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(.module:
[lux #*
[control
["." monad (#+ do)]
["ex" exception (#+ exception:)]
equivalence]
[data
[bit ("bit/." Equivalence<Bit>)]
["." number]
["e" error ("error/." Monad<Error>)]
["." maybe]
[text
format]
[collection
["." list ("list/." Fold<List>)]
["dict" dictionary (#+ Dictionary)]]]]
["." //// ("operation/." Monad<Operation>)]
["." /// (#+ Pattern Variant Operation)])
(def: cases
(-> (Maybe Nat) Nat)
(|>> (maybe.default +0)))
(def: (variant sum-side)
(-> (Either Pattern Pattern) (Variant Pattern))
(loop [lefts +0
variantP sum-side]
(case variantP
(#.Left valueP)
(case valueP
(#///.Complex (#///.Sum value-side))
(recur (inc lefts) value-side)
_
{#///.lefts lefts
#///.right? #0
#///.value valueP})
(#.Right valueP)
{#///.lefts lefts
#///.right? #1
#///.value valueP})))
## The coverage of a pattern-matching expression summarizes how well
## all the possible values of an input are being covered by the
## different patterns involved.
## Ideally, the pattern-matching has "exhaustive" coverage, which just
## means that every possible value can be matched by at least 1
## pattern.
## Every other coverage is considered partial, and it would be valued
## as insuficient (since it could lead to runtime errors due to values
## not being handled by any pattern).
## The #Partial tag covers arbitrary partial coverages in a general
## way, while the other tags cover more specific cases for bits
## and variants.
(type: #export #rec Coverage
#Partial
(#Bit Bit)
(#Variant (Maybe Nat) (Dictionary Nat Coverage))
(#Seq Coverage Coverage)
(#Alt Coverage Coverage)
#Exhaustive)
(def: #export (exhaustive? coverage)
(-> Coverage Bit)
(case coverage
(#Exhaustive _)
#1
_
#0))
(def: #export (determine pattern)
(-> Pattern (Operation Coverage))
(case pattern
(^or (#///.Simple #///.Unit)
(#///.Bind _))
(operation/wrap #Exhaustive)
## Primitive patterns always have partial coverage because there
## are too many possibilities as far as values go.
(^template [<tag>]
(#///.Simple (<tag> _))
(operation/wrap #Partial))
([#///.Nat]
[#///.Int]
[#///.Rev]
[#///.Frac]
[#///.Text])
## Bits are the exception, since there is only "#1" and
## "#0", which means it is possible for bit
## pattern-matching to become exhaustive if complementary parts meet.
(#///.Simple (#///.Bit value))
(operation/wrap (#Bit value))
## Tuple patterns can be exhaustive if there is exhaustiveness for all of
## their sub-patterns.
(#///.Complex (#///.Product [left right]))
(do ////.Monad<Operation>
[left (determine left)
right (determine right)]
(case right
(#Exhaustive _)
(wrap left)
_
(wrap (#Seq left right))))
(#///.Complex (#///.Sum sum-side))
(let [[variant-lefts variant-right? variant-value] (variant sum-side)]
## Variant patterns can be shown to be exhaustive if all the possible
## cases are handled exhaustively.
(do ////.Monad<Operation>
[value-coverage (determine variant-value)
#let [variant-idx (if variant-right?
(inc variant-lefts)
variant-lefts)]]
(wrap (#Variant (if variant-right?
(#.Some variant-idx)
#.None)
(|> (dict.new number.Hash<Nat>)
(dict.put variant-idx value-coverage))))))))
(def: (xor left right)
(-> Bit Bit Bit)
(or (and left (not right))
(and (not left) right)))
## The coverage checker not only verifies that pattern-matching is
## exhaustive, but also that there are no redundant patterns.
## Redundant patterns will never be executed, since there will
## always be a pattern prior to them that would match the input.
## Because of that, the presence of redundant patterns is assumed to
## be a bug, likely due to programmer carelessness.
(def: redundant-pattern
(e.Error Coverage)
(e.fail "Redundant pattern."))
(def: (flatten-alt coverage)
(-> Coverage (List Coverage))
(case coverage
(#Alt left right)
(list& left (flatten-alt right))
_
(list coverage)))
(structure: _ (Equivalence Coverage)
(def: (= reference sample)
(case [reference sample]
[#Exhaustive #Exhaustive]
#1
[(#Bit sideR) (#Bit sideS)]
(bit/= sideR sideS)
[(#Variant allR casesR) (#Variant allS casesS)]
(and (n/= (cases allR)
(cases allS))
(:: (dict.Equivalence<Dictionary> =) = casesR casesS))
[(#Seq leftR rightR) (#Seq leftS rightS)]
(and (= leftR leftS)
(= rightR rightS))
[(#Alt _) (#Alt _)]
(let [flatR (flatten-alt reference)
flatS (flatten-alt sample)]
(and (n/= (list.size flatR) (list.size flatS))
(list.every? (function (_ [coverageR coverageS])
(= coverageR coverageS))
(list.zip2 flatR flatS))))
_
#0)))
(open: "coverage/." Equivalence<Coverage>)
