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(.module: {#.doc "Rational numbers."}
[lux #*
[abstract
[equivalence (#+ Equivalence)]
[order (#+ Order)]
[monoid (#+ Monoid)]
[number (#+ Number)]
[codec (#+ Codec)]
[monad (#+ do)]]
[control
["." function]
["p" parser]]
[data
["." error]
["." product]
["." maybe]
[number
["." nat ("#@." decimal)]]
["." text ("#@." monoid)]]
["." math]
["." macro
["." code]
["s" syntax (#+ Syntax syntax:)]]])
(type: #export Ratio
{#numerator Nat
#denominator Nat})
(def: (equalize parameter subject)
(-> Ratio Ratio [Nat Nat])
[(n/* (get@ #denominator subject)
(get@ #numerator parameter))
(n/* (get@ #denominator parameter)
(get@ #numerator subject))])
(def: (normalize (^slots [#numerator #denominator]))
(-> Ratio Ratio)
(let [common (math.n/gcd numerator denominator)]
{#numerator (n// common numerator)
#denominator (n// common denominator)}))
(structure: #export equivalence (Equivalence Ratio)
(def: (= parameter subject)
(and (n/= (get@ #numerator parameter)
(get@ #numerator subject))
(n/= (get@ #denominator parameter)
(get@ #denominator subject)))))
(`` (structure: #export order (Order Ratio)
(def: &equivalence ..equivalence)
(~~ (template [<name> <op>]
[(def: (<name> parameter subject)
(let [[parameter' subject'] (..equalize parameter subject)]
(<op> parameter' subject')))]
[< n/<]
[<= n/<=]
[> n/>]
[>= n/>=]
))
))
(template [<name> <comp>]
[(def: #export (<name> left right)
(-> Ratio Ratio Ratio)
(if (:: ..order <comp> left right)
right
left))]
[min <]
[max >]
)
(def: (- parameter subject)
(let [[parameter' subject'] (..equalize parameter subject)]
(normalize [(n/- parameter' subject')
(n/* (get@ #denominator parameter)
(get@ #denominator subject))])))
(structure: #export number
(Number Ratio)
(def: (+ parameter subject)
(let [[parameter' subject'] (..equalize parameter subject)]
(normalize [(n/+ parameter' subject')
(n/* (get@ #denominator parameter)
(get@ #denominator subject))])))
(def: - ..-)
(def: (* parameter subject)
(normalize [(n/* (get@ #numerator parameter)
(get@ #numerator subject))
(n/* (get@ #denominator parameter)
(get@ #denominator subject))]))
(def: (/ parameter subject)
(let [[parameter' subject'] (..equalize parameter subject)]
(normalize [subject' parameter'])))
(def: (% parameter subject)
(let [[parameter' subject'] (..equalize parameter subject)
quot (n// parameter' subject')]
(..- (update@ #numerator (n/* quot) parameter)
subject)))
(def: (negate (^slots [#numerator #denominator]))
{#numerator denominator
#denominator numerator})
(def: abs function.identity)
(def: (signum x)
{#numerator 1
#denominator 1})
)
(def: separator Text ":")
(structure: #export codec (Codec Text Ratio)
(def: (encode (^slots [#numerator #denominator]))
($_ text@compose (nat@encode numerator) separator (nat@encode denominator)))
(def: (decode input)
(case (text.split-with separator input)
(#.Some [num denom])
(do error.monad
[numerator (nat@decode num)
denominator (nat@decode denom)]
(wrap (normalize {#numerator numerator
#denominator denominator})))
#.None
(#.Left (text@compose "Invalid syntax for ratio: " input)))))
(syntax: #export (ratio numerator {?denominator (p.maybe s.any)})
{#.doc (doc "Rational literals."
(ratio numerator denominator)
"The denominator can be omitted if it's 1."
(ratio numerator))}
(wrap (list (` ((~! ..normalize) {#..numerator (~ numerator)
#..denominator (~ (maybe.default (' 1)
?denominator))})))))
(template [<identity> <compose> <name>]
[(structure: #export <name>
(Monoid Ratio)
(def: identity (..ratio <identity>))
(def: compose (:: ..number <compose>))
)]
[0 + addition]
[1 * multiplication]
)
|
