Does Clojure have any functions similar to sow/reap from Mathematica? - clojure

Are there functions in the Clojure, which emulate the Mathemaica functions sow/reap? The main usage of sow and reap involve collecting expressions that were generated in the course of evaluation.
Example)
input in Mathematica: Reap[Sow[w = 2];w+=Sow[w^3];w=Sqrt[w + w^3]]
output: {Sqrt[1010], {{2, 8}}}
Giving intermediate results 2 and 8.

The wonderful thing about a homoiconic language like clojure is that you can define new syntaxes as you need them.
(defmacro reap
[& body]
`(let [state# (atom [])
~'sow (fn sow [v#] (swap! state# conj v#) v#)]
[(do ~#body) #state#]))
For simplicity's sake I used jvm interop for math, instead of clojure.numeric-tower so we get floating point rather than exact output:
user> (reap (let [w (sow 2)
w (+ w (sow (Math/pow w 3)))
w (Math/sqrt (+ w (Math/pow w 3)))]
w))
[31.78049716414141 [2 8.0]]
user> (= 31.78049716414141 (Math/sqrt 1010))
true
Edit: now that I see the docs for sow, it also has support for tagging and selecting by tag
since this is clojure grabbing things by key is trivial, so I will just show a variant that makes the tags:
(defmacro reap
[& body]
`(let [state# (atom {})
~'sew (fn sew [& [v# tag#]]
(swap! state# #(update-in % [tag#] conj v#)) v#)]
[(do ~#body) #state#]))
user> (reap (let [w (sew 2 :a)
w (+ w (sew (Math/pow w 3)))
w (Math/sqrt (+ w (Math/pow w 3)))]
w))
[31.78049716414141 {nil (8.0), :a (2)}]

