Call-by-push-value is an evaluation strategy that determines when arguments to functions are evaluated. Call-by-value is what every mainstream language does: arguments are evaluated before the function is called. Call-by-name substitutes arguments directly into a function, so they may be evaluated multiple times or not at all. For example, the following pseudocode:
function foo(n, m) {
sum = 0
for i in 1 to 4 {
sum = n + sum
}
if false {
print(m)
}
print(sum)
}
foo({print("1"); 2}, {print("3"); 4})
evaluated with Call-by-Value prints:
1
3
8
evaluated with Call-by-Name prints:
1
1
1
1
8
Call-by-push-value combines both by having two "kinds" of parameters: values which are evaluated immediately (call-by-value), and computations which are substituted (call-by-name). So the following code:
function foo(value n, computation m) {
sum = 0
for i in 1 to 4 {
sum = n + sum
}
if false {
print(m)
}
print(sum)
}
foo({print("1"); 2}, {print("3"); 4})
would print
1
8
The reason call-by-push-value may be useful is because both call-by-name and call-by-value have their advantages, especially with side-effects. Besides enabling programmers to write both traditional functions and custom loops/conditionals, CBPV is particularly useful for an IR to generate efficient code.
Currently, Scala has syntactic sugar for by-name parameters, and some languages like Kotlin and Swift make zero-argument closure syntax very simple (which does allow custom loops and conditionals, though it's debatable whether this is CBPV). Other languages like Rust and C have macros, which can emulate call-by-name, albeit not ideally (you have hygiene issues and duplicating syntax makes compilation slower). I don't know of any mainstream work on CBPV in the IR side.