Appendix: Binary compute_signature

When an OpDef provides a binary compute_signature function, and an operation node uses that OpDef:

• the node provides a list of TypeArgs, at least as many as the \(n\) TypeParams declared by the OpDef

• the first \(n\) of those are passed to the binary compute_signature

• if the binary function returns an error, the operation is invalid;

• otherwise, compute_signature returns a type scheme (which may itself be polymorphic)

• any remaining TypeArgs in the node (after the first \(n\)) are then substituted into that returned type scheme (the number remaining in the node must match exactly). Note this allows the binary function to use the values (TypeArgs) passed in—e.g. by looking inside List or Opaque TypeArgs—to determine the structure (and degree of polymorphism) of the returned type scheme.

• We require that the TypeArgs to be passed to compute_signature (the first \(n\)) must not refer to any type variables (declared by ancestor nodes in the Hugr - the nearest enclosing FuncDefn); these first \(n\) must be static constants unaffected by substitution. This restriction does not apply to TypeArgs after the first \(n\).