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Diffstat (limited to '')
| -rw-r--r-- | stdlib/source/lux/abstract/interval.lux | 193 |
1 files changed, 0 insertions, 193 deletions
diff --git a/stdlib/source/lux/abstract/interval.lux b/stdlib/source/lux/abstract/interval.lux deleted file mode 100644 index e43529890..000000000 --- a/stdlib/source/lux/abstract/interval.lux +++ /dev/null @@ -1,193 +0,0 @@ -## https://en.wikipedia.org/wiki/Interval_(mathematics) -(.module: - [lux #*] - [// - [equivalence (#+ Equivalence)] - ["." order] - [enum (#+ Enum)]]) - -(interface: #export (Interval a) - {#.doc "A representation of top and bottom boundaries for an ordered type."} - (: (Enum a) - &enum) - - (: a - bottom) - - (: a - top)) - -(def: #export (between enum bottom top) - (All [a] (-> (Enum a) a a (Interval a))) - (implementation - (def: &enum enum) - (def: bottom bottom) - (def: top top))) - -(def: #export (singleton enum elem) - (All [a] (-> (Enum a) a (Interval a))) - (implementation - (def: &enum enum) - (def: bottom elem) - (def: top elem))) - -(template [<name> <comp>] - [(def: #export (<name> interval) - (All [a] (-> (Interval a) Bit)) - (let [(^open ",\.") interval] - (<comp> ,\bottom ,\top)))] - - [inner? (order.> ,\&order)] - [outer? ,\<] - [singleton? ,\=] - ) - -(def: #export (within? interval elem) - (All [a] (-> (Interval a) a Bit)) - (let [(^open ",\.") interval] - (cond (inner? interval) - (and (order.>= ,\&order ,\bottom elem) - (order.<= ,\&order ,\top elem)) - - (outer? interval) - (or (order.>= ,\&order ,\bottom elem) - (order.<= ,\&order ,\top elem)) - - ## singleton - (and (,\= ,\bottom elem) - (,\= ,\top elem))))) - -(template [<name> <limit>] - [(def: #export (<name> elem interval) - (All [a] (-> a (Interval a) Bit)) - (let [(^open ".") interval] - (= <limit> elem)))] - - [starts_with? bottom] - [ends_with? top] - ) - -(def: #export (borders? interval elem) - (All [a] (-> (Interval a) a Bit)) - (or (starts_with? elem interval) - (ends_with? elem interval))) - -(def: #export (union left right) - (All [a] (-> (Interval a) (Interval a) (Interval a))) - (implementation - (def: &enum (get@ #&enum right)) - (def: bottom (order.min (\ right &order) (\ left bottom) (\ right bottom))) - (def: top (order.max (\ right &order) (\ left top) (\ right top))))) - -(def: #export (intersection left right) - (All [a] (-> (Interval a) (Interval a) (Interval a))) - (implementation - (def: &enum (get@ #&enum right)) - (def: bottom (order.max (\ right &order) (\ left bottom) (\ right bottom))) - (def: top (order.min (\ right &order) (\ left top) (\ right top))))) - -(def: #export (complement interval) - (All [a] (-> (Interval a) (Interval a))) - (let [(^open ".") interval] - (implementation - (def: &enum (get@ #&enum interval)) - (def: bottom (succ top)) - (def: top (pred bottom))))) - -(def: #export (precedes? reference sample) - (All [a] (-> (Interval a) (Interval a) Bit)) - (let [(^open ".") reference - limit (\ reference bottom)] - (and (< limit (\ sample bottom)) - (< limit (\ sample top))))) - -(def: #export (succeeds? reference sample) - (All [a] (-> (Interval a) (Interval a) Bit)) - (precedes? sample reference)) - -(template [<name> <comp>] - [(def: #export (<name> reference sample) - (All [a] (-> a (Interval a) Bit)) - (let [(^open ",\.") sample] - (and (<comp> reference ,\bottom) - (<comp> reference ,\top))))] - - [before? ,\<] - [after? (order.> ,\&order)] - ) - -(def: #export (meets? reference sample) - (All [a] (-> (Interval a) (Interval a) Bit)) - (let [(^open ",\.") reference - limit (\ reference bottom)] - (and (,\= limit (\ sample top)) - (order.<= ,\&order limit (\ sample bottom))))) - -(def: #export (touches? reference sample) - (All [a] (-> (Interval a) (Interval a) Bit)) - (or (meets? reference sample) - (meets? sample reference))) - -(template [<name> <eq_side> <ineq> <ineq_side>] - [(def: #export (<name> reference sample) - (All [a] (-> (Interval a) (Interval a) Bit)) - (let [(^open ",\.") reference] - (and (,\= (\ reference <eq_side>) - (\ sample <eq_side>)) - (<ineq> ,\&order - (\ reference <ineq_side>) - (\ sample <ineq_side>)))))] - - [starts? ,\bottom order.<= ,\top] - [finishes? ,\top order.>= ,\bottom] - ) - -(implementation: #export equivalence (All [a] (Equivalence (Interval a))) - (def: (= reference sample) - (let [(^open ",\.") reference] - (and (,\= ,\bottom (\ sample bottom)) - (,\= ,\top (\ sample top)))))) - -(def: #export (nested? reference sample) - (All [a] (-> (Interval a) (Interval a) Bit)) - (cond (or (singleton? sample) - (and (inner? reference) (inner? sample)) - (and (outer? reference) (outer? sample))) - (let [(^open ",\.") reference] - (and (order.>= ,\&order (\ reference bottom) (\ sample bottom)) - (order.<= ,\&order (\ reference top) (\ sample top)))) - - (or (singleton? reference) - (and (inner? reference) (outer? sample))) - #0 - - ## (and (outer? reference) (inner? sample)) - (let [(^open ",\.") reference] - (or (and (order.>= ,\&order (\ reference bottom) (\ sample bottom)) - (order.> ,\&order (\ reference bottom) (\ sample top))) - (and (,\< (\ reference top) (\ sample bottom)) - (order.<= ,\&order (\ reference top) (\ sample top))))) - )) - -(def: #export (overlaps? reference sample) - (All [a] (-> (Interval a) (Interval a) Bit)) - (let [(^open ",\.") reference] - (and (not (\ ..equivalence = reference sample)) - (cond (singleton? sample) - #0 - - (singleton? reference) - (nested? sample reference) - - (or (and (inner? sample) (outer? reference)) - (and (outer? sample) (inner? reference))) - (or (order.>= ,\&order (\ reference bottom) (\ sample top)) - (order.<= ,\&order (\ reference top) (\ sample bottom))) - - ## both inner - (inner? sample) - (inner? (intersection reference sample)) - - ## both outer - (not (nested? reference sample)) - )))) |