In duncantl/RTypeInference: Infer Types of Inputs and Outputs for R Expressions

This document examines how type constraints should be generated for assignments.

Every assignment must have a symbol as its write operand [is this true for call assignments?]. Here we'll consider different cases of read operands. In all cases, it's assumed that assignment changes the type of the write symbol, so a new type variable is bound to that symbol and marked as current reaching type.

Literals

x = 3.0

Literals are the most straightforward case because their type is known. A new constraint is added to the system with the literal's type.

Assuming x previously had type x1:

1. The write operand is bound to x2.
2. The reaching type of x is set to x2.
3. The constraint x2 <=> RealType is added to the constraint set.

Symbols

x = y

Symbols are not much more complicated than literals. The write operand is handled as described for literals. The read operand is not mutated, so its type variable does not need to be changed. The constraint $x2 ~ y1$ is added to the constraint set.

[What should happen if y has no reaching type?]

Binary Operations & Calls

x = 3.0 + 4.1

The return type of the call is resolved immediately by the upcasting rules.

Unresolved Types

x = 3.0 + y

Assuming x, y previously had types x1, y1:

1. The write operand is bound to x2.
2. The reaching type of x is set to x2.
3. The constraint x2 <=> UnresolvedCall("+", RealType, y1) is added to the constraint set.

This defers inference for the return type of + until it's demanded by the unification algorithm. When the type is needed, (the hope is that) the type of y1 will already have been inferred.

We may also need to capture the environment the call was made in. For instance, consider this example:

sum = function(...) "Hi, I'm sum!"

sum(4, 3)

Overrides for functions may also occur in an ancestor of the inference environment, and these must be found and handled correctly. Thus lookup for calls needs to proceed from the environment associated with the code.

duncantl/RTypeInference documentation built on Jan. 16, 2021, 12:30 a.m.