCES clause was not available. A rule like "Every ORDER must be placed by a known CUSTOMER" is really just that, a rule, thus : a single ASSERTION. However, we all know that such a rule can always be violated in two ways : inserting an ORDER (in this example), and deleting a CUSTOMER. Now, in line with the foregoing MAN/WOMEN example, if we wanted to implement this single rule/ASSERTION using CHECK constraints, then we'd have to write a CHECK constraint that checks CUSTOMER existence upon insertions into ORDER, but what CHECK constraint could we write that does whatever is needed upon deletion from CUSTOMER ? They simply aren't designed for that purpose, as far as I can tell. There's your second difference : CHECK constraints are tied to INSERTs exclusively, ASSERTIONS can define rules that will also be checked upon DELETEs.
Third case : Imagine a table COMPOS (componentID:... percentage:INTEGER), and a rule to the effect that "the sum of all percentages must at all times be equal to 100". That's a single rule, and an ASSERTION is capable of specifying that. But try and imagine how you would go about enforcing such a rule with CHECK constraints ... If you have a valid table with, say, three nonzero rows adding up to a hundred, how would you apply any change to this table that could survive your CHECK constraint ? You can't delete or update(decrease) any row without having to add other replacing rows, or update the remaining rows, that sum up to the same percentage. Likewise for insert or update (increase). You'd need deferred constraint checking at the very least, and then what are you going to CHECK ? There's your third difference : CHECK constraints are targeted to individual rows, while ASSERTIONs can also define/express rules that "span" several rows (i.e. rules about aggregations of rows).