Related

Dispatching function calls on different formats of maps

I'm writing an agar.io clone. I've lately seen a lot of suggestions to limit use of records (like here), so I'm trying to do the whole project only using basic maps.*
I ended up creating constructors for different "types" of bacteria like
(defn new-bacterium [starting-position]
{:mass 0,
:position starting-position})
(defn new-directed-bacterium [starting-position starting-directions]
(-> (new-bacterium starting-position)
(assoc :direction starting-directions)))
The "directed bacterium" has a new entry added to it. The :direction entry will be used to remember what direction it was heading in.
Here's the problem: I want to have one function take-turn that accepts the bacterium and the current state of the world, and returns a vector of [x, y] indicating the offset from the current position to move the bacterium to. I want to have a single function that's called because I can think right now of at least three kinds of bacteria that I'll want to have, and would like to have the ability to add new types later that each define their own take-turn.
A Can-Take-Turn protocol is out the window since I'm just using plain maps.
A take-turn multimethod seemed like it would work at first, but then I realized that I'd have no dispatch values to use in my current setup that would be extensible. I could have :direction be the dispatch function, and then dispatch on nil to use the "directed bacterium"'s take-turn, or default to get the base aimless behavior, but that doesn't give me a way of even having a third "player bacterium" type.
The only solution I can think of it to require that all bacterium have a :type field, and to dispatch on it, like:
(defn new-bacterium [starting-position]
{:type :aimless
:mass 0,
:position starting-position})
(defn new-directed-bacterium [starting-position starting-directions]
(-> (new-bacterium starting-position)
(assoc :type :directed,
:direction starting-directions)))
(defmulti take-turn (fn [b _] (:type b)))
(defmethod take-turn :aimless [this world]
(println "Aimless turn!"))
(defmethod take-turn :directed [this world]
(println "Directed turn!"))
(take-turn (new-bacterium [0 0]) nil)
Aimless turn!
=> nil
(take-turn (new-directed-bacterium [0 0] nil) nil)
Directed turn!
=> nil
But now I'm back to basically dispatching on type, using a slower method than protocols. Is this a legitimate case to use records and protocols, or is there something about mutlimethods that I'm missing? I don't have a lot of practice with them.
* I also decided to try this because I was in the situation where I had a Bacterium record and wanted to create a new "directed" version of the record that had a single field direction added to it (inheritance basically). The original record implemented protocols though, and I didn't want to have to do something like nesting the original record in the new one, and routing all behavior to the nested instance. Every time I created a new type or changed a protocol, I would have to change all the routing, which was a lot of work.
You can use example-based multiple dispatch for this, as explained in this blog post. It is certainly not the most performant way to solve this problem, but arguably more flexible than multi-methods as it does not require you to declare a dispatch-method upfront. So it is open for extension to any data representation, even other things than maps. If you need performance, then multi-methods or protocols as you suggest, is probably the way to go.
First, you need to add a dependency on [bluebell/utils "1.5.0"] and require [bluebell.utils.ebmd :as ebmd]. Then you declare constructors for your data structures (copied from your question) and functions to test those data strucutres:
(defn new-bacterium [starting-position]
{:mass 0
:position starting-position})
(defn new-directed-bacterium [starting-position starting-directions]
(-> (new-bacterium starting-position)
(assoc :direction starting-directions)))
(defn bacterium? [x]
(and (map? x)
(contains? x :position)))
(defn directed-bacterium? [x]
(and (bacterium? x)
(contains? x :direction)))
Now we are going to register those datastructures as so called arg-specs so that we can use them for dispatch:
(ebmd/def-arg-spec ::bacterium {:pred bacterium?
:pos [(new-bacterium [9 8])]
:neg [3 4]})
(ebmd/def-arg-spec ::directed-bacterium {:pred directed-bacterium?
:pos [(new-directed-bacterium [9 8] [3 4])]
:neg [(new-bacterium [3 4])]})
For each arg-spec, we need to declare a few example values under the :pos key, and a few non-examples under the :neg key. Those values are used to resolve the fact that a directed-bacterium is more specific than just a bacterium in order for the dispatch to work properly.
Finally, we are going to define a polymorphic take-turn function. We first declare it, using declare-poly:
(ebmd/declare-poly take-turn)
And then, we can provide different implementations for specific arguments:
(ebmd/def-poly take-turn [::bacterium x
::ebmd/any-arg world]
:aimless)
(ebmd/def-poly take-turn [::directed-bacterium x
::ebmd/any-arg world]
:directed)
Here, the ::ebmd/any-arg is an arg-spec that matches any argument. The above approach is open to extension just like multi-methods, but does not require you to declare a :type field upfront and is thus more flexible. But, as I said, it is also going to be slower than both multimethods and protocols, so ultimately this is a trade-off.
Here is the full solution: https://github.com/jonasseglare/bluebell-utils/blob/archive/2018-11-16-002/test/bluebell/utils/ebmd/bacteria_test.clj
Dispatching a multimethod by a :type field is indeed polymorphic dispatch that could be done with a protocol, but using multimethods allows you to dispatch on different fields. You can add a second multimethod that dispatches on something other than :type, which might be tricky to accomplish with a protocol (or even multiple protocols).
Since a multimethod can dispatch on anything, you could use a set as the dispatch value. Here's an alternative approach. It's not fully extensible, since the keys to select are determined within the dispatch function, but it might give you an idea for a better solution:
(defmulti take-turn (fn [b _] (clojure.set/intersection #{:direction} (set (keys b)))))
