Transducers: Ergonomic, efficient data processing

I think Transducers are a fundamental primitive that decouples critical logic from list/sequence processing, and if I had to do Clojure all over I would put them at the bottom.

– Rich Hickey

Transducers are an ergonomic and extremely memory-efficient way to process a data source. Here “data source” means simple collections like Lists or Vectors, but also potentially large files or generators of infinite data.

Transducers…

• allow the chaining of operations like map and filter without allocating memory between each step.
• aren’t tied to any specific data type; they need only be implemented once.
• vastly simplify “data transformation code”.
• have nothing to do with “lazy evaluation”.
• are a joy to use!

Example: While skipping every second line of a file, sum the lengths of only evenly-lengthed lines.

(in-package :transducers)

(transduce
  ;; How do we want to process each element?
  (comp (step 2) (map #'length) (filter #'evenp))
  ;; How do we want to combine all the elements together?
  #'+
  ;; What's our original data source?
  #p"README.org")

7026

This library has been confirmed to work with SBCL, CCL, ECL, Clasp and LispWorks 8.

⚠ ABCL cannot be used due to lack of support for tail-call elimination within labels.

Looking for Transducers in other Lisps? Check out the Emacs Lisp and Fennel implementations!

History and Motivation

Originally invented in Clojure and adapted to Scheme as SRFI-171, Transducers are an excellent way to think about - and efficiently operate on - collections or streams of data. Transduction operations are strict and don’t involve “laziness” or “thunking” in any way, yet only process the exact amount of data you ask them to.

This library draws inspiration from both the original Clojure and SRFI-171, while adding many other convenient operations commonly found in other languages.

Installation

This library is available on Quicklisp and Ultralisp. To download the main system:

(ql:quickload :transducers)

For the JSON extensions:

(ql:quickload :transducers/jzon)

Usage and Theory

Importing

Since this library reuses some symbol names also found in :cl, it is expected that you import transducers as follows in your defpackage:

(defpackage foo
  (:use :cl)
  (:local-nicknames (:t :transducers)))

You can then make relatively clean calls like:

(t:transduce (t:map #'1+) #'t:vector '(1 2 3))
;; => #(2 3 4)

However, many of the examples below use (in-package :transducers) for brevity in the actual function calls. You should still use a nickname in your own code.

Transducers, Reducers, and Sources

;; The fundamental pattern.
(transduce <transducer-chain> <reducer> <source>)

Data processing largely has three concerns:

1. Where is my data coming from? (sources)
2. What do I want to do to each element? (transducers)
3. How do I want to collect the results? (reducers)

Each full “transduction” requires all three. We pass one of each to the transduce function, which drives the process. It knows how to pull values from the source, feed them through the transducer chain, and wrap everything together via the reducer.

• Typical transducers are map, filter, and take.
• Typical reducers are +, count, t:cons, and fold.
• Typical sources are lists, vectors, strings, hash tables, and files.

Generators are a special kind of source that yield infinite data. Typical generators are repeat, cycle, and ints.

Let’s sum the squares of the first 1000 odd integers:

(in-package :transducers)

(transduce
 (comp (filter #'oddp)             ;; (2) Keep only odd numbers.
       (take 1000)                 ;; (3) Keep the first 1000 filtered odds.
       (map (lambda (n) (* n n)))) ;; (4) Square those 1000.
 #'+       ;; (5) Reducer: Add up all the squares.
 (ints 1)) ;; (1) Source: Generate all positive integers.

1333333000

Two things of note here:

1. comp is used here to chain together different transducer steps. Notice that the order appears “backwards” from usual function composition. It may help to imagine that comp is acting like the ->> macro here. comp is supplied here as a convenience; you’re free to use alexandria:compose if you wish.
2. The reduction via + is listed as Step 5, but really it’s occuring throughout the transduction process. Each value that makes it through the composed transducer chain is immediately added to an internal accumulator.

Explore the other transducers and reducers to see what’s possible! You’ll never write a loop again.

