Sequence Expressions
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Sequence Expressions. Similar to regular expressions but able to describe arbitrary sequences of values (not just characters).


Works with Clojure 1.5 and up.

Updated to 2.0.1 - Fix se/ord bug with 2.0, started new n01se.syntax.repl namespace intended to be used at the repl for nice error messages and syntax docs.

Updated to 2.0 - generally simplified the API, added new syntax library. Added syntax.clj which applies seqexes to the task of defining macros. Added a couple of example files: trees.clj and math.clj.

Quick Start

(require '[n01se.seqex :as se])

(defn digit? [x] (contains? (set "123456789") x))
(defn alpha? [x] (contains? (set "abcdefghijklmnopqrstuvwxyz") x))
(def num (se/rep+ digit?))
(def word (se/cat alpha? (se/rep* alpha? digit?)))

(se/valid? num "42")       ;=> true
(se/valid? num "")         ;=> false
(se/valid? word "hello42") ;=> true
(se/valid? word "4hello2") ;=> false


These functions are available to work with Seqexes by applying them to a sequence of tokens.

  • se/exec: returns both the end models and a final verdict of Matching or Invalid.
  • se/valid?: returns true if the input stream matched the seqex constraints.
  • se/parse: returns captured models, prints an error otherwise.

Composing Seqexes

Most of the time, Seqexes can be composed of the following Seqexes plus Clojure's standard values:

  • se/cat: concatenated seqexes.
  • se/alt: alternate seqexes (choosing one).
  • se/opt: optional seqexes (choosing zero or one).
  • se/rep+: one or more repeating seqexes (in any order).
  • se/rep*: zero or more repeating seqexes (in any order).
  • se/rep: a specific number of repeating seqexes (in any order).

Clojure's standard values: numbers, characters, strings, symbols, keywords, lists, vectors, sets, and maps are all extended to implement the SeqEx protocol such that they match exactly one occurance of themselves. Examples:

(se/valid? \a "a")          ;=> true
(se/valid? \a "")           ;=> false
(se/valid? 1 [1])           ;=> true
(se/valid? 1 [1 1])         ;=> false
(se/valid? {:a 1} [{:a 1}]) ;=> true

Functions are treated as predicates that must be true for exactly one token in a sequence.

Recursive expressions are defined by using delays which are assumed to wrap a Seqex. See math.clj for an example.

Nested expressions (e.g., a tree structure) may be expressed with se/subex.

Basic Concepts (protocols, verdicts and models)

SeqEx Protocol

All sequence expressions implement the SeqEx protocol defined primarily by two methods se/begin- and se/continue-. These functions are called before and during parsing a sequence of tokens respectively. se/begin- returns an inital verdict (i.e., a verdict after looking at a zero length sequence) and the initial state of the Seqex. se/continue- takes the previous state of the Seqex and the next token in the sequence and returns a new Seqex state and new verdict. se/continue- is repeatedly called with tokens until no more tokens remain or the returned verdict is se/Passed or se/Failed.

Once the sequence expression is done being applied to the tokens, one of the two secondary methods se/error- or se/model- is applied to the state if the final verdict is se/Failed or se/Passed respectively.


Underlying all sequence expressions is the idea of returning a 'verdict' after examining each token. Verdicts are actually a pair of boolean values: one indictating matching (or not matching) and the other indicating continuing (or not continuing). If the verdict indicates matching, it means that the specific constraints of the Seqex have been fully met through the most recent token examined. On the other hand, If the verdict indicates continuing, then the Seqex is ready to examine the next token in the sequence (if any). There are four possible verdicts: se/Passing, se/Failing, se/Passed and se/Failed.

As an example of how verdicts might look over time, assume a specific Seqex that requires a sequence of characters \c \a followed by one or more \t. The verdicts for the input sequence "cattle" would look like this:

[ \c \a \t \t \l \e ] ;; Input sequence
 0  0  0  1  1  0  ,  ;; Matching bit (commas indicate not examined)
 1  1  1  1  1  0  ,  ;; Continue bit

Another example, this time matching \c \a followed by an optional \t. The verdicts for the same input sequence are:

[ \c \a \t \t \l \e ] ;; Input sequence
 0  0  1  1  ,  ,  ,  ;; Matching bit (commas indicate not examined)
 1  1  1  0  ,  ,  ,  ;; Continue bit

By specifing both flags, a Seqex is able to communicate both when the input tokens are matching and when it is done examining the input tokens.


When a seqex has passed or is passing with no more tokens, a sequence of 'models' are extracted from the tokens examined.

The models are finalized and returned when se/model- is called and the models are initialized and updated up when se/begin- and se/continue- are called. Most standard Seqexes do not build any models at all and so return an empty sequence of models. The exceptions to this are the standard capturing seqexes: se/cap, se/recap, and se/recap-map.

se/cap is used to capture a vector of all tokens examined by the seqex enclosed by se/cap. If an optional function is given, it is applied to the vector of tokens. In either case, any the captured result is consed onto the sequence of models returned by the enclosed seqex.

se/recap is used to combine all models captured by its enclosed seqex. This is accomplished by applying a function to the sequence of models captured and treating the return value of the function a single model.

se/recap-map applies the function to all captured models and must return a sequence of models.

Most of the standard Seqexes (e.g., se/cat, se/rep+) will return a list of models from seqexes below them. Also, se/subex will return a list of models built from the Seqex it wraps.

There are a lot of interesting possiblities with model building but I need to experiment with this before saying much more about it. I will say that combining constraints with arbitrary model building is quite powerful. You have been warned.


When a seqex has failed or is failing with no more tokens, an error message is returned based on the state of the seqex. At the moment, this error message is represented as a sequence of strings to be printed.


Examples can be found in the examples directory.

  • math.clj parse a string of infix math expressions.
  • trees.clj reshape tree data structures.

Macro Syntax

There is a new syntax.clj file that defines a first attempt at applying seqexes to macro parameters and providing syntax documentation in addition to the existing error messages.


Copyright (C) 2013 Jonathan Claggett

Distributed under the Eclipse Public License, the same as Clojure.