(defmethod take-turn #{} [this world]
(println "Aimless turn!"))
(defmethod take-turn #{:direction} [this world]
(println "Directed turn!"))
Fast paths exist for a reason, but Clojure doesn't stop you from doing anything you want to do, per say, including ad hoc predicate dispatch. The world is definitely your oyster. Observe this super quick and dirty example below.
First, we'll start off with an atom to store all of our polymorphic functions:
(def polies (atom {}))
In usage, the internal structure of the polies would look something like this:
{foo ; <- function name
{:dispatch [[pred0 fn0 1 ()] ; <- if (pred0 args) do (fn0 args)
[pred1 fn1 1 ()]
[pred2 fn2 2 '&]]
:prefer {:this-pred #{:that-pred :other-pred}}}
bar
{:dispatch [[pred0 fn0 1 ()]
[pred1 fn1 3 ()]]
:prefer {:some-pred #{:any-pred}}}}
Now, let's make it so that we can prefer predicates (like prefer-method):
(defn- get-parent [pfn x] (->> (parents x) (filter pfn) first))
(defn- in-this-or-parent-prefs? [poly v1 v2 f1 f2]
(if-let [p (-> #polies (get-in [poly :prefer v1]))]
(or (contains? p v2) (get-parent f1 v2) (get-parent f2 v1))))
(defn- default-sort [v1 v2]
(if (= v1 :poly/default)
1
(if (= v2 :poly/default)
-1
0)))
(defn- pref [poly v1 v2]
(if (-> poly (in-this-or-parent-prefs? v1 v2 #(pref poly v1 %) #(pref poly % v2)))
-1
(default-sort v1 v2)))
(defn- sort-disp [poly]
(swap! polies update-in [poly :dispatch] #(->> % (sort-by first (partial pref poly)) vec)))
(defn prefer [poly v1 v2]
(swap! polies update-in [poly :prefer v1] #(-> % (or #{}) (conj v2)))
(sort-disp poly)
nil)
Now, let's create our dispatch lookup system:
(defn- get-disp [poly filter-fn]
(-> #polies (get-in [poly :dispatch]) (->> (filter filter-fn)) first))
(defn- pred->disp [poly pred]
(get-disp poly #(-> % first (= pred))))
(defn- pred->poly-fn [poly pred]
(-> poly (pred->disp pred) second))
(defn- check-args-length [disp args]
((if (= '& (-> disp (nth 3) first)) >= =) (count args) (nth disp 2)))
(defn- args-are? [disp args]
(or (isa? (vec args) (first disp)) (isa? (mapv class args) (first disp))))
(defn- check-dispatch-on-args [disp args]
(if (-> disp first vector?)
(-> disp (args-are? args))
(-> disp first (apply args))))
(defn- disp*args? [disp args]
(and (check-args-length disp args)
(check-dispatch-on-args disp args)))
(defn- args->poly-fn [poly args]
(-> poly (get-disp #(disp*args? % args)) second))
Next, let's prepare our define macro with some initialization and setup functions:
(defn- poly-impl [poly args]
(if-let [poly-fn (-> poly (args->poly-fn args))]
(-> poly-fn (apply args))
(if-let [default-poly-fn (-> poly (pred->poly-fn :poly/default))]
(-> default-poly-fn (apply args))
(throw (ex-info (str "No poly for " poly " with " args) {})))))
(defn- remove-disp [poly pred]
(when-let [disp (pred->disp poly pred)]
(swap! polies update-in [poly :dispatch] #(->> % (remove #{disp}) vec))))
(defn- til& [args]
(count (take-while (partial not= '&) args)))
(defn- add-disp [poly poly-fn pred params]
(swap! polies update-in [poly :dispatch]
#(-> % (or []) (conj [pred poly-fn (til& params) (filter #{'&} params)]))))
(defn- setup-poly [poly poly-fn pred params]
(remove-disp poly pred)
(add-disp poly poly-fn pred params)
(sort-disp poly))
With that, we can finally build our polies by rubbing some macro juice on there:
(defmacro defpoly [poly-name pred params body]
`(do (when-not (-> ~poly-name quote resolve bound?)
(defn ~poly-name [& args#] (poly-impl ~poly-name args#)))
(let [poly-fn# (fn ~(symbol (str poly-name "-poly")) ~params ~body)]
(setup-poly ~poly-name poly-fn# ~pred (quote ~params)))
~poly-name))
Now you can build arbitrary predicate dispatch:
;; use defpoly like defmethod, but without a defmulti declaration
;; unlike defmethods, all params are passed to defpoly's predicate function
(defpoly myinc number? [x] (inc x))
(myinc 1)
;#_=> 2
(myinc "1")
;#_=> Execution error (ExceptionInfo) at user$poly_impl/invokeStatic (REPL:6).
;No poly for user$eval187$myinc__188#5c8eee0f with ("1")
(defpoly myinc :poly/default [x] (inc x))
(myinc "1")
;#_=> Execution error (ClassCastException) at user$eval245$fn__246/invoke (REPL:1).
;java.lang.String cannot be cast to java.lang.Number
(defpoly myinc string? [x] (inc (read-string x)))
(myinc "1")
;#_=> 2
(defpoly myinc
#(and (number? %1) (number? %2) (->> %& (filter (complement number?)) empty?))
[x y & z]
(inc (apply + x y z)))
(myinc 1 2 3)
;#_=> 7
(myinc 1 2 3 "4")
;#_=> Execution error (ArityException) at user$poly_impl/invokeStatic (REPL:5).
;Wrong number of args (4) passed to: user/eval523/fn--524
; ^ took the :poly/default path
And when using your example, we can see:
(defn new-bacterium [starting-position]
{:mass 0,
:position starting-position})
(defn new-directed-bacterium [starting-position starting-directions]
(-> (new-bacterium starting-position)
(assoc :direction starting-directions)))
(defpoly take-turn (fn [b _] (-> b keys set (contains? :direction)))
[this world]
(println "Directed turn!"))
;; or, if you'd rather use spec
(defpoly take-turn (fn [b _] (->> b (s/valid? (s/keys :req-un [::direction])))
[this world]
(println "Directed turn!"))
(take-turn (new-directed-bacterium [0 0] nil) nil)
;#_=> Directed turn!
;nil
(defpoly take-turn :poly/default [this world]
(println "Aimless turn!"))
(take-turn (new-bacterium [0 0]) nil)
;#_=> Aimless turn!
;nil
(defpoly take-turn #(-> %& first :show) [this world]
(println :this this :world world))
(take-turn (assoc (new-bacterium [0 0]) :show true) nil)
;#_=> :this {:mass 0, :position [0 0], :show true} :world nil
;nil
Now, let's try using isa? relationships, a la defmulti:
(derive java.util.Map ::collection)
(derive java.util.Collection ::collection)
;; always wrap classes in a vector to dispatch off of isa? relationships
(defpoly foo [::collection] [c] :a-collection)
(defpoly foo [String] [s] :a-string)
(foo [])
;#_=> :a-collection
(foo "bob")
;#_=> :a-string
And of course we can use prefer to disambiguate relationships:
(derive ::rect ::shape)
(defpoly bar [::rect ::shape] [x y] :rect-shape)
(defpoly bar [::shape ::rect] [x y] :shape-rect)
(bar ::rect ::rect)
;#_=> :rect-shape
(prefer bar [::shape ::rect] [::rect ::shape])
(bar ::rect ::rect)
;#_=> :shape-rect
Again, the world's your oyster! There's nothing stopping you from extending the language in any direction you want.

