Let and Bind

In Hakaru, we can give names for expressions to our programs with =, which we call Let. This gives us the ability to share computation that might be needed in the program.

x = 2
x + 3

We can use = to give a name to any expression in our language. The name you assign is in scope for the rest of the body it was defined in.

Bind

Hakaru also has the operator <~. This operator, which call Bind can only be used with expressions that denote probability distributions. Bind allows us to talk about draws from a distribution using a name for any particular value that could have come from that distribution.

# Bad
x <~ 2 + 3
x

# Good
x <~ normal(0,1)
return x

Because Bind is about draws from a distribution, the rest of the body must also denote a probability distribution.

# Bad
x <~ normal(0,1)
x

# Good
x <~ normal(0,1)
return x

To help distinguish Let and Bind. Here is a probabilistic program, where we let f be equal to the normal distribution, and take draws from f.

f = normal(0,1)
x <~ f
return x*x