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Pattern Matching & Predicate Dispatch
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Dynamic programming languages are powerful, productive
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Dynamic programming languages are powerful, productive Errors from dynamic typing are not fun
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Dynamic programming languages are powerful, productive Errors from dynamic typing are not fun Too much type information is trapped inside
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Dynamic programming languages are powerful, productive Errors from dynamic typing are not fun Too much type information is trapped inside We can do better without resorting to static types
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closed versus open
(cond (map? x) ... (vector? x) ... (list? x) ... :else ...)
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better but...
(extend-type IPersistentMap ...) (extend-type IPersistentVector ...) (extend-type IPersistentList ...)
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we want to enumerate what is allowed duck-typing doesnt let us specify a specific set of things which are allowed
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we want to enumerate what is allowed duck-typing doesnt let us specify a specific set of things which are allowed
Types are often too coarse a granularity for the kind of dispatch we would like to specify
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we want to enumerate what is allowed duck-typing doesnt let us specify a specific set of things which are allowed
Types are often too coarse a granularity for the kind of dispatch we would like to specify Duck-typing can be a source of pain.
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we want to enumerate what is allowed duck-typing doesnt let us specify a specific set of things which are allowed
Types are often too coarse a granularity for the kind of dispatch we would like to specify Duck-typing can be a source of pain. Pre and post conditions are also trapped inside functions
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we often reach into a data structure to pull it part ... but isnt this just like what we do w/ cond + map? vector?
(cond (= (first s) 1) ... (= (first s) 2) ... (= (second s) :foo) ... ...)
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destructuring does make it more convenient... but something is still missing
(let [[x & r] s] (cond (= x 1) ... (= x 2) ... (= (second s) :foo) ... ...))
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this where we are today with match... well talk about this but note that this is very much a chocolate fudge machine infused cond
(match [x] [[1 & r]] ... [[2 & r]] ... [[_ :foo & r]] ... ...)
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but this is where wed like to be
(extend-pred foo [[1 & r]] ...) (extend-pred foo [[2 & r]] ...) (extend-pred foo [[_ :foo & r]] ...)
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Goals
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Goals
As fast or faster than destructuring for matches with few cases
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Goals
As fast or faster than destructuring for matches with few cases Pattern matching should follow destructuring syntax when possible
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Goals
As fast or faster than destructuring for matches with few cases Pattern matching should follow destructuring syntax when possible Extensible (!)
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Goals
As fast or faster than destructuring for matches with few cases Pattern matching should follow destructuring syntax when possible Extensible (!) Testbed for predicate dispatch
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pattern matching
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Popular feature among functional programming languages - Standard ML, Erlang, Haskell, OCaml, Scala
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Popular feature among functional programming languages - Standard ML, Erlang, Haskell, OCaml, Scala Literature on ecient pattern matching in the ML language family is extensive
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Popular feature among functional programming languages - Standard ML, Erlang, Haskell, OCaml, Scala Literature on ecient pattern matching in the ML language family is extensive Decisions trees and backtracking automata popular approaches
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Pattern matching in ML restricts the types in the columns
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Pattern matching in ML restricts the types in the columns We want pattern matching to work across types
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Luc Maranget
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Compiling Pattern Matching to Good Decision Trees
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Compiling Pattern Matching to Good Decision Trees Simple compilation algorithm
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Compiling Pattern Matching to Good Decision Trees Simple compilation algorithm Big idea is choosing which column to test based on the notion of necessity from lazy pattern matching
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How it works in match
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false and true are literals, _ is a wildcard pattern, it will match anything
(match [x y z] [_ false true] 1 [false true _ ] 2 [_ _ false] 3 [_ _ true] 4 :else 5)
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x [_ [f [_ [_ [_
y f t _ _ _
z t] _] f] t] _]
1 2 3 4 5
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top down evaluation order, we dont need to test anything below a wildcard
x [_ [f [_ [_ [_
y f t _ _ _
z t] _] f] t] _]
1 2 3 4 5
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y column has the largest useful (non-wildcard) patterns
y [_ [f [_ [_ [_ f t _ _ _ t] _] f] t] _]1 2 3 4 5
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swap y column to the front, now we need to specialize
y [f [t [_ [_ [_
x _ f _ _ _
z t] _] f] t] _]
1 2 3 4 5
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Matrix Specialization
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set constructors in the y column
#{t f}
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we remove the rows that dont match the value for y. we drop the y column. here are the next pattern matrices for the t wo values of y
t
x [f [_ [_ [_ x [_ [_ [_ [_
z _] f] t] _] z t] f] t] _]
2 3 4 5
f
1 3 4 5
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rinse, repeat
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(cond (= y false) (cond (= z false) (let [] 3) (= z true) (let [] 1) :else (throw (java.lang.Exception. "Found FailNode"))) (= y true) (cond (= x false) (let [] 2) :else (cond (= z false) 3 (= z true) 4 :else (throw (java.lang.Exception. "Found FailNode")))) :else (cond (= z false) (let [] 3) (= z true) (let [] 4) :else (throw (java.lang.Exception. "Found FailNode"))))
we can take that process and produce a nested conditional. note that the order testing matches what we saw in previous slides
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a pattern matrix is composed of pattern rows
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a pattern matrix is composed of pattern rows pattern rows contain all the specied patterns in addition to an action
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a pattern matrix is composed of pattern rows pattern rows contain all the specied patterns in addition to an action pattern rows must all be of the same size (equal number of patterns)
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Patterns in match are implemented as deftypes
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Patterns in match are implemented as deftypes The key protocol for a pattern to extend is ISpecializeMatrix which denes a single protocol fn - specialize-matrix
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Patterns in match are implemented as deftypes The key protocol for a pattern to extend is ISpecializeMatrix which denes a single protocol fn - specialize-matrix The pattern produces the new matrix after specialization. This may involve introducing new occurrences.29
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what are occurrences?