Threadsafe pop in clojure?

I've found this code on http://www.learningclojure.com/2010/11/yet-another-way-to-write-factorial.html, but I don't understand if/how the pop-task is supposed to be threadsafe. Doesn't it allow to return twice the same head ?
(def to-do-list (atom '()))
(defn add-task![t] (swap! to-do-list #(cons t %)))
(defn pop-task![] (let [h (first #to-do-list)] (swap! to-do-list rest) h))
If so, is it possible to keep using atom and write the peek and swap! atomically, or is this a job for the ref mechanism ?
Or you drop to a lower level.
(def to-do-list (atom nil))
(defn add-task!
[t]
(swap! to-do-list conj t))
(defn pop-task!
[]
(let [[h & r :as l] #to-do-list]
(if (compare-and-set! to-do-list l r)
h
(recur))))
Yeah, that code isn't thread safe. You can make it thread-safe by taking advantage of the fact that swap! returns the new value of the atom, which implies you need to combine the queue with the "popped" value.
(def to-do-list
(atom {}))
(defn add-task!
[t]
(swap! to-do-list
(fn [tl]
{:queue (cons t (:queue tl))})))
(defn pop-task!
[]
(let [tl (swap! to-do-list
(fn [old]
{:val (first (:queue old))
:queue (rest (:queue old))}))]
(:val tl)))

