Type Inference

This code infers the types of all local variables. The main recursive function takes an arbitrary form and returns a form in which the head of each operation has been replaced by a vector [type head].

The types of most forms are determined by rule:

• Numbers and booleans are handled in the obvious way.
• Symbols are looked up in the local symbol table. Because we have no recursion, it is an error if the type of a symbol is not known by the time we ask for it.
• References to other coprocessor functions are resolved by looking them up in the coprocessor's table.
• Envision functions are looked up in the compiler's table of known functions, and their output type determined by rule based on the types of their inputs. The rule system can handle types parameterized by dimensionality.
• Most functions introduced by earlier stages of the compiler are also handled by rule.
• If a form is already headed by a typed operator, type inference accepts that type and simply examines the inputs.

Special type rules are required for forms headed by: begin, set!, multiple-set!, constant-set!, values, while, unary-if, binary-if, make-point, scan, return, no-value (used to drop an output value on the floor), and begin.

In particular, the type of a unary-if statement is unspecified. The type of a binary-if form is the common type of its two clauses if they have the same type, and unspecified otherwise.

When the type of a symbol is first recorded, we might not have complete type information. It might be assigned an integer value when it is really a real. It might be assigned only a missing value. If the value is reset, the information from the two instances is fused. If fusion is impossible, an error is triggered.

In the first pass (step 5a), type inference is run twice. The first time is used to mark types for all the variables. Notice that the type of a variable may be upgraded (e.g. from integer to real) as this proceeds through the code. Type inference is run a second time to add type markings to subforms.

If an integer value is assigned to a real variable, the integer value is converted to a real using exact->inexact.

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