Prop \(\mathsf{Prop}\) — Propositions-as-Types Universe (Prop, MKTD2)
The propositions-as-types universe Prop in Variant 2 (MKTD2), where each proposition A : Prop is a type whose inhabitants are constructive proof terms p : A.
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
Prop
\(\mathsf{Prop}\)
|
| Category | Conglomerate Types & Sorts |
| SML AST Constructor | Kernel AST Symbol / Sort Constructor in typetheory.ML (Class_p / Truth_p / EXP / UCol) |
| Constructor Arguments | Typed arguments as specified by the Signature / Sort field above |
| Metatype / Signature | Type Universe (Variant 2 Propositions-as-Types) |
| Binder Status | See Category & Signature above |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | \mathsf{Prop} |
| How to Understand It | Semantics: In Variant 2 ( |
| Canonical Law / Usage | Π(A : Prop), A → A |
| Related Symbols & Kernel Entries |