## After determining the coverage of each individual pattern, it is
## necessary to merge them all to figure out if the entire
## pattern-matching expression is exhaustive and whether it contains
## redundant patterns.
(def: #export (merge addition so-far)
(-> Coverage Coverage (e.Error Coverage))
(case [addition so-far]
## The addition cannot possibly improve the coverage.
[_ #Exhaustive]
redundant-pattern
## The addition completes the coverage.
[#Exhaustive _]
(error/wrap #Exhaustive)
[#Partial #Partial]
(error/wrap #Partial)
## 2 bit coverages are exhaustive if they complement one another.
(^multi [(#Bit sideA) (#Bit sideSF)]
(xor sideA sideSF))
(error/wrap #Exhaustive)
[(#Variant allA casesA) (#Variant allSF casesSF)]
(cond (not (n/= (cases allSF) (cases allA)))
(e.fail "Variants do not match.")
(:: (dict.Equivalence<Dictionary> Equivalence<Coverage>) = casesSF casesA)
redundant-pattern
## else
(do e.Monad<Error>
[casesM (monad.fold @
(function (_ [tagA coverageA] casesSF')
(case (dict.get tagA casesSF')
(#.Some coverageSF)
(do @
[coverageM (merge coverageA coverageSF)]
(wrap (dict.put tagA coverageM casesSF')))
#.None
(wrap (dict.put tagA coverageA casesSF'))))
casesSF (dict.entries casesA))]
(wrap (if (let [case-coverages (dict.values casesM)]
(and (n/= (cases allSF) (list.size case-coverages))
(list.every? exhaustive? case-coverages)))
#Exhaustive
(#Variant allSF casesM)))))
[(#Seq leftA rightA) (#Seq leftSF rightSF)]
(case [(coverage/= leftSF leftA) (coverage/= rightSF rightA)]
## There is nothing the addition adds to the coverage.
[#1 #1]
redundant-pattern
## The 2 sequences cannot possibly be merged.
[#0 #0]
(error/wrap (#Alt so-far addition))
## Same prefix
[#1 #0]
(do e.Monad<Error>
[rightM (merge rightA rightSF)]
(if (exhaustive? rightM)
## If all that follows is exhaustive, then it can be safely dropped
## (since only the "left" part would influence whether the
## merged coverage is exhaustive or not).
(wrap leftSF)
(wrap (#Seq leftSF rightM))))
## Same suffix
[#0 #1]
(do e.Monad<Error>
[leftM (merge leftA leftSF)]
(wrap (#Seq leftM rightA))))
## The left part will always match, so the addition is redundant.
(^multi [(#Seq left right) single]
(coverage/= left single))
redundant-pattern
## The right part is not necessary, since it can always match the left.
(^multi [single (#Seq left right)]
(coverage/= left single))
(error/wrap single)
## When merging a new coverage against one based on Alt, it may be
## that one of the many coverages in the Alt is complementary to
## the new one, so effort must be made to fuse carefully, to match
## the right coverages together.
## If one of the Alt sub-coverages matches the new one, the cycle
## must be repeated, in case the resulting coverage can now match
## other ones in the original Alt.
## This process must be repeated until no further productive
## merges can be done.
[_ (#Alt leftS rightS)]
(do e.Monad<Error>
[#let [fuse-once (: (-> Coverage (List Coverage)
(e.Error [(Maybe Coverage)
(List Coverage)]))
(function (_ coverage possibilities)
(loop [alts possibilities]
(case alts
#.Nil
(wrap [#.None (list coverage)])
(#.Cons alt alts')
(case (merge coverage alt)
(#e.Success altM)
(case altM
(#Alt _)
(do @
[[success alts+] (recur alts')]
(wrap [success (#.Cons alt alts+)]))
_
(wrap [(#.Some altM) alts']))
(#e.Error error)
(e.fail error))
))))]
[success possibilities] (fuse-once addition (flatten-alt so-far))]
(loop [success success
possibilities possibilities]
(case success
(#.Some coverage')
(do @
[[success' possibilities'] (fuse-once coverage' possibilities)]
(recur success' possibilities'))
#.None
(case (list.reverse possibilities)
(#.Cons last prevs)
(wrap (list/fold (function (_ left right) (#Alt left right))
last
prevs))
#.Nil
(undefined)))))
_
(if (coverage/= so-far addition)
## The addition cannot possibly improve the coverage.
redundant-pattern
## There are now 2 alternative paths.
(error/wrap (#Alt so-far addition)))))
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