Several questions in one file¶

The sequence of chapter 4 can be asked three ways: both parts, the term alone, or the sum alone. A file can declare all three over the same rules.

# The sequence of chapter 4, asked three ways.

random first = integer_between(-10, 10)
random step  = nonzero_integer_between(-6, 6)
random n     = integer_between(8, 15)

let nth = first + (n - 1) * step
let sum = n * (2 * first + (n - 1) * step) / 2

synth kind on Q

start Q

Q -> "arithmetic" { kind = "arithmetic" }

# The file-level prompt is the question `main`: both parts.
prompt "An arithmetic sequence has first term [`a_1 = {first}`] and common
difference [`d = {step}`].

(a) Find [`a_{{{n}}}`]. {answer nth}

(b) Find the sum of its first [`{n}`] terms. {answer sum}"

question nth {
  start Q
  prompt "An arithmetic sequence has first term [`a_1 = {first}`] and common
difference [`d = {step}`]. Find [`a_{{{n}}}`]. {answer nth}"
}

question sum {
  start Q
  prompt "An arithmetic sequence has first term [`a_1 = {first}`] and common
difference [`d = {step}`]. Find the sum of its first [`{n}`] terms. {answer sum}"
}

$ rhema list questions.rhm
questions:
  main           start Q, context Numeric
  nth            start Q, context Numeric
  sum            start Q, context Numeric

$ rhema run questions.rhm --question sum --count 1
 1. An arithmetic sequence has first term [`a_1 = -2`] and common
difference [`d = 5`]. Find the sum of its first [`14`] terms. [___]
    answer: 427

Named questions¶

A question block declares one more question type:

question sum {
  start Q
  prompt "... Find the sum of its first [`{n}`] terms. {answer sum}"
}

It holds what a file otherwise says once at the top level: start, prompt, answer, and optionally context and width. Everything else, the productions, attributes, randoms and lets, belongs to the file and is shared by all its questions. Two questions differ only in where they start and how they ask.

The top-level start, prompt and answer are themselves a question, named main. That is the one rhema generates unless told otherwise:

$ rhema run questions.rhm                      # main
$ rhema run questions.rhm --question nth       # one named question

A file made only of question blocks has no main; its first block is the default.

Starting where you need to¶

A block may start at a different symbol from the file, which is how one grammar offers its parts separately. The library's calculus.rhm builds a derivative under D and an integral under I, and declares:

question derivative { start D  prompt "{D.text}"  answer D.answer_value }
question integral   { start I  prompt "{I.text}"  answer I.answer_value  cost = 7 }

cost = 7 in a block sets the budget the question starts with, in place of the file's attribute cost = ... line. --set cost=N still overrides it.

Mistakes are reported with the block's name¶

$ rhema run questions.rhm --question last
questions.rhm: error: 'last' is not a question of this grammar; it has main, nth, sum

The checker treats each block as it treats the top level: a missing start or prompt, a prompt naming a symbol other than the block's start, an attribute the file does not declare, are each reported with the name of the block.

Next: chapter 6 uses questions and expressions from the library in a file of your own.