Syntax of the Lambda Calculus (Cont.)


Some examples of lambda expressions are These examples show that the number of parentheses in lambda expressions can become quite large. The following notational conventions allow abbreviations that reduce the number of parentheses:
  1. Uppercase letters and identifiers beginning with capital letters will be used as metavariables ranging over lambda expressions.

  2. Function application associates to the left.
         E1 E2 E3  means  ( ( E1 E2 ) E3 )
  3. The scope of “λ<variable>“ in an abstraction extends as far to the right as possible.
       λx.E1 E2 E3 means (λx.(E1 E2 E3)) and not ((λx.E1 E2) E3)