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Bmg, a relational algebra (Alf's successor)!

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Bmg is a relational algebra implemented as a ruby library. It implements the Relation as First-Class Citizen paradigm contributed with Alf a few years ago.

Bmg can be used to query relations in memory, from various files, SQL databases, and any data source that can be seen as serving relations. Cross data-sources joins are supported, as with Alf. For differences with Alf, see a section further down this README.



require 'bmg'
require 'json'

suppliers =[
  { sid: "S1", name: "Smith", status: 20, city: "London" },
  { sid: "S2", name: "Jones", status: 10, city: "Paris"  },
  { sid: "S3", name: "Blake", status: 30, city: "Paris"  },
  { sid: "S4", name: "Clark", status: 20, city: "London" },
  { sid: "S5", name: "Adams", status: 30, city: "Athens" }

by_city = suppliers
  .exclude(status: 30)
  .extend(upname: ->(t){ t[:name].upcase })
  .group([:sid, :name, :status], :suppliers_in)

puts JSON.pretty_generate(by_city)
# [{...},...]

Where are base relations coming from?

Bmg sees relations as sets/enumerable of symbolized Ruby hashes. The following sections show you how to get them in the first place, to enter Relationland.

Memory relations

If you have an Array of Hashes -- in fact any Enumerable -- you can easily get a Relation using either or Bmg.in_memory.

# this...
r = [{id: 1}, {id: 2}]

# is the same as this...
r = Bmg.in_memory [{id: 1}, {id: 2}]

# entire algebra is available on `r`

Connecting to SQL databases

Bmg currently requires sequel >= 3.0 to connect to SQL databases. You also need to require bmg/sequel.

require 'sqlite3'
require 'bmg'
require 'bmg/sequel'

Then Bmg.sequel serves relations for tables of your SQL database:

DB = Sequel.connect("sqlite://suppliers-and-parts.db")
suppliers = Bmg.sequel(:suppliers, DB)

The entire algebra is available on those relations. As long as you keep using operators that can be translated to SQL, results remain SQL-able:

big_suppliers = suppliers
  .exclude(status: 30)
  .project([:sid, :name])

puts big_suppliers.to_sql
# SELECT `t1`.`sid`, `t1`.`name` FROM `suppliers` AS 't1' WHERE (`t1`.`status` != 30)

Operators not translatable to SQL are available too (such as group below). Bmg fallbacks to memory operators for them, but remains capable of pushing some operators down the tree as illustrated below (the restriction on :city is pushed to the SQL server):

Bmg.sequel(:suppliers, sequel_db)
  .project([:sid, :name, :city])
  .group([:sid, :name], :suppliers_in)
  .restrict(city: ["Paris", "London"])

# (group
#   (sequel SELECT `t1`.`sid`, `t1`.`name`, `t1`.`city` FROM `suppliers` AS 't1' WHERE (`t1`.`city` IN ('Paris', 'London')))
#   [:sid, :name, :status]
#   :suppliers_in
#   {:array=>false})

Reading files (csv, excel, text)

Bmg provides simple adapters to read files and reach Relationland as soon as possible.

CSV files

csv_options = { col_sep: ",", quote_char: '"' }
r = Bmg.csv("path/to/a/file.csv", csv_options)

Options are directly transmitted to, check ruby's standard library.

Excel files

You will need to add roo to your Gemfile to read .xls and .xlsx files with Bmg.

roo_options = { skip: 1 }
r = Bmg.excel("path/to/a/file.xls", roo_options)

Options are directly transmitted to, check roo's documentation.

Text files

There is also a straightforward way to read text files and convert lines to tuples.

r = Bmg.text_file("path/to/a/file.txt")
# => [:line, :text]

Without options tuples will have :line and :text attributes, the former being the line number (starting at 1) and the latter being the line itself (stripped).

The are a couple of options (see Bmg::Reader::Textfile). The most useful one is the use a of a Regexp with named captures to automatically extract attributes:

r = Bmg.text_file("path/to/a/file.txt", parse: /GET (?<url>([^\s]+))/)
# => [:line, :url]

In this scenario, non matching lines are skipped. The :line attribute keeps being used to have at least one candidate key (so to speak).

Your own relations

As noted earlier, Bmg has a simple relation interface where you only have to provide an iteration of symbolized tuples.

class MyRelation
  include Bmg::Relation

  def each
    yield(id: 1, name: "Alf", year: 2014)
    yield(id: 2, name: "Bmg", year: 2018)
  .restrict(, 2015))

As shown, creating adapters on top of various data source is straighforward. Adapters can also participate to query optimization (such as pushing restrictions down the tree) by overriding the underscored version of operators (e.g. _restrict).

Have a look at Bmg::Algebra for the protocol and Bmg::Sql::Relation for an example. Keep in touch with the team if you need some help.

