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Extensible Pattern Matching via a Lightweight
Language Extension ? Survey

• POPL meeting 7/25
• Kazuhiro Inaba
• kinaba_at_is.s.u-tokyo.ac.jp

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??

• Extensible Pattern Matching via a Lightweight
  Language ExtensionDon Syme, Gregory Neverov,
  James MargetsonAccepted for ICFP 2007
• F ? Active Pattern ???????????
• ????????????????????????

(Submitted Draft?Web??????)
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Motivation
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Motivation

• Abstract Data Type ????????????
• ???View???????????

type complex abstract let my_function c obj
match c with Polar(r, t) -gt zoom r
(rotate t obj) let another_function c match
c with Rect(x, y) -gt x y
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Motivation

• ??????????????????
• ?????????????
• ?????
• ??Case-Analysis???????????
• (nil?, head, tail ???????????????)
• Exhaustiveness ???????????

type complex abstract let my_function c obj
zoom (abs c) (rotate (arg c) obj)
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Examples
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Active Patterns by Examples

• Total Patterns
• Single Total Patterns
• Decomposition with Recognizers
• Partial Patterns

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Single Total Patterns

• (???) ???????????

• type complex Rect of float float
• type complex Rect of float float
• let (Polar) c
• match c with
• Rect(x,y) -gt (atan2 y x, sqrt(xxyy))
• val (Polar) complex -gt float float

• ????????? (let (r,t) (Polar) c in ???)

• let my_function c obj
• match c with
• Polar(r, t) -gt zoom r (rotate t obj)

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Decomposition

• (?????????) ???????????

• let (SnocNil) lst
• if lst
• then Nil
• else Snoc(rev(tl(rev lst)), hd(rev lst))
• val (SnocNil)
• a list -gt Choicelt(a lista),unitgt

• ?????????

• match 123 with
• Nil -gt
• Snoc(hh, t) -gt t _at_ hh
• Val it int list 3 1 2

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Decomposition

• ?????????????

• match 123 with Snoc(hh,t) -gt t _at_ hh
• match 123 with Snoc(hh,t) -gt t _at_ hh
• stdin(59,0) warning FS0025 Incomplete pattern
  match.
• val it int list 3 1 2

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Partial Patterns

• ??????????????????????
• ??complete???
• ?case?distinct????
• ???case???????????????

type value IntVal of int FloatVal
of float ColorVal of int int
int match str with ParseInt i -gt IntVal i
ParseFloat f -gt FloatVal f ParseColor c -gt
ColorVal c _ -gt failwith invalid input
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Partial Patterns

• (???_) ???????????

• let (ParseInt_) s
• let i ref 0 in
• if Int32.TryParse (s,i) then Some !i
• else None
• val (ParseInt_) string -gt int option

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Advanced Topics

• Parameterized Patterns
• Recursive Definition of Patterns

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Parameterized Patterns

• ???????????????

• let (ParseRegex_) re s
• if match re s then Some s else None
• val (ParseRegex_)
• regex -gt string -gt string option
• match str with
• ParseRegex \\d s -gt dec s
• ParseRegex 0x\\dA-Fa-f s -gt hex s

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Recursive Definition

• ????????????????????

• type a joinlist Empty
• Single of a
• Join of a joinlist a joinlist
• let rec (NilCons) function
• Empty -gt Nil
• Single(x) -gt Cons(x, Empty)
• Join(Nil, Nil) -gt Nil
• Join(Nil,Cons(x,xs))-gt Cons(x,xs)
• Join(Cons(x,xs),ys) -gt Cons(x,Join(xs,ys))

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Semantics
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Semantics

• Naïve Operational Semantics
• Okasaki Condition
• Implementation

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Naïve Operational Semantics

• ???????
• pat1 ? v ?????????
• ?????????????expr1??????????
• pat2 ? v ?????????
• ?????????????expr2??????????

match v with pat1 -gt expr1 pat2 -gt expr2

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Naïve Operational Semantics

• pat1 ? v ??????????
• ??????????????(?????)?????
• Active Pattern p ?? v ??????????????????? (p)
  v ?????????

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Naïve Semantics (?)

• let (SnocNil)
• match 123 with
• Nil -gt
• Snoc(hh, t) -gt t _at_ hh

( Nil -gt ) match (SnocNil) 123
with Choice_2_1 () -gt _ -gt (
Snoc(hh,t) -gt t _at_ hh ) match (SnocNil)
123 with Choice_2_2 (hh,t) -gt t _at_ hh
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Okasaki Condition

• Naïve Semantics ????????
• ???

( Nil -gt ) match (SnocNil) 123
with Choice_2_1 () -gt _ -gt (
Snoc(hh,t) -gt t _at_ hh ) match (SnocNil)
123 with Choice_2_2 (hh,t) -gt t _at_ hh
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Okasaki Condition

• Active Pattern?????????????????????? (SnocNil)
  ???????????
• ?????????Exhaustive?match???????semantics??fail??
  ??????

( Nil -gt ) match (SnocNil) 123
with Choice_2_1 () -gt _ -gt (
Snoc(hh,t) -gt t _at_ hh ) match (SnocNil)
123 with Choice_2_2 (hh,t) -gt t _at_ hh
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Okasaki Condition

• Chris Okasaki, Views for Standard ML, 1998
• Sensible?Semantic?????????????????1???????????????
  ????????? ????????
• ???match????????????????????1?????????????????????
  ?2??????????????????

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Implementation

• ? ??(??????)???? Okasaki Condition ???????? ?
  Future Work
• Scott and Ramsey 2000 Algorithm (????Decision
  Tree???Heuristics) ? Active Pattern
  ?????????????????

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Conclusion
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Related Work

• ?????????View??????????????????? (Reference??)
• Peyton Jones 2007 ?????
• Parameterized Patterns
• Partial Patterns
• Total Patterns
• Nesting
• Patterns as first-class values
• ????????????Active Pattern?????

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Future Work

• ???F ???Haskell???????Active Pattern
  ??????????????????????
• E.g. Monadic Pattern Matching
• Partial Pattern ??????? match ?? Maybe
  ???????????????????? MonadPlus ??????????/?????