Processing JSON Data

The system transducers/jzon provides automatic JSON streaming support via the jzon library. Like transducers itself, it is expected that you import this system with a nickname:

(:local-nicknames (#:j #:transducers/jzon))

Only two functions are exposed: read and write.

• read is a source that accepts a pathname, open stream, or a string. It produces parsed JSON values as Lisp types. JSON Objects become Hash Tables.
• write is a reducer that expects an open stream. It writes the stream of Lisp types into their logical JSON equivalents.

Here is a simple example of reading some JSON data from a string, doing nothing to it, and outputting it again to a new string:

(in-package :transducers)

(with-output-to-string (stream)
  (transduce #'pass
             (transducers/jzon:write stream)
             (transducers/jzon:read "[{\"name\": \"A\"}, {\"name\": \"B\"}]")))

[{"name":"A"},{"name":"B"}]

Note that the JSON data must be a JSON array. There is otherwise no size limit; the library can handle any amount of JSON input.

For more examples, see the Gallery below.

API

The examples here use (in-package :transducers) for brevity in the actual function calls and to allow them to be runnable directly in this README, but as mentioned above it’s recommended to nickname the library to :t due to some overlap with :cl.

Transducers

Transducers describe how to alter the items of some stream of values. Some transducers, like take, can short-circuit.

Multiple transducer functions can be chained together with comp.

pass, map

Just pass along each value of the transduction.

(in-package :transducers)
(transduce #'pass #'cons '(1 2 3))

(1 2 3)

Apply a function F to all elements of the transduction.

(in-package :transducers)
(transduce (map #'1+) #'cons '(1 2 3))

(2 3 4)

filter, filter-map, unique, dedup

Only keep elements from the transduction that satisfy PRED.

(in-package :transducers)
(transduce (filter #'evenp) #'cons '(1 2 3 4 5))

(2 4)

Apply a function F to the elements of the transduction, but only keep results that are non-nil.

(in-package :transducers)
(transduce (filter-map #'cl:first) #'cons '(() (2 3) () (5 6) () (8 9)))

(2 5 8)

Only allow values to pass through the transduction once each. Stateful; this uses a hash table internally so could get quite heavy if you’re not careful.

(in-package :transducers)
(transduce #'unique #'cons '(1 2 1 3 2 1 2 "abc"))

(1 2 3 "abc")

Remove adjacent duplicates from the transduction.

(in-package :transducers)
(transduce #'dedup #'cons '(1 1 1 2 2 2 3 3 3 4 3 3))

(1 2 3 4 3)

drop, drop-while, take, take-while

Drop the first N elements of the transduction.

(in-package :transducers)
(transduce (drop 3) #'cons '(1 2 3 4 5))

(4 5)

Drop elements from the front of the transduction that satisfy PRED.

(in-package :transducers)
(transduce (drop-while #'evenp) #'cons '(2 4 6 7 8 9))

(7 8 9)

Keep only the first N elements of the transduction.

(in-package :transducers)
(transduce (take 3) #'cons '(1 2 3 4 5))

(1 2 3)

Keep only elements which satisfy a given PRED, and stop the transduction as soon as any element fails the test.

(in-package :transducers)
(transduce (take-while #'evenp) #'cons '(2 4 6 8 9 2))

(2 4 6 8)

uncons, concatenate, flatten

Split up a transduction of cons cells.

(in-package :transducers)
(transduce #'uncons #'cons '((:a . 1) (:b . 2) (:c . 3)))

(:A 1 :B 2 :C 3)

Concatenate all the sublists in the transduction.

(in-package :transducers)
(transduce #'concatenate #'cons '((1 2 3) (4 5 6) (7 8 9)))

(1 2 3 4 5 6 7 8 9)

Entirely flatten all lists in the transduction, regardless of nesting.

(in-package :transducers)
(transduce #'flatten #'cons '((1 2 3) 0 (4 (5) 6) 0 (7 8 9) 0))

(1 2 3 0 4 5 6 0 7 8 9 0)

segment, window, group-by

Partition the input into lists of N items. If the input stops, flush any accumulated state, which may be shorter than N.

