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/*
A module that specifies and defines general purpose functions over orders.
All definitions are explicit and executable.
*/
module Ord
exports functions min[@a]: @a * @a +> @a
minWith[@a]: (@a * @a +> bool) +> @a * @a +> @a
max[@a]: @a * @a +> @a
maxWith[@a]: (@a * @a +> bool) +> @a * @a +> @a
definitions
values
functions
/*
The function defined below a simple in nature, and of limited value in their own right.
They can be used in other modules where it is necessary to pass min/max functions as
arguments to other functions without the need to define auxiliary functions.
*/
-- The minimum of two values.
min[@a]: @a * @a +> @a
min(x,y) == if x < y then x else y;
-- pre The type parameter admits an order relation.
-- The minimum of two values with respect to a relation.
minWith[@a]: (@a * @a +> bool) +> @a * @a +> @a
minWith(o)(x,y) == if o(x,y) then x else y;
-- pre 'o' is a partial order relation.
-- The maximum of two values.
max[@a]: @a * @a +> @a
max(x,y) == if y < x then x else y;
-- pre The type parameter admits an order relation.
-- The maximum of two values with respect to a relation.
maxWith[@a]: (@a * @a +> bool) +> @a * @a +> @a
maxWith(o)(x,y) == if o(y,x) then x else y;
-- pre 'o' is a partial order relation.
end Ord
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