y [f [t [_ [_
x _ f _ _
z t] _] f] t]
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consider this seq pattern match
(match [[1 [[2 [[3
[x] & r] 1 & r] 2 & r] 3)
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x [[1 & r]] [[2 & r]] [[3 & r]]
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when the matrix is specialized by SeqPattern we get this new pattern matrix. We have the occurrence that represents the head of the list and the tail of the list.
xh xt [1 r] [2 r] [3 r]
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The Decision TreeThursday, August 18, 11 34
occurrences will end up being represented as switch nodes
1 SwitchNodex 2 3 fail
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We end up with a tree of switch nodes. Each switch nodes represents a occurrence/binding and a multiway test which points to other switch nodes, leaf nodes, or fail nodes.
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We end up with a tree of switch nodes. Each switch nodes represents a occurrence/binding and a multiway test which points to other switch nodes, leaf nodes, or fail nodes. This is the decision tree.
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Examples
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Seq pattern matching note that the length of the seq patterns do no matter!
(match [x] [[1] :a0 [[1 2]] :a1 [[1 2 nil nil nil]] :a2 :else :a3)
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note the rest pattern syntax support just like destructuring. notice that we can introduce bindings anywhere we would use a wildcard
(match [x] [[1]] :a0 [[_ 2 & [a & b]]] [:a1 a b] :else :a2)
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map pattern matching
(match [x] [{_ :a 2 :b}] :a0 [{1 :a _ :c}] :a1 [{3 :c _ :d 4 :e}] :a2 :else :a3)
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we can restrict that only maps with the exact keys will match
(match [x] [{_ :a 2 :b :only [:a :b]}] :a0 [{1 :a c :c}] :a1 [{3 :c d :d 4 :e}] :a2 :else :a3)
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or patterns!
(match [x y z] [[1 (3 | 4) 3]] :a0 [[1 (2 | 3) 3]] :a1 :else :a2)
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Guards!
(match [y] [[_ (a :when even?) _ _]] :a0 [[_ (b :when [odd? div3?]) _ _]] :a1 :else :a2)
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sometimes you want to match a specific portion and bind that to a local name
(match [v] [[3 1]] :a0 [[([1 a] :as b)]] [:a1 a b] :else :a2)
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you can pattern match Java classes!
(extend-type java.util.Date IMatchLookup (val-at* [this k not-found] (case k :year (.getYear this) :month (.getMonth this) :date (.getDate this) :hours (.getHours this) :minutes (.getMinutes this) not-found)))
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(let [d (java.util.Date. 2010 10 1 12 30)] (match [d] [{2009 :year a :month}] [:a0 a] [{(2010 | 2011) :year b :month}] [:a1 b]))
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problems
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problems
Pattern matching is closed
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problems
Pattern matching is closed We want the matching to happen at the level of our most powerful abstraction functions
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problems
Pattern matching is closed We want the matching to happen at the level of our most powerful abstraction functions Without open dispatch, all we have is a chocolate fudge machine powered cond
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multimethods?
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problems
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problems
Hard coded dispatch function
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problems
Hard coded dispatch function In order to specify complex matches we have to construct a collection
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problems
Hard coded dispatch function In order to specify complex matches we have to construct a collection For complex matches, performance is less than we would like
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future directions
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future directions
Vector patterns: for any data type that supports random access and fast slicing - PersistentVector, primitive arrays, buers, etc.
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future directions
Vector patterns: for any data type that supports random access and fast slicing - PersistentVector, primitive arrays, buers, etc. Predicate Dispatch (huh?)
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predicate dispatch
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pattern matching vs. predicate dispatch
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pattern matching vs. predicate dispatch
static vs. dynamic
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pattern matching vs. predicate dispatch
static vs. dynamic closed vs. open
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pattern matching vs. predicate dispatch
static vs. dynamic closed vs. open fast vs. slow (ouch)
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Goals
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Goals
move the matching to level of function, as with multimethods
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Goals
move the matching to level of function, as with multimethods this change is in conict with the semantics of pattern matching - pattern matching is ordered
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Goals
move the matching to level of function, as with multimethods this change is in conict with the semantics of pattern matching - pattern matching is ordered We need some way to know where to put new pattern rows in the matrix
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A Sketch
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A Sketch
Use core.logic to order the pattern rows
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A Sketch
Use core.logic to order the pattern rows A high performance in-memory DAG representation of the decision tree
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A Sketch
Use core.logic to order the pattern rows A high performance in-memory DAG representation of the decision tree Perhaps we can go the route of deftypeinline patterns get best performance
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Challenges
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Challenges
How much of the pattern matching syntax can we bring over?
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Challenges
How much of the pattern matching syntax can we bring over? How close can we get to the performance of static code?
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Challenges
How much of the pattern matching syntax can we bring over? How close can we get to the performance of static code? Can we limit the scope of changes to namespaces?
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(defpred foo ([{a :a} 0] ...) ([{a :a} (y :when even?)] ...)) (extend-pred foo [{c :c} 3] ...)
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Questions?
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