(in-package :transducers)
(transduce (segment 3) #'cons '(1 2 3 4 5))

((1 2 3) (4 5))

Yield N-length windows of overlapping values. This is different from segment which yields non-overlapping windows. If there were fewer items in the input than N, then this yields nothing.

(in-package :transducers)
(transduce (window 3) #'cons '(1 2 3 4 5))

((1 2 3) (2 3 4) (3 4 5))

Group the input stream into sublists via some function F. The cutoff criterion is whether the return value of F changes between two consecutive elements of the transduction.

(in-package :transducers)
(transduce (group-by #'evenp) #'cons '(2 4 6 7 9 1 2 4 6 3))

((2 4 6) (7 9 1) (2 4 6) (3))

intersperse, enumerate, step, scan

Insert an ELEM between each value of the transduction.

(in-package :transducers)
(transduce (intersperse 0) #'cons '(1 2 3))

(1 0 2 0 3)

Index every value passed through the transduction into a cons pair. Starts at 0.

(in-package :transducers)
(transduce #'enumerate #'cons '("a" "b" "c"))

((0 . "a") (1 . "b") (2 . "c"))

Only yield every Nth element of the transduction. The first element of the transduction is always included.

(in-package :transducers)
(transduce (step 2) #'cons '(1 2 3 4 5 6 7 8 9))

(1 3 5 7 9)

Build up successsive values from the results of previous applications of a given function F.

(in-package :transducers)
(transduce (scan #'+ 0) #'cons '(1 2 3 4))

(0 1 3 6 10)

once

Inject some ITEM onto the front of the transduction.

(in-package :transducers)
(transduce (comp (filter (lambda (n) (> n 10)))
                 (once 'hello)
                 (take 3))
           #'cons (ints 1))

(HELLO 11 12)

log

Call some LOGGER function for each step of the transduction. The LOGGER must accept the running results and the current element as input. The original items of the transduction are passed through as-is.

(in-package :transducers)
(transduce (log (lambda (_ n) (format t "Got: ~a~%" n))) #'cons '(1 2 3 4 5))

Got: 1
Got: 2
Got: 3
Got: 4
Got: 5

These are STDOUT results. The actual return value is the result of the reducer, in this case cons, thus a list.

from-csv, into-csv

Interpret the data stream as CSV data.

The first item found is assumed to be the header list, and it will be used to construct useable hashtables for all subsequent items.

Note: This function makes no attempt to convert types from the original parsed strings. If you want numbers, you will need to further parse them yourself.

(in-package :transducers)
(transduce (comp #'from-csv
                 (map (lambda (hm) (gethash "Name" hm))))
           #'cons '("Name,Age" "Alice,35" "Bob,26"))

("Alice" "Bob")

Given a sequence of HEADERS, rerender each item in the data stream into a CSV string. It’s assumed that each item in the transduction is a hash table whose keys are strings that match the values found in HEADERS.

(in-package :transducers)
(transduce (comp #'from-csv
                 (into-csv '("Name" "Age")))
           #'cons '("Name,Age,Hair" "Alice,35,Blond" "Bob,26,Black"))

("Name,Age" "Alice,35" "Bob,26")

Reducers

Reducers describe how to fold the stream of items down into a single result, be it either a new collection or a scalar.

Some reducers, like first, can also force the entire transduction to short-circuit.

cons, snoc, vector, string, hash-table

Collect all results as a list.

(in-package :transducers)
(transduce #'pass #'cons '(1 2 3))

(1 2 3)

Collect all results as a list, but results are reversed. In theory, slightly more performant than cons since it performs no final reversal.

(in-package :transducers)
(transduce #'pass #'snoc '(1 2 3))

(3 2 1)

Collect a stream of values into a vector.

(in-package :transducers)
(transduce #'pass #'vector '(1 2 3))

#(1 2 3)

Collect a stream of characters into to a single string.

