Expressions Overview

What is an Expression?

Hail’s expressions are lazy representations of data.

Each data type in Hail has its own Expression class. For example, an Int32Expression represents a 32-bit integer, and a BooleanExpression represents a boolean value of True or False.

>>> hl.int32(5)
<Int32Expression of type int32>
>>> hl.bool(True)
<BooleanExpression of type bool>

Expressions can be combined with operations to form new expressions. Much like you would add two integers in Python, you can also add two Int32Expression objects in Hail.

>>> hl.int32(5) + hl.int32(6)
<Int32Expression of type int32>

The result of adding two Int32Expression objects is another Int32Expression object.

We say Hail’s expressions are lazy, because they are not evaluated until the result of the expression is needed. Let’s explore what this means by comparing a Python expression to a Hail expression.

In Python, an expression such as 5+6 will be immediately evaluated. If you enter this expression into Python, you’ll see the result, 11, right away.

>>> x = 5
>>> y = 6
>>> z = x + y
>>> z

The equivalent code written with Hail’s expressions would look like:

>>> x = hl.int32(5)
>>> y = hl.int32(6)
>>> z = x + y
>>> z
<Int32Expression of type int32>

Notice that when we enter z, we don’t see the result, 11, like we did with Python. Hail is not running Python code on your data. Instead, Hail is keeping track of the computations applied to your data, compiling these computations into native code, and running them in parallel.

The result of the expression is computed only when it is needed. So z is an expression representing the computation of x + y, but not the actual value.

To peek at the value of this computation, there are two options: eval(), which returns a Python value, and, which prints a human-readable representation of an expression.

>>> hl.eval(z)
| <expr> |
|  int32 |
|     11 |

Hail’s expressions are especially important for interacting with fields in tables and matrix tables. Throughout Hail documentation and tutorials, you will see code like this:

>>> ht2 = ht.annotate(C4 = ht.C3 + 3 * ht.C2 ** 2)

This snippet of code is adding a field, C4, to a table, ht, and returning the result as a new table, ht2. The code passed to the Table.annotate() method is an expression that references the fields C3 and C2 in ht.

Notice that 3 and 2 are not wrapped in constructor functions like hl.int32(3). In the same way that Hail expressions can be combined together via operations like addition and multiplication, they can also be combined with Python objects.

For example, we can add a Python int to an Int32Expression.

>>> x + 3
<Int32Expression of type int32>

Addition is commutative, so we can also add an Int32Expression to an int.

>>> 3 + x
<Int32Expression of type int32>

Note that Hail expressions cannot be used in other modules, like numpy or scipy.

Hail has many subclasses of Expression – one for each Hail type. Each subclass has its own constructor method. For example, if we have a list of Python integers, we can convert this to a Hail ArrayNumericExpression with array():

>>> a = hl.array([1, 2, -3, 0, 5])
>>> a
<ArrayNumericExpression of type array<int32>>

Expression objects keep track of their data type, which is why we can see that a is of type array<int32> in the output above. An expression’s type can also be accessed with Expression.dtype().

>>> a.dtype

Hail arrays can be indexed and sliced like Python lists or numpy arrays:

>>> a[1]
<Int32Expression of type int32>
>>> a[1:-1]
<ArrayNumericExpression of type array<int32>>

In addition to constructor methods like array() and bool(), Hail expressions can also be constructed with the literal() method, which will impute the type of of the expression.

>>> hl.literal([0,1,2])
<ArrayNumericExpression of type array<int32>>

Boolean Logic

Unlike Python, a Hail BooleanExpression cannot be used with the Python keywords and, or, and not. The Hail substitutes are &, |, and ~.

>>> s1 = hl.int32(3) == 4
>>> s2 = hl.int32(3) != 4
>>> s1 & s2
<BooleanExpression of type bool>
>>> s1 | s2
<BooleanExpression of type bool>
>>> ~s1
<BooleanExpression of type bool>

Remember that you can use eval(): to evaluate the expression.

>>> hl.eval(~s1)


The operator precedence of & and | is different from and and or. You will need parentheses around expressions like this:

>>> (x == 3) & (x != 4)

Conditional Expressions

If/Else Statements

Python if / else statements do not work with Hail expressions. Instead, you must use the if_else(), case(), and switch() functions.

A conditional expression has three components: the condition to evaluate, the consequent value to return if the condition is True, and the alternate to return if the condition is False. For example:

if (x > 0):
    return 1
    return 0

In the above conditional, the condition is x > 0, the consequent is 1, and the alternate is 0.

Here is the Hail expression equivalent with if_else():

>>> hl.if_else(x > 0, 1, 0)
 <Int32Expression of type int32>

This example returns an Int32Expression which can be used in more computations. We can add the conditional expression to our array a from earlier:

>>> a + hl.if_else(x > 0, 1, 0)
<ArrayNumericExpression of type array<int32>>

Case Statements

More complicated conditional statements can be constructed with case(). For example, we might want to return 1 if x < -1, 2 if -1 <= x <= 2 and 3 if x > 2.

>>> (
...   .when(x < -1, 1)
...   .when((x >= -1) & (x <= 2), 2)
...   .when(x > 2, 3)
...   .or_missing())
<Int32Expression of type int32>

Notice that this expression ends with a call to or_missing(), which means that if none of the conditions are met, a missing value is returned.

Cases started with case() can end with a call to or_missing(), default(), or or_error(), depending on what you want to happen if none of the when clauses are met.

It’s important to note that missingness propagates up in Hail, so if the value of the discriminant in a case statement is missing, then the result will be missing as well.

>>> y = hl.null(hl.tint32)
>>> result = > 0, 1).default(-1)
>>> hl.eval(result)

The value of result will be missing, not 1 or -1, because the discriminant, y, is missing.

Switch Statements

Finally, Hail has the switch() function to build a conditional tree based on the value of an expression. In the example below, csq is a StringExpression representing the functional consequence of a mutation. If csq does not match one of the cases specified by when(), it is set to missing with or_missing(). Other switch statements are documented in the SwitchBuilder class.

>>> csq = hl.str('nonsense')
>>> (hl.switch(csq)
...    .when("synonymous", False)
...    .when("intron", False)
...    .when("nonsense", True)
...    .when("indel", True)
...    .or_missing())
<BooleanExpression of type bool>

As with case statements, missingness will propagate up through a switch statement. If we changed the value of csq to the missing value hl.null(hl.tstr), then the result of the switch statement above would also be missing.


In Hail, all expressions can be missing. An expression representing a missing value of a given type can be generated with the null() function, which takes the type as its single argument.

An example of generating a Float64Expression that is missing is:

>>> hl.null('float64')
<Float64Expression of type float64>

These can be used with conditional statements to set values to missing if they don’t satisfy a condition:

>>> hl.if_else(x > 2.0, x, hl.null(hl.tfloat))
<Float64Expression of type float64>

The Python representation of a missing value is None. For example, if we define cnull to be a missing value with type tcall, calling the method is_het will return None and not False.

>>> cnull = hl.null('call')
>>> hl.eval(cnull.is_het())


In addition to the methods exposed on each Expression, Hail also has numerous functions that can be applied to expressions, which also return an expression.

Take a look at the Functions page for full documentation.