Data.ExactPi.TypeLevel

A type-level representation of a non-negative rational multiple of an integer power of pi.

Each type in this kind can be exactly represented at the term level by a value of type ExactPi, provided that its denominator is non-zero.

Note that there are many representations of zero, and many representations of dividing by zero. These are not excluded because doing so introduces a lot of extra machinery. Play nice! Future versions may not include a representation for zero.

Of course there are also many representations of every value, because the numerator need not be comprime to the denominator. For many purposes it is not necessary to maintain the types in reduced form, they will be appropriately reduced when converted to terms.

A KnownDimension is one for which we can construct a term-level representation.

Each validly constructed type of kind ExactPi' has a KnownExactPi instance, provided that its denominator is non-zero.

Forms the product of ExactPi' types (in the arithmetic sense).

Forms the quotient of ExactPi' types (in the arithmetic sense).

Forms the reciprocal of an ExactPi' type.

Converts a type-level natural to an ExactPi' type.

The ExactPi' type representing the number 1.

The ExactPi' type representing the number pi.

Determines the minimum context required for a numeric type to hold the value associated with a specific ExactPi' type.

Converts an ExactPi' type to a numeric value with the minimum required context.

When the value is known to be an integer, it can be returned as any instance of Num. Similarly, rationals require Fractional, and values that involve pi require Floating.