Piping data through arbitrary functions in Clojure

I know that the -> form can be used to pass the results of one function result to another:
(f1 (f2 (f3 x)))
(-> x f3 f2 f1) ; equivalent to the line above
(taken from the excellent Clojure tutorial at ociweb)
However this form requires that you know the functions you want to use at design time. I'd like to do the same thing, but at run time with a list of arbitrary functions.
I've written this looping function that does it, but I have a feeling there's a better way:
(defn pipe [initialData, functions]
(loop [
frontFunc (first functions)
restFuncs (rest functions)
data initialData ]
(if frontFunc
(recur (first restFuncs) (rest restFuncs) (frontFunc data) )
data )
) )
What's the best way to go about this?
I must admit I'm really new to clojure and I might be missing the point here completely, but can't this just be done using comp and apply?
user> (defn fn1 [x] (+ 2 x))
user> (defn fn2 [x] (/ x 3))
user> (defn fn3 [x] (* 1.2 x))
user> (defn pipe [initial-data my-functions] ((apply comp my-functions) initial-data))
user> (pipe 2 [fn1 fn2 fn3])
2.8
You can do this with a plain old reduce:
(defn pipe [x fs] (reduce (fn [acc f] (f acc)) x fs))
That can be shortened to:
(defn pipe [x fs] (reduce #(%2 %1) x fs))
Used like this:
user> (pipe [1 2 3] [#(conj % 77) rest reverse (partial map inc) vec])
[78 4 3]
If functions is a sequence of functions, you can reduce it using comp to get a composed function. At a REPL:
user> (def functions (list #(* % 5) #(+ % 1) #(/ % 3)))
#'user/my-list
user> ((reduce comp functions) 9)
20
apply also works in this case because comp takes a variable number of arguments:
user> (def functions (list #(* % 5) #(+ % 1) #(/ % 3)))
#'user/my-list
user> ((apply comp functions) 9)
20

Project Euler #14 and memoization in Clojure

As a neophyte clojurian, it was recommended to me that I go through the Project Euler problems as a way to learn the language. Its definitely a great way to improve your skills and gain confidence. I just finished up my answer to problem #14. It works fine, but to get it running efficiently I had to implement some memoization. I couldn't use the prepackaged memoize function because of the way my code was structured, and I think it was a good experience to roll my own anyways. My question is if there is a good way to encapsulate my cache within the function itself, or if I have to define an external cache like I have done. Also, any tips to make my code more idiomatic would be appreciated.
(use 'clojure.test)
(def mem (atom {}))
(with-test
(defn chain-length
([x] (chain-length x x 0))
([start-val x c]
(if-let [e (last(find #mem x))]
(let [ret (+ c e)]
(swap! mem assoc start-val ret)
ret)
(if (<= x 1)
(let [ret (+ c 1)]
(swap! mem assoc start-val ret)
ret)
(if (even? x)
(recur start-val (/ x 2) (+ c 1))
(recur start-val (+ 1 (* x 3)) (+ c 1)))))))
(is (= 10 (chain-length 13))))
(with-test
(defn longest-chain
([] (longest-chain 2 0 0))
([c max start-num]
(if (>= c 1000000)
start-num
(let [l (chain-length c)]
(if (> l max)
(recur (+ 1 c) l c)
(recur (+ 1 c) max start-num))))))
(is (= 837799 (longest-chain))))
Since you want the cache to be shared between all invocations of chain-length, you would write chain-length as (let [mem (atom {})] (defn chain-length ...)) so that it would only be visible to chain-length.
In this case, since the longest chain is sufficiently small, you could define chain-length using the naive recursive method and use Clojure's builtin memoize function on that.
Here's an idiomatic(?) version using plain old memoize.
(def chain-length
(memoize
(fn [n]
(cond
(== n 1) 1
(even? n) (inc (chain-length (/ n 2)))
:else (inc (chain-length (inc (* 3 n))))))))
(defn longest-chain [start end]
(reduce (fn [x y]
(if (> (second x) (second y)) x y))
(for [n (range start (inc end))]
[n (chain-length n)])))
If you have an urge to use recur, consider map or reduce first. They often do what you want, and sometimes do it better/faster, since they take advantage of chunked seqs.
(inc x) is like (+ 1 x), but inc is about twice as fast.
You can capture the surrounding environment in a clojure :
(defn my-memoize [f]
(let [cache (atom {})]
(fn [x]
(let [cy (get #cache x)]
(if (nil? cy)
(let [fx (f x)]
(reset! cache (assoc #cache x fx)) fx) cy)))))
(defn mul2 [x] (do (print "Hello") (* 2 x)))
(def mmul2 (my-memoize mul2))
user=> (mmul2 2)
Hello4
user=> (mmul2 2)
4
You see the mul2 funciton is only called once.
So the 'cache' is captured by the clojure and can be used to store the values.