(in-package :transducers)
(transduce (map #'char-upcase) #'string "hello")

HELLO

Collect a stream of key-value cons pairs into a hash table.

(in-package :transducers)
(transduce #'enumerate #'hash-table '("a" "b" "c"))

#<COMMON-LISP:HASH-TABLE :TEST EQUAL :COUNT 3 {1004E83BF3}>

count, average

Count the number of elements that made it through the transduction.

(in-package :transducers)
(transduce #'pass #'count '(1 2 3 4 5))

5

Calculate the average value of all numeric elements in a transduction.

(in-package :transducers)
(transduce #'pass #'average '(1 2 3 4 5 6))

7/2

anyp, allp

Yield t if any element in the transduction satisfies PRED. Short-circuits the transduction as soon as the condition is met.

(in-package :transducers)
(transduce #'pass (anyp #'evenp) '(1 3 5 7 9 2))

T

Yield t if all elements of the transduction satisfy PRED. Short-circuits with NIL if any element fails the test.

(in-package :transducers)
(transduce #'pass (allp #'oddp) '(1 3 5 7 9))

T

first, last, find

Yield the first value of the transduction. As soon as this first value is yielded, the entire transduction stops.

(in-package :transducers)
(transduce (filter #'oddp) #'first '(2 4 6 7 10))

7

Yield the last value of the transduction.

(in-package :transducers)
(transduce #'pass #'last '(2 4 6 7 10))

10

Find the first element in the transduction that satisfies a given PRED. Yields NIL if no such element were found.

(in-package :transducers)
(transduce #'pass (find #'evenp) '(1 3 5 6 9))

6

fold

fold is the fundamental reducer. fold creates an ad-hoc reducer based on a given 2-argument function. An optional SEED value can also be given as the initial accumulator value, which also becomes the return value in case there were no input left in the transduction.

Functions like + and * are automatically valid reducers, because they yield sane values even when given 0 or 1 arguments. Other functions like cl:max cannot be used as-is as reducers since they can’t be called without arguments. For functions like this, fold is appropriate.

(in-package :transducers)
(transduce #'pass (fold #'cl:max) '(1 2 3 4 1000 5 6))

1000

With a seed:

(in-package :transducers)
(transduce #'pass (fold #'cl:max 0) '())

0

In Clojure this function is called completing.

for-each

Run through every item in a transduction for their side effects. Throws away all results and yields t.

(in-package :transducers)
(transduce (map (lambda (n) (format t "~a~%" n))) #'for-each #(1 2 3 4))

T

Sources

Data is pulled in an on-demand fashion from Sources. They can be either finite or infinite in length. A list is an example of a simple Source, but you can also pull from files and endless number generators.

ints, random

Yield all integers, beginning with START and advancing by an optional STEP value which can be positive or negative. If you only want a specific range within the transduction, then use take-while within your transducer chain.

(in-package :transducers)
(transduce (take 10) #'cons (ints 0 :step 2))

(0 2 4 6 8 10 12 14 16 18)

Yield an endless stream of random numbers, based on a given LIMIT.

(in-package :transducers)
(transduce (take 20) #'cons (random 10))

(8 0 5 6 6 2 2 4 2 7 9 2 0 0 2 4 4 9 9 9)

(in-package :transducers)
(transduce (take 5) #'cons (random 1.0))

(0.4115485 0.35940528 0.0056368113 0.31019592 0.4214077)

cycle, repeat, shuffle

Yield the values of a given SEQ endlessly.

(in-package :transducers)
(transduce (take 10) #'cons (cycle '(1 2 3)))

(1 2 3 1 2 3 1 2 3 1)

Endlessly yield a given ITEM.

(in-package :transducers)
(transduce (take 4) #'cons (repeat 9))

(9 9 9 9)

Endlessly yield random elements from a given vector.

