1. M4sh

While the result of the autoconf stage is a complete script compatible with POSIX sh, the language used to write the configure.ac is called M4sh, to make clear that it's based off both sh and the macro language M4.

The reason the M4sh language is often confused with simple sh syntax is because it actually is based on that, augmented with the autoconf proper macros and a few more macros that replace part of the sh syntax.

The major change between the standard sh syntax and M4sh is found in two macros: AS_IF and AS_CASE. The two macros, as it's easy to guess, replace two constructs from sh: if..then..elif..else..fi and case..esac.

The two macros are actually replaced with the standard sh syntax after autoconf processing, but they exist for good reasons: they make it known to autoconf the conditional segments of the script. This in turn helps resolving issues with macros and conditionality.

1.1. M4sh syntax

The basic M4sh macros have a syntax that is directly translatable to sh syntax. It is thus easier to just see how the macros translate:

AS_IF([test], [true], [false])

if test; then
  true
else
  false
fi

AS_IF([test1], [true], [test2], [true2], [false])
if test1; then
  true
elif test2; then
  true2
else
  false
fi

As you can see, the parameters to the macro aren't in a fixed number: you can chain a series of alternative conditions as you would with the usual sh script.

The parameters are positional: the parameters in odd position (the first, the third, …) with the exception of the last one are the truth conditions (the tests); the parameters in even position are the conditional code executed if the previous parameter results true, and if there is a last odd parameter, it's considered the final alternative condition (the else condition).

Similarly, for AS_CASE:

AS_CASE([$variable], [foo*], [run1], [bar*], [run2], [catchall])

case $variable in
  foo*) run1 ;;
  bar*) run2 ;;
  *) catchall ;;
esac

As for AS_IF, the parameters here are positional, but since the first parameter is reserved to be the argument to the case statement, the even places are for the compared expressions, and the odd ones (starting from the third) contain the code that is executed, conditionally. Finally, almost identical to the previous macro, the last parameter is the code executed when nothing else matched up.