Lambda Calculator - Entering Special Symbols

When using the Lambda Calculator, you will be asked to enter predicate logic expressions. You can use the guide below to enter special symbols not found on your keyboard.

Constants and Variables

• Primes can be entered with the apostrophe.
• To use subscript notation to indicate the type of a constant or variable, such as x_e, use an underscore, e.g.

  x_e
  P_<e,t>

Logical Connectives

• To enter some of the logical connectives, you hit a particular key or multiple keys on your keyboard but a different symbol appears on screen:

  Connective	You Type
  ¬	~
  ≠	!=
  ∧	& or ^
  →	->
  ↔	<->
  ⊕	+
  ⊑	<:

• Other connectives require that you hold down either the ALT key on Windows and Linux computers or the CONTROL key on Macintosh computers while pressing another key:

  Connective	You Type
  ∨	ALT/CONTROL + V

Quantifiers and Other Binders

• Quantifiers and other binders require that you hold down either the ALT key on Windows and Linux computers or the CONTROL key on Macintosh computers while pressing another key:

  Quantifier	You Type
  ∃	ALT/CONTROL + E
  ∀	ALT/CONTROL + A
  λ	ALT/CONTROL + L
  ι	ALT/CONTROL + I

Sets

• The set operators require that you hold down SHIFT and either the ALT key on Windows and Linux computers or the CONTROL key on Macintosh computers while pressing another key:

  Operator	You Type
  ∩	ALT/CONTROL + SHIFT + ^
  ∪	ALT/CONTROL + SHIFT + V
  ⊆	ALT/CONTROL + < (i.e. SHIFT+,)
  ⊇	ALT/CONTROL + > (i.e. SHIFT+.)

• Some more complicated set operators require typing multiple keys:

  Operator	You Type
  ⊈	!, then ALT/CONTROL + <
  ⊊	type ALT/CONTROL + < twice
  ⊉	!, then ALT/CONTROL + >
  ⊋	type ALT/CONTROL + > twice

• The empty set symbol ∅ can be entered by pressing ALT/CONTROL plus 0 (zero).

Numeric Connectives

• Numeric connectives are available as well. You just type the usual keys:

  Connective	You Type
  ⋅	*	(multiplication)
  <	<
  ≤	<=
  >	>
  ≥	>=