Writing a word problem

Invoke the author tool by:

./create

Create a new problem to be saved into file fruit.pl

scala: val p = new Problem("fruit.pl")
p: wp.Problem = Problem with 0 statements

We could use the Statement class to add new statements to the problem with the += operator. However, it is more convenient to define a statement factory for entering them in natural language (denoted by its 3-letter ISO code):

scala: val en = new StatementFactory("Eng")

We can now use a predictive parser to enter a new sentence into the problem:

scala: p += en.read
Eng: John has seven fruit .

Notice the final period. We can keep track of how many statements our problem has by:

scala: p
res1: wp.Problem = Problem with 1 statements

Let us add some more facts:

scala: p += en.read
Eng: John has two apples , some oranges and three bananas .
scala: p += en.read
Eng: how many oranges does John have ?

To take a look to the internal representation of the problem, use print:

scala: p.print

We can check if the problem is consistent (it does not contain contradictory statements) or complete (it has a single solution) by using the methods consistent and complete:

scala: p.complete
res3: Boolean = true

Remember to save the problem:

scala: p.save()
Saved to 'fruit.pl'

and now we can exit:

:q

Solving the problem

We can now try to solve our problem, by calling model with the file containing the problem:

 ./model fruit.pl 

It shows us the statement of the problem:

John has seven fruit .
John has two apples , some oranges and three bananas .
how many oranges does John have ?

and displays the prompt:

 ?

We can always press return at the prompt (or type help) for the system to suggest the proper action:

you must assign a variable to the oranges that John has .

But we do not know how to assign variables. Let us ask for an example:

? give me an example
let $x$ denote the animals that Mary has

Using this template we can now compose a definition for the variable x:

? let x denote the oranges that Mary has
you must assign a variable to the oranges that John has .

I forgot that we were dealing with John's fruit, not Mary's:

? let x denote the oranges that John has
it is right .

Press again return for the next suggestion:

you must split the fruit that John has .

This means that we have to specify how John's fruit are split in different classes:

 ? the fruit that John has are the apples that John has and the bananas that John has
 you must consider oranges .

Yes, there are oranges too. Let us correct it:

 ? the fruit that John has are the apples that John has , the bananas that John has and the oranges that John has
 it is right .

Good. Next suggestion:

you must write an equation which says that the fruit that John has are the bananas that John has , 
the oranges that John has and the apples that John has .

What about this?

? y plus 2 plus 3 is equal to 7
it doesn't follow .

This means that the proposed equation can not be deduced from the statement of the problem. Let us see what is wrong with the variable y:

? tell me about y
nothing is known about it .

Perhaps we used a different variable to denote the amount of oranges:

? tell me about the oranges that John has
the oranges that John has are $x$ oranges .

So we used x for it. Just to confirm it:

  ? tell me about x
  $x$ denotes the oranges that John has .

We rewrite the equation using x:

? x plus 2 plus 3 is equal to 7
it is right .

Now the problem is correctly modeled. The next action will give us the solution:

the oranges that John has are two oranges .

Going multilingual

To run the same problem but in Spanish, add the 3-letter-ISO code of the language as second argument:

./model examples/fruit.pl spa
...
Juan tiene siete frutas .
Juan tiene dos manzanas , algunas naranjas y tres plátanos .
¿ cuantas naranjas tiene Juan ?

Asking for help:

? 
debes asignar una variable a las naranjas que Juan tiene .

Asking for an example:

? dame un ejemplo
denota las cartas que María tiene por $z$