flat \(\mathrm{flat}\) — Flat Proper Values Predicate (flat, AST Constructor: TpFlat)
Unary predicate asserting that proper-class fibers of F are stored directly via their elements (Entry DefFlatValues (3.30)).
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
flat
\(\mathrm{flat}\)
|
| Category | Predicate Symbol (Unary Class Predicate) |
| SML AST Constructor | HP (TpFlat of 'Class_EXP) [in datatype Truth_p, typetheory.ML:672] |
| Constructor Arguments | 1. Relation class F : Class |
| Metatype / Signature | Class → Bool |
| Binder Status | No — Unary Predicate Symbol |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | \mathrm{flat} |
| How to Understand It | SML AST Constructor: |
| Canonical Law / Usage | (F has flat proper values) ⟷ ∀(x∈Dom(F))((F(x) proper) → ∀(y:Class)(((x,y)∈F) ⟷ (y∈F(x)))) |
| Related Symbols & Kernel Entries |