A formula extension for tshistory, providing computed series.
funcs/doy: add day of year operations and tests
http: better json representation for the bindings_for api point
2260e91e61b5 draft — Arnaud Campeas 12 days ago
interpreter: remove a pair of prints


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This tshistory component provides a formula language to build computed series.

Formulas are defined using a simple lisp-like syntax, using a pre-defined function library.

Formulas are read-only series (you can't update or replace values).

They also have an history, which is built, time stamps wise, using the union of all constituent time stamps, and value wise, by applying the formula.

Because of this the staircase operator is available on formulae. Some staircase operations can have a very fast implementation if the formula obeys commutativity rules.


#General Syntax

Formulas are expressed in a lisp-like syntax using operators, positional (mandatory) parameters and keyword (optional) parameters.

The general form is:

(<operator> <param1> ... <paramN> #:<keyword1> <value1> ... #:<keywordN> <valueN>)

Here are a couple examples:

  • (add (series "wallonie") (series "bruxelles") (series "flandres"))

Here we see the two fundamental add and series operators at work.

This would form a new synthetic series out of three base series (which can be either raw series or formulas themselves).

Some notes:

  • operator names can contain dashes or arbitrary caracters

  • literal values can be: 3 (integer), 5.2 (float), "hello" (string) and #t or #f (true ot false)

#Pre-defined operators


Performs a scalar product on a series.

Example: (* -1 (series "positive-things"))


Add a constant quantity to a series.

Example: (+ 42 (series "i-feel-undervalued"))


Perform a scalar division between numbers or a series and a scalar.

Example: (/ (series "div-me") (/ 3 2))


Linear combination of two or more series. Takes a variable number of series as input.

Example: (add (series "wallonie") (series "bruxelles") (series "flandres"))

To specify the behaviour of the add operation in the face of missing data, the series can be built with the fill keyword. This option is only really applied when several series are combined. By default, if an input series has missing values for a given time stamp, the resulting series has no value for this timestamp (unless a fill rule is provided).


Set an upper/lower threashold for a series. Takes a series as positional parameter and accepts two optional keywords min and max which must be numbers (integers or floats).

Example: (clip (series "must-be-positive") #:min 0)


Produces an utc timestamp from its input string date in iso format.

The tz keyword allows to specify an alternate time zone. The naive keyword forces production of a naive timestamp. Both tz and naive keywords are mutually exlcusive.


Element wise division of two series.

Example: (div (series "$-to-€") (series "€-to-£"))


Computes the row-wise minimum of its input series.

Example: (min (series "station0") (series "station1") (series "station2"))


Computes the row-wise maximum of its input series.

Example: (max (series "station0") (series "station1") (series "station2"))


Element wise multiplication of series. Takes a variable number of series as input.

Example: (mul (series "banana-spot-price ($)") (series "$-to-€" #:fill 'ffill'))

This might convert a series priced in dollars to a series priced in euros, using a currency exchange rate series with a forward-fill option.


Allow demoting a series from a tz-aware index (strongly recommended) to a tz-naive index (unfortunately sometimes unavoidable for interop with other tz-naive series).

One must provide a country code and a target timezone.

Example: (naive (series "tz-aware-series-from-poland") "PL" "Europe/Warsaw")


The priority operator combines its input series as layers. For each timestamp in the union of all series time stamps, the value comes from the first series that provides a value.

Example: (priority (series "realized") (series "nominated") (series "forecasted"))

Here realized values show up first, and any missing values come from nominated first and then only from forecasted.


Resamples its input series using freq and the aggregation method method (as described in the pandas documentation).

Example: (resample (series "hourly") "D")


This operator computes the row-wise mean of its input series using the series weight option if present. The missing points are handled as if the whole series were absent.

Example: (row-mean (series "station0") (series "station1" #:weight 2) (series "station2"))

Weights are provided as a keyword to series. No weight is interpreted as 1.


The series operator accepts several keywords:

  • fill to specify a filling policy to avoid nans when the series will be added with others; accepted values are "ffill" (forward-fill), "bfill" (backward-fill) or any floating value.

For instance in (add (series "a" #:fill 0) (series "b") will make sure that series a, if shorter than series b will get zeroes instead of nans where b provides values.


This allows cutting a series at date points. It takes one positional parameter (the series) and two optional keywords fromdate and todate which must be strings in the iso8601 format.

Example: (slice (series "cut-me") #:fromdate "2018-01-01")


Computes the standard deviation over its input series.

Example: (std (series "station0") (series "station1") (series "station2"))


Takes a timestamp and a number of years, months, weekds, days, hours, minutes (int) and computes a new date according to the asked delta elements.

Example: (timedelta (date "2020-1-1") #:weeks 1 #:hours 2)


Produces a timezone-aware timestamp as of today

The tz keyword allows to specify an alternate time zone. The naive keyword forces production of a naive timestamp. Both tz and naive keywords are mutually exlcusive.

