Fresh \(\mathrm{Fresh}\) — Variable Freshness Hygiene Predicate (Fresh)
Metalevel-1 syntactic hygiene predicate asserting that a variable name does not occur in a given syntactic expression or context.
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
Fresh
\(\mathrm{Fresh}\)
|
| Category | Predicate Symbol (Metatheoretic Side-Condition Predicate) |
| 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 | Variable × A.Expression → Bool |
| Binder Status | See Category & Signature above |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | \mathrm{Fresh} |
| How to Understand It | Semantics: Ensures absence of variable collisions when introducing fresh binder variables in metatheoretic rules. |
| Canonical Law / Usage | Fresh(v, 𝛗) |
| Related Symbols & Kernel Entries |