An Introduction to Functional Programming Through Lambda Calculus

- 224 -λx.(not (not (not x))) true => ... =>not (not (not true)) => ... =>((not (not true)) false true) => ... =>((not true) false true) false true => ... =>((true false true) false true) false true => ... =>(false false true) false true => ... =>true false true => ... => falseiv)a) - see 1) aboveb) λx.λy.(not (and x (not y))) false false => ... =>not (and false (not false)) => ... =>(and false (not false)) false true => ... =>(false (not false) false) false true) => ... =>false false true => ... => trueλx.λy.(not (and x (not y))) false true => ... =>not (and false (not true)) => ... =>(and false (not true)) false true => ... =>(false (not true) false) false true => ... =>false false true => ... => trueλx.λy.(not (and x (not y))) true false => ... =>not (and true (not false)) => ... =>(and true (not false)) false true => ... =>(true (not false) false) false true => ... =>(not false) false true => ... =>true false true => ... => falseλx.λy.(not (and x (not y))) true true => ... =>not (and true (not true)) => ... =>(and true (not true)) false true => ... =>(true (not true) false) false true => ... =>(not true) false true => ... =>false false true => ... => truev) a) - see 2) aboveb) λx.λy.(and (implies x y) (implies y x)) false false => ... =>and (implies false false) (implies false false) => ... =>(implies false false) (implies false false) false => ... =>(false false true) (implies false false) false => ... =>true (implies false false) false => ... =>implies false false => ... =>false false true => ... => trueλx.λy.(and (implies x y) (implies y x)) false true => ... =>and (implies false true) (implies true false)(implies false true) (implies true false) false => ... =>(false true true) (implies true false) false => ... =>true (implies true false) false => ... =>implies true false => ... =>true false false => ... => falseλx.λy.(and (implies x y) (implies y x)) true false => ... =>and (implies true false) (implies false true)(implies true false) (implies false true) false => ... =>(true false true) (implies false true) false => ... =>