Mathematical constant providers
Core expression arithmetic promotes supported scalar values into constant nodes. .ExpressionConstant(value) explicitly constructs one, and .ExpressionConstantInfo(value) accepts either a scalar or a constant node. It inspects capabilities without evaluating an expression or refining a real.
e := ::x + (0:1);
.ExpressionConstantInfo(e.Operands()[2])[:denotation] ##@ == :setEnclosure;
.ExpressionHasExtendedConstants(e) ##@ == 1;
.ExpressionConstant(0:1)==(2:3) ##@ == _;
.ExpressionConstant(1:1)==1 ##@ == 1;
p := 1~{pi};
.ExpressionConstantInfo(p)[:provider] ##@ == :exactScalar;
.ExpressionConstant(p)==p ##@ == 1;
.ExpressionConstant(p)!=_ ##@ == 1;Supported providers
| Provider | Denotation | Available laws |
|---|---|---|
| Finite Integer/Rational | Exact singleton | Commutative, associative, distributive; cancellation with its ordinary nonzero precondition |
| Bounded RationalInterval | Set enclosure, even when endpoints coincide | Addition/multiplication are commutative and associative; no general distributivity or cancellation |
| Core exact generator/expression | Exact scalar | Commutative, associative, distributive; cancellation undecided |
| Explicit adapted singleton real | Singleton with certified enclosure and procedure | Real scalar laws, subject to the provider’s singleton guarantee |
These are laws of the provider’s addition and multiplication, not blanket claims about division, exponentiation, or partially defined expressions. User-defined exact polynomial quotients need not be fields, so cancellation is deliberately ? for exact scalars. 1~{pi} uses the core exact scalar registry; it is not a numerical approximation to pi or a refinement oracle.
The inspection record has schema rix.math.constant-provider@1, provider, denotation, exact, refinable, commutative, associative, distributive, cancellation, and enclosure. Decisions use 1, _, or ?. The refinable flag is _ for the rational, interval, and exact-generator adapters, including trivially exactly known rationals. Explicit real adapters return 1. Intervals expose their unchanged oriented enclosure; adapted reals expose their accumulated enclosure. Rational and exact-generator providers return _ in that field. Unsupported objects and nonfinite rational components error instead of acquiring inferred capabilities from a schema label.
Equality and structural identity
_ is absence, not an unresolved mathematical value. Expressions compare unequal to _, preserving ordinary optional-result and diagnostic checks.
Overlapping nonsingleton interval constants compare as ?, including two identical interval records. Disjoint interval constants compare unequal, and matching point intervals can establish equality. General expression trees containing intervals remain undecided; structural matching must not become a proof about unknown values in an enclosure.
Exact constant equality uses the core exact scalar normal forms. Matching forms prove equality; different generator forms remain undecided rather than claiming mathematical inequality. Two distinct generators with the same display name have different structural keys. Constants’ keys are built from rational components, oriented endpoints, generator IDs, and term powers—not display strings. Keys are session-local structural data, not saved-file IDs.
Remaining adapters and consumer work
The explicit refinable-real adapter uses the Numerics protocol; merely wrapping a map with a real-looking schema is not supported. Physical quantities need dimension-aware operations; quaternion/octonion values need their own noncommutative/nonassociative laws. They are not included by accepting the unrelated commutative core exact-generator representation.
The old calculus/CAS and range/specification paths reject extended constants until their provider-aware conversion lands. Rational-only plugin expressions still work. Core construction and inspection work without loading a plugin. Portable mathematical serialization is a separate stage.