Required value analysis
-----------------------

This analysis checks for each operation in a Curry program whether
the arguments must have a particular shape in order to
compute some value.
For instance, the negation operation `not` defined by

    not True  = False
    not False = True

requires the argument value `False` in order to compute the result
`True` and it requires the argument `True` to compute the result
`False`. This property is expressed by the following abstract type:

    not : (True -> False) | (False -> True)

Hence, each abstract type is a constructor which represents
all expressions rooted by this constructor.
Moreover, the abstract type `cons` denotes any constructor-rooted
expression and the abstract type `any` denotes any expression.
The abstract type `_|_` denotes an impossible required type, i.e.,
an argument which is required but for which no applicable value exists.
For instance, the operation

    f x = solve (x && not x)

has the required value typing

    f: (_|_ -> {True})

A detailed description of this analysis and its application can be found in the
[LOPSTR'15 paper](http://www.informatik.uni-kiel.de/~mh/papers/LOPSTR15.html).