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Begin {
(show 'h1 "LOGIC")
(show 'h2 "TRUE/FALSE")
(show 'bool true)
(show 'bool false)
(show 'h2 "NOT")
(show 'bool (not true))
(show 'bool (not false))
(show 'h2 "AND")
(show 'bool ((and true) true))
(show 'bool ((and true) false))
(show 'bool ((and false) true))
(show 'bool ((and false) false))
(show 'h2 "OR")
(show 'bool ((or true) true))
(show 'bool ((or true) false))
(show 'bool ((or false) true))
(show 'bool ((or false) false))
(show 'h1 "CHURCH NUMERALS")
(show 'h2 "ZERO/SUCC")
(show 'nat zero)
(show 'nat one)
(show 'nat two)
(show 'nat three)
(show 'h2 "PRED")
(show 'nat (pred zero))
(show 'nat (pred one))
(show 'nat (pred two))
(show 'nat (pred three))
(show 'h2 "ADD")
(show 'nat ((add three) two))
(show 'h2 "MUL")
(show 'nat ((mul zero) two))
(show 'nat ((mul two) zero))
(show 'nat ((mul three) two))
(show 'h2 "FACT")
(show 'nat (fact zero))
(show 'nat (fact one))
(show 'nat (fact two))
(show 'nat (fact three))
(show 'nat (fact four))
(show 'nat (fact five))
(show 'h2 "FIB")
(show 'nat (fib zero))
(show 'nat (fib one))
(show 'nat (fib two))
(show 'nat (fib three))
(show 'nat (fib four))
(show 'nat (fib five))
}
Where
Define (show class x)
Open Package "stdio" { :print_line }
Open Package "z" { :Infix + :show show_int }
In
Begin Match class {
| 'h1
(print_line "")
(print_line x)
(print_line "---")
| 'h2
(print_line "")
(print_line x)
| 'bool
(print_line ((x "t") "f"))
| 'nat
Define (increment x)
[x + 1]
(print_line (show_int ((x increment) 0)))
}
Let fib
Define [[x] -> f] (f x)
In
Define ((f fib) n)
Define (case_small _)
one
Define (case_big _)
((add (fib (pred n))) (fib (pred (pred n))))
In
[{} -> (((is_zero (pred n)) case_small) case_big)]
In
(z f)
Let fact
Define [[x] -> f] (f x)
In
Define ((f fact) n)
Define (case_zero _)
one
Define (case_nonzero _)
((mul (fact (pred n))) n)
In
[{} -> (((is_zero n) case_zero) case_nonzero)]
In
(z f)
Where
Define (not b)
((b false) true)
Define ((and b1) b2)
((b1 b2) false)
Define ((or b1) b2)
((b1 true) b2)
Define ((mul a) b)
Define ([[g] << f] x) (g (f x))
In
[a << b]
Let add
Let BITTER
Func a Func b Func f Func x ((a f) ((b f) x))
Let SWEET
Define ([[g] << f] x) (g (f x))
In
Define (((add a) b) f)
[(a f) << (b f)]
In
add
In
BITTER
Define (is_zero n)
((n (const false)) true)
Define (((pred n) f) x)
Define ((compose g) h)
(h (g f))
In
(((n compose) (const x)) id)
Let one (succ zero)
Let two (succ (succ zero))
Let three (succ (succ (succ zero)))
Let four (succ (succ (succ (succ zero))))
Let five (succ (succ (succ (succ (succ zero)))))
Where
Let z
Let BITTER
Func f (Func x (f Func v ((x x) v)) Func x (f Func v ((x x) v)))
Let SWEET
Define (z f)
Define (x x)
Define (self v)
((x x) v)
In
(f self)
In
(x x)
In
z
Let SWEETEST
Define (z f)
Unfold {}
Define (self v)
((Fold) v)
In
(f self)
In
z
In
SWEETEST
Define ((true x) y)
x
Define ((false x) y)
y
Define ((zero f) x)
x
Define (((succ n) f) x)
(f ((n f) x))
Define ((const x) u)
x
Define (id x)
x
|