Example: (today)

#Registering new operators

This is a fundamental need. Operators are fixed python functions exposed through a lispy syntax. Applications need a variety of fancy operators.

#declaring a new operator

One just needs to decorate a python with the func decorator:

from tshistory_formula.registry import func

  def identity(series):
      return series

The operator will be known to the outer world by the name given to @func, not the python function name (which can be arbitrary).

This is enough to get a working transformation operator. However operators built to construct series rather than just transform pre-existing series are more complicated.

#custom series operator

We start with an example, a shifted operator that gets a series with shifted from_value_date/to_value_date boundaries by a constant delta amount.

We would use it like this: (shifted "shiftme" #:days -1)

As we can see the standard series operator won't work there, that is applying a shift operator ((shift (series "shiftme"))) after the call to series is too late. The from/to implicit parameters have already been handled by series itself and there is nothing left to shift.

Hence shifted must be understood as an alternative to series itself. Here is a possible implementation:

from tshistory_formula.registry import func, finder

  def shifted(__interpreter__, name, days=0):
      args = __interpreter__.getargs.copy()
      fromdate = args.get('from_value_date')
      todate = args.get('to_value_date')
      if fromdate:
          args['from_value_date'] = fromdate + timedelta(days=days)
      if todate:
          args['to_value_date'] = todate + timedelta(days=days)

      return __interpreter__.get(name, args)

  def find_series(cn, tsh, tree):
      return {
          tree[1]: tsh.metadata(cn, tree[1])

As we can see, we use a new finder protocol. But first let's examine how the shiftme operator is implemented.

First it takes a special __interpreter__ parameter, which will receive the formula interpreter object, providing access to an important internal API of the evaluation process.

Indeed from the interpreter we can read the getargs attribute, which contains a dictionary of the actual query mapping. We are specially interested in the from_value_date and to_value_date items in our example, but all the parameters of tshistory.get are available there.

Once we have shifted the from/to value date parameter we again use the interpreter to make a call to get which will in turn perform a call to the underlying tshistory.get (which, we don't know in advance, may yield a primary series or another formula computed series).

Implementing the operator this way, we actually miss two important pieces of information:

  • the system cannot determine a series is produced by the shifted operator like it can with series

  • and because of this it cannot know the technical metadata of the produced series (e.g. the tzaware attribute)

This is where the finder protocol and its decorator function comes into play. For shifted we define a finder. It is a function that takes the db connection (cn), time series protocol handler (tsh) and formula syntax tree (tree), and must return a mapping from series name to its metadata.

The tree is an obvious Python data structure representing a use of the operator in a formula.

For instance because of the shifted python signature, any use will be like that:

  • in lisp ... (shifted "shift-me" #:hours +1) ... (the dots indicate that it can be part of a larger formula)

  • tree in python: ['shifted', "shift-me", 'hours', 1]

The name is always in position 1 in the list. Hence the implementation of the shifted finder:

return {
          tree[1]: tsh.metadata(cn, tree[1])

For the metadata we delegate the computation to the underlying series metadata.

We might want to provide an ad-hoc metadata dictionary if we had a proxy operator that would forward the series from an external source:

  def proxy(
          series_uid: str,
          default_start: date,
          default_end : date) -> pd.Series:
      i = __interpreter__
      args = i.getargs.copy()
      from_value_date = args.get('from_value_date') or default_start
      to_value_date = args.get('to_value_date') or default_end

      proxy = ProxyClient()
      return proxy.get(

  def proxy(cn, tsh, tree):
      return {
          tree[1]: {
              'index_type': 'datetime64[ns]',
              'tzaware': False,
              'value_type': 'float64'

Here, because we have no other means to know (and the proxy provides some useful documentation), we write the metadata ourselves explicitly.

Also note how accessing the __interpreter__ again is used to forward the query arguments.

#Editor Infos

The tshistory_formula package provides a custom callback for the editor capabilities of tshistory_editor.

A dedicated protocol is available to inform the editor on the way to decompose/display a formula.

Example of such a function:

from tshistory_formula.registry import editor_info

 def operator_with_series(builder, expr):
     for subexpr in expr[1:]:
         with builder.series_scope(subexpr):

The exact ways to use the builder will be provided soon.

#Series API

A few api calls are added to the tshistory base:

  • .register_formula to define a formula

  • .eval_formula to evaluate on-the-fly a formula (useful to check that it computes before registering it)



      '(* 3.14 (series "going-round"))'



>>> tsa.eval_formula('(* 3.14 (series "going-round"))')
 2020-01-01    3.14
 2020-01-02    6.28
 2020-01-03    9.42
 dtype: float64

#Command line

The tsh command carries formula specific subcommands. The output below shows only the specific formula subcommands:

$ tsh
Usage: tsh [OPTIONS] COMMAND [ARGS]...

  --help  Show this message and exit.

  ingest-formulas           ingest a csv file of formulas Must be a...