Supported operators

r.allbut([:a, :b, ...])                      # remove specified attributes
r.autowrap(split: '_')                       # structure a flat relation, split: '_' is the default
r.autosummarize([:a, :b, ...], x: :sum)      # (experimental) usual summarizers supported
r.constants(x: 12, ...)                      # add constant attributes (sometimes useful in unions)
r.extend(x: ->(t){ ... }, ...)               # add computed attributes
r.exclude(predicate)                         # shortcut for restrict(!predicate)[:a, :b, ...], :x)                   # relation-valued attribute from attributes
r.image(right, :x, [:a, :b, ...])            # relation-valued attribute from another relation
r.join(right, [:a, :b, ...])                 # natural join on a join key
r.join(right, :a => :x, :b => :y, ...)       # natural join after right reversed renaming
r.left_join(right, [:a, :b, ...], {...})     # left join with optional default right tuple
r.left_join(right, {:a => :x, ...}, {...})   # left join after right reversed renaming
r.matching(right, [:a, :b, ...])             # semi join, aka where exists
r.matching(right, :a => :x, :b => :y, ...)   # semi join, after right reversed renaming
r.not_matching(right, [:a, :b, ...])         # inverse semi join, aka where not exists
r.not_matching(right, :a => :x, ...)         # inverse semi join, after right reversed renaming[[:a, :asc], ...], 12, page_size: 10) # paging, using an explicit ordering
r.prefix(:foo_, but: [:a, ...])              # prefix kind of renaming
r.project([:a, :b, ...])                     # keep specified attributes only
r.rename(a: :x, b: :y, ...)                  # rename some attributes
r.restrict(a: "foo", b: "bar", ...)          # relational restriction, aka where
r.rxmatch([:a, :b, ...], /xxx/)              # regex match kind of restriction
r.summarize([:a, :b, ...], x: :sum)          # relational summarization
r.suffix(:_foo, but: [:a, ...])              # suffix kind of renaming
t.transform(:to_s)                           # all-attrs transformation
t.transform(&:to_s)                          # similar, but Proc-driven
t.transform(:foo => :upcase, ...)            # specific-attrs tranformation
t.transform([:to_s, :upcase])                # chain-transformation
r.union(right)                               # relational union
r.where(predicate)                           # alias for restrict(predicate)

How is this different?

... from similar libraries?

  1. The libraries you probably know (Sequel, Arel, SQLAlchemy, Korma, jOOQ, etc.) do not implement a genuine relational algebra. Their support for chaining relational operators is thus limited (restricting your expression power and/or raising errors and/or outputting wrong or counterintuitive SQL code). Bmg always allows chaining operators. If it does not, it's a bug.

    For instance the expression below is 100% valid in Bmg. The last where clause applies to the result of the summarize (while SQL requires a HAVING clause, or a SELECT ... FROM (SELECT ...) r).

      .summarize(...)   # aka group by
  2. Bmg supports in memory relations, json relations, csv relations, SQL relations and so on. It's not tight to SQL generation, and supports queries accross multiple data sources.

  3. Bmg makes a best effort to optimize queries, simplifying both generated SQL code (low-level accesses to datasources) and in-memory operations.

  4. Bmg supports various structuring operators (group, image, autowrap, autosummarize, etc.) and allows building 'non flat' relations.

  5. Bmg can use full ruby power when that helps (e.g. regular expressions in WHERE clauses or ruby code in EXTEND clauses). This may prevent Bmg from delegating work to underlying data sources (e.g. SQL server) and should therefore be used with care though.

... from Alf?

If you use Alf (or used it in the past), below are the main differences between Bmg and Alf. Bmg has NOT been written to be API-compatible with Alf and will probably never be.

  1. Bmg's implementation is much simpler than Alf and uses no ruby core extention.

  2. We are confident using Bmg in production. Systematic inspection of query plans is advised though. Alf was a bit too experimental to be used on (critical) production systems.

  3. Alf exposes a functional syntax, command line tool, restful tools and many more. Bmg is limited to the core algebra, main Relation abstraction and SQL generation.

  4. Bmg is less strict regarding conformance to relational theory, and may actually expose non relational features (such as support for null, left_join operator, etc.). Sharp tools hurt, use them with care.

  5. Unlike Alf::Relation instances of Bmg::Relation capture query-trees, not values. Currently two instances r1 and r2 are not equal even if they define the same mathematical relation. As a consequence joining on relation-valued attributes does not work as expected in Bmg until further notice.

  6. Bmg does not implement all operators documented on, even if we plan to eventually support most of them.

  7. Bmg has a few additional operators that prove very useful on real production use cases: prefix, suffix, autowrap, autosummarize, left_join, rxmatch, etc.

  8. Bmg optimizes queries and compiles them to SQL on the fly, while Alf was building an AST internally first. Strictly speaking this makes Bmg less powerful than Alf since optimizations cannot be turned off for now.


Please use github issues and pull requests for all questions, bug reports, and contributions. Don't hesitate to get in touch with us with an early code spike if you plan to add non trivial features.


This software is distributed by Enspirit SRL under a MIT Licence. Please contact Bernard Lambeau ( with any question.

Enspirit ( and Klaro App ( are both actively using and contributing to the library.


Bmg, Alf's successor, A Ruby Relational Algebra




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