Joachim Breitner

Showcasing Applicative

Published 2016-10-26 in sections English, Haskell.

My plan for this week’s lecture of the CIS 194 Haskell course at the University of Pennsylvania is to dwell a bit on the concept of Functor, Applicative and Monad, and to highlight the value of the Applicative abstraction.

I quite like the example that I came up with, so I want to share it here. In the interest of long-term archival and stand-alone presentation, I include all the material in this post.1


In case you want to follow along, start with these imports:

EBNF. This might look as follows, for a CSV file:

cell = '"', {not-quote}, '"';
line = (cell, {',', cell} | ''), newline;
csv  = {line};

It is straightforward to create a Haskell data type to represent an EBNF syntax description. Here is a simple EBNF library (data type and pretty-printer) for your convenience:


homework is to define a parser/grammar-generator for EBNF itself, as specified in this variant:

identifier = letter, {letter | digit | '-'};
spaces = {' ' | newline};
quoted-char = non-quote-or-backslash | '\\', '\\' | '\\', '\'';
terminal = '\'', {quoted-char}, '\'', spaces;
non-terminal = identifier, spaces;
option = '[', spaces, rhs, spaces, ']', spaces;
repetition = '{', spaces, rhs, spaces, '}', spaces;
group = '(', spaces, rhs, spaces, ')', spaces;
atom = terminal | non-terminal | option | repetition | group;
sequence = atom, {spaces, ',', spaces, atom}, spaces;
choice = sequence, {spaces, '|', spaces, sequence}, spaces;
rhs = choice;
production = identifier, spaces, '=', spaces, rhs, ';', spaces;
bnf = production, {production};

This grammar is set up so that the precedence of , and | is correctly implemented: a , b | c will parse as (a, b) | c.

In this syntax for BNF, terminal characters are quoted, i.e. inside '…', a ' is replaced by \' and a \ is replaced by \\ – this is done by the function quote in ppRHS.

If you do this, you should able to round-trip with the pretty-printer, i.e. parse back what it wrote:

  1. enumerations using Applicative yesterday.↩︎

  2. I like how in this alignment of <*> and <* the > point out where the arguments are that are being passed to the function on the left.↩︎


Have something to say? You can post a comment by sending an e-Mail to me at <>, and I will include it here.