Symbol Reference: IF ๐›™ THEN A ELSE B FI — Class Conditional Functional Symbol (IF..THEN..ELSE..FI, AST Constructor: CpIf)

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IF ๐›™ THEN A ELSE B FI \(\mathrm{IF}\;\psi\;\mathrm{THEN}\;A\;\mathrm{ELSE}\;B\;\mathrm{FI}\) — Class Conditional Functional Symbol (IF..THEN..ELSE..FI, AST Constructor: CpIf)

3-ary mixfix class conditional IF ๐›™ THEN A ELSE B FI defined by class comprehension (Entry DefClassConditional (3.22)). Clicking any of IF, THEN, ELSE, or FI navigates to this single symbol page.

Field Mathematical & Kernel Specification (MKTD1 / MKTD2)
Symbol
IF ๐›™ THEN A ELSE B FI
\(\mathrm{IF}\;\psi\;\mathrm{THEN}\;A\;\mathrm{ELSE}\;B\;\mathrm{FI}\)
Category Functional Symbol (3-ary Mixfix Class Operator)
SML AST Constructor HC (CpIf of ('Truth_EXP * 'Class_EXP * 'Class_EXP)) [in datatype Class_p, typetheory.ML:562]
Constructor Arguments 1. Condition ๐›™ : Fm/Bool; 2. Then-class A : Class; 3. Else-class B : Class
Metatype / Signature Bool/Fm ร— Class ร— Class โ†’ Class
Binder Status No โ€” 3-ary Mixfix Functional Symbol (All tokens IF, THEN, ELSE, FI link here)
Defining Kernel Entries (ML Labels) See Related Symbols & Kernel Entries below.
LaTeX Form \mathrm{IF}\;\psi\;\mathrm{THEN}\;A\;\mathrm{ELSE}\;B\;\mathrm{FI}
How to Understand It

SML AST Constructor: HC (CpIf of ('Truth_EXP * 'Class_EXP * 'Class_EXP)) in Class_p (typetheory.ML:562). Takes 3 arguments: condition ๐›™ : Fm/Bool, true-branch A : Class, and false-branch B : Class.

Canonical Law / Usage โŸฆIF โŸฆ๐›™โŸง THEN A ELSE B FIโŸง = {โฆƒvโฆ„ | (โŸฆ๐›™โŸง โˆง (โฆƒvโฆ„โˆˆA)) โˆจ ((ยฌโŸฆ๐›™โŸง) โˆง (โฆƒvโฆ„โˆˆB))}
Related Symbols & Kernel Entries