diff options
Diffstat (limited to 'lambda-calculus.html.markdown')
| -rw-r--r-- | lambda-calculus.html.markdown | 9 |
1 files changed, 7 insertions, 2 deletions
diff --git a/lambda-calculus.html.markdown b/lambda-calculus.html.markdown index 3d080de7..53a7a7cd 100644 --- a/lambda-calculus.html.markdown +++ b/lambda-calculus.html.markdown @@ -85,7 +85,7 @@ Using `IF`, we can define the basic boolean logic operators: `a OR b` is equivalent to: `λab.IF a T b` -`a NOT b` is equivalent to: `λa.IF a F T` +`NOT a` is equivalent to: `λa.IF a F T` *Note: `IF a b c` is essentially saying: `IF((a b) c)`* @@ -111,7 +111,7 @@ we use the successor function `S(n) = n + 1` which is: Using successor, we can define add: -`ADD = λab.(a S)n` +`ADD = λab.(a S)b` **Challenge:** try defining your own multiplication function! @@ -139,6 +139,7 @@ Take the church number 2 for example: `2 = λf.λx.f(f x)` For the inner part `λx.f(f x)`: + ``` λx.f(f x) = S (λx.f) (λx.(f x)) (case 3) @@ -147,6 +148,7 @@ For the inner part `λx.f(f x)`: ``` So: + ``` 2 = λf.λx.f(f x) @@ -156,6 +158,7 @@ So: ``` For the first argument `λf.(S (K f))`: + ``` λf.(S (K f)) = S (λf.S) (λf.(K f)) (case 3) @@ -164,6 +167,7 @@ For the first argument `λf.(S (K f))`: ``` For the second argument `λf.(S (K f) I)`: + ``` λf.(S (K f) I) = λf.((S (K f)) I) @@ -174,6 +178,7 @@ For the second argument `λf.(S (K f) I)`: ``` Merging them up: + ``` 2 = S (λf.(S (K f))) (λf.(S (K f) I)) |