(in-package :transducers)
(transduce (take 5) #'cons (shuffle #("Alice" "Bob" "Dennis")))

("Alice" "Bob" "Alice" "Dennis" "Bob")

Recall also that strings are vectors too:

(in-package :transducers)
(transduce (take 15) #'string (shuffle "Númenor"))

eeúúrúmnnremmno

plist

Yield key-value pairs from a Property List, usually known as a ‘plist’. The pairs are passed as a cons cell.

(in-package :transducers)
(transduce (map #'cdr) #'+ (plist '(:a 1 :b 2 :c 3)))

6

See also the uncons transducer for another way to handle incoming cons cells.

Utilities

comp, const

Function composition. You can pass as many functions as you like and they are applied from right to left.

(in-package :transducers)
(funcall (comp #'length #'reverse) #(1 2 3))

3

For transducer functions specifically, they are composed from right to left, but their effects are applied from left to right. This is due to how the reducer function is chained through them all internally via transduce.

Notice here how drop is clearly applied first:

(in-package :transducers)
(transduce (comp (drop 3) (take 2)) #'cons '(1 2 3 4 5 6))

(4 5)

Return a function that ignores its argument and returns ITEM instead.

(in-package :transducers)
(funcall (comp (const 108) (lambda (n) (* 2 n)) #'1+) 1)

108

make-reduced, reduced-p, reduced-val

When writing your own transducers and reducers, these functions allow you to short-circuit the entire operation.

Here is a simplified definition of first:

(in-package :transducers)
(defun first (&optional (acc nil a-p) (input nil i-p))
  (cond ((and a-p i-p) (make-reduced :val input))
        ((and a-p (not i-p)) acc)
        (t acc)))

You can see make-reduced being used to wrap the return value. transduce sees this wrapping and immediately halts further processing.

reduced-p and reduced-val can similarly be used (mostly within transducer functions) to check if some lower transducer (or the reducer) has signaled a short-circuit, and if so potentially perform some clean-up. This is important for transducers that carry internal state.

Example Gallery

Reading lines from a File

Pathnames can be passed as-is as a Source. This yields their lines one by one.

Counting words:

(in-package :transducers)
(transduce (comp (map #'str:words)
                 #'concatenate)
           #'count #p"README.org")

3661

Reducing into Property Lists and Assocation Lists

There is no special reducer function for plists, because none is needed. If you have a stream of cons cells, you can break it up with uncons and then collect with cons as usual:

(in-package :transducers)
(transduce (comp (map (lambda (pair) (cl:cons (car pair) (1+ (cdr pair)))))
                 #'uncons)
           #'cons (plist '(:a 1 :b 2 :c 3)))

(:A 2 :B 3 :C 4)

Likewise, Association Lists are already lists-of-cons-cells, so no special treatment is needed:

(in-package :transducers)
(transduce #'pass #'cons '((:a . 1) (:b . 2) (:c . 3)))

((:A . 1) (:B . 2) (:C . 3))

JSON: Calculating average age

Since JSON Objects are parsed as Hash Tables, we use the usual functions to retrieve fields we want.

(in-package :transducers)
(transduce (filter-map (lambda (ht) (gethash "age" ht)))
           #'average
           (transducers/jzon:read "[{\"age\": 34}, {\"age\": 25}]"))

59/2

Sieve of Eratosthenes

An ancient method of calculating Prime Numbers.

(in-package :transducers)
(let ((xf (comp (inject (lambda (prime) (filter (lambda (n) (/= 0 (mod n prime))))))
                (take 10))))
  (cl:cons 2 (transduce xf #'cons (ints 3 :step 2))))

(2 3 5 7 11 13 17 19 23 29 31)

Limitations

1. This library is generally portable, but assumes your CL implementation supports tail-call elimination within labels.
2. A way to model the common zip function has not yet been found, but I suspect the answer lies in being able to pass multiple sources as &rest arguments.

Resources

• Clojure: Transducers
• Clojure: What are good uses cases for transducers?
• Youtube: Inside Transducers (Rich Hickey)
• Emacs Lisp: Transducers