why do we need special type-4 lsa (route to asbr) for ASBR can't we reach ASBR router using type-3 LSA when it is not a ASBR. so when a router turns into ASBR by redistributing external networks why is it that we need another type-4 LSA
Assume that you are in area 1 that has a single ABR. In some other areas, there are two ASBRs redistributing a route, say, 192.0.2.0/24, as a Type 2 external route. Furthermore, assume that one of those ASBRs is considerably closer to you (in means of metric) than the other.
Now, the Type 2 external route has a constant metric that is set when first redistributing a route into OSPF domain but that is not incremented anymore. But that makes the Type 2 external route quite hard to handle - if two different ASBRs are announcing a Type 2 external route with the same metric, shall we use any of them? Certainly not! We would like to route our packets through that ASBR which is closer to us.
This is where the LSA-4 comes in. Because you are in a different area than the ASBR, you do not know the exact network topology between you and the ASBR to be able to decide which one is closer to you. The LSA-4 serves this very purpose. It describes the distance from your ABR to individual ASBRs announcing some external routes so you can choose which ASBR is the closest to you for a particular external route.
The logic for choosing the best Type2 route to a destination is as follows:
1.) Take the route that has the lowest metric
2.) If there are multiple routes with the lowest metric, take the one whose ASBR is the closest to you (the distance between you and the ASBR is distance from you to your ABR plus distance from your ABR to the ASBR given by LSA-4)
Note that LSA-4 is also necessary for Type 1 external routes but on Type 2, it is more evident why we need it.
Just to add to Giuseppe's perfect explanation: There is no logical reason to filter out LSA-4 while permitting LSA-5. The LSA-4 does not by itself contain information about reachable subnets. It is merely a topological component that is necessary to build the topological representation of your network. The LSA-5 depends on LSA-4 (with a single exception that I am not going to discuss right now). If it was possible to filter out LSA-4 while retaining the LSA-5, the LSA-5 would become unusable, because it would refer to a "puzzle piece" that would not be present in the topological database.
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