A + ば, B
Meanings when B is non-past:
"If (and only if) A, B"
"If one does something, B state/event will be brought"
"If A state, one will do something or event will be brought"

Meanings when B is past:
"If A had happened, B could / would have happened"

Functions:
- Describe what will happen or what one will do under a hypothesized state or situation.
- Describe what would have happened or could have happened under a hypothesized state or situation.

Rules:
A can be volitional or non-volitional.
B can be volitional only if A is non-volitional.
(This means B can be a volitional action, desire, command, request, invitation, suggestion, or advice--only if A is not.)
(When both A and B are volitional, use ~たら.)

Examples:
1. A non-volitional, B volitional: implies a lack of choice
明日天気がよければ、シカゴへあそびに行こうと思っています。
If the weather is good tomorrow, I think I might go hang out in Chicago.


2. A non-volitional, B non-volitional: usually used in past tense "would/could have"
このページを読めば、この問題の答えが分かります。
If I was able to read this page, I could solve this problem.
(Maybe I can't see the page clearly, or I can't read the words.)

夕べ、となりの部屋が静かならば、今ねむくなかった。
Last night if it had been quiet next door, I wouldn't be so sleepy now.


3. A volitional, B non-volitional: expresses a desired outcome
今日宿題をすれば、明日あそびにいきます。
Only if I study today will I go have fun tomorrow.