Can I get a this variable in a def?

Is there a way to mimic a this variable in something like (def foo {:two 2 :three (inc (:two this))})? Even better would be something like (def foo {:two 2 :three (inc ::two)}). I was told that there is a library that does exactly this, but I can't really find anything similar.
Thanks!
If you want a temporary name for something, that's what let is for.
(def foo (let [x {:two 2}]
(assoc x :three (inc (:two x)))))
I don't know of any library that does what you want. Every once in a while, someone suggests a "generalized arrow", like -> but with a magic symbol you can stick in the intermediary expressions which will be replaced by something else. See for example here and here. But this idea tends to be shot down because it's more complex and confusing for little benefit. let is your friend. See Rich's example:
(let [x []
x (conj x 1)
x (into x [2 3])
x (map inc x)]
...)
(Update: Rearranged & reworked. build-map and (a sketch of) -m> macros added.)
You could write this particular example as
(def foo (zipmap [:two :three] (iterate inc 2)))
The easiest general solution which occurs to me at this moment is
user> (-> {} (assoc :two 2) (#(assoc % :three (inc (:two %)))))
{:three 3, :two 2}
It's actually very flexible, although it does require you to write out assoc repeatedly.
To enable syntax similar to that from the question text, you could use something like this:
(defn build-map* [& kvs]
(reduce (fn [m [k v]]
(assoc m k (v m)))
{}
kvs))
(defmacro build-map [& raw-kvs]
(assert (even? (count raw-kvs)))
(let [kvs (map (fn [[k v]] [k `(fn [m#] (let [~'this m#] ~v))])
(partition 2 raw-kvs))]
`(build-map* ~#kvs)))
user> (build-map :two 2 :three (inc (:two this)))
{:three 3, :two 2}
You could easily change this to use a user-supplied symbol rather than the hardcoded this. Or you could switch to %, which is just a regular symbol outside anonymous function literals. Maybe add an explicit initial map argument, call it -m> (for map threading) and you can do
(-m> {} :two 2 :three (inc (:two %)))
for the same result.
Another funky way (mostly for the fun):
;;; from Alex Osborne's debug-repl,
;;; see http://gist.github.com/252421
;;; now changed to use &env
(defmacro local-bindings
"Produces a map of the names of local bindings to their values."
[]
(let [symbols (map key &env)]
(zipmap (map (fn [sym] `(quote ~sym)) symbols) symbols)))
(let [two 2
three (inc two)]
(into {} (map (fn [[k v]] [(keyword k) v]) (local-bindings))))
{:two 2, :three 3}
Note that this will also capture the bindings introduced by any outer let forms...