Symbol Reference: Variable / Expression / Name — Syntactic Variable & Class-Expression AST Sorts

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Variable / Expression / Name \(\mathsf{Variable} \; / \; \mathsf{Expression} \; / \; \mathsf{Name}\) — Syntactic Variable & Class-Expression AST Sorts

Variable (or Name) is the sort of syntactic variable identifiers; Expression is the sort of syntactic class terms interpreted by μ_A : Expression → Class.

Field Mathematical & Kernel Specification (MKTD1 / MKTD2)
Symbol
Variable / Expression / Name
\(\mathsf{Variable} \; / \; \mathsf{Expression} \; / \; \mathsf{Name}\)
Category Metatheoretic AST 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 Syntactic Sorts (Reflection Layer)
Binder Status See Category & Signature above
Defining Kernel Entries (ML Labels) See Related Symbols & Kernel Entries below.
LaTeX Form \mathsf{Variable} \; / \; \mathsf{Expression} \; / \; \mathsf{Name}
How to Understand It

In Section 4 (Metalogical Laws, Entries DefMetaInstantiation (4.01)–AxmMetaClassComprehension (4.06)), meta-quantification distinguishes between object classes (x : Class), syntactic variable names (v : Variable), and syntactic class expressions (e : Expression):

  • A syntactic variable v : Variable can be checked for freshness (NFV(e, v)) and bound in comprehension schemas.
  • A syntactic expression e : Expression is evaluated into a semantic class via μ_A(e) : Class or coded into a class via Enc(e) : Class.
Canonical Law / Usage ∀(v:Variable). ∀(e:Expression). (μ_A(e) : Class)
Related Symbols & Kernel Entries