Intermediate Representation (IR)

This crate contains the intermediate representation for AirScript, AirIR.

The purpose of the AirIR is to provide a simple and accurate representation of an AIR that allows for optimization and translation to constraint evaluator code in a variety of target languages.

Generating the AirIR

Generate an AirIR from an AirScript AST (the output of the AirScript parser) using the from_source method. The from_source method will return a new AirIR or an Error of type SemanticError if it encounters any errors while processing the AST.

The from_source method will first iterate through the source sections that contain declarations to build a symbol table with trace columns, public inputs, and periodic columns. It will return a SemanticError if it encounters a duplicate, incorrect, or missing declaration. Once the symbol table is built, the constraints in the boundary_constraints and transition_constraints sections of the AST are processed. Finally, from_source returns a Result containing the AirIR or a SemanticError.

Example usage:

```Rust // parse the source string to a Result containing the AST or an Error let ast = parse(source.as_str()).expect("Parsing failed");

// process the AST to get a Result containing the AirIR or an Error let ir = AirIR::from_source(&ast) ```

AirIR

Although generation of an AirIR uses a symbol table while processing the source AST, the internal representation only consists of the following:

• Name of the AIR definition represented by the AirIR.
• Public inputs, represented by a vector that maps an identifier to a size for each public input that was declared. (Currently, public inputs can only be declared as fixed-size arrays.)
• Periodic columns, represented by an ordered vector that contains each periodic column's repeating pattern (as a vector).
• Boundary constraints, stored as mappings from trace column indices to expressions, with a separate mapping for each boundary (first and last) of each trace segment (main and auxiliary).
• Transition constraints, represented by the combination of:
  • a directed acyclic graph (DAG) without duplicate nodes.
  • a vector of NodeIndex for each of the main and auxiliary trace segments, which contains the node index in the graph where each of the respective trace segment's constraints starts.