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rational
integer
nat
pos
rationalp
integerp
natp
posp
<
>
<=
>=
+
-
*
/
unary--
unary-/

4 Numbers🔗ℹ

type

rational

type

integer

type

nat

type

pos

procedure

(rationalp v)  boolean

  v : all
A recognizer for rational numbers.

> (rationalp 5/12)

t

> (rationalp 6)

t

> (rationalp -8)

t

procedure

(integerp v)  boolean

  v : all
A recognizer for integers.

> (integerp 5/12)

nil

> (integerp 42)

t

> (integerp -9)

t

procedure

(natp v)  boolean

  v : all
A recognizer for natural numbers. The natural numbers are the integers starting from zero and counting up.

> (natp 0)

t

> (natp 1)

t

> (natp 14)

t

> (natp -2)

nil

> (natp 5/3)

nil

> (natp 1138)

t

procedure

(posp v)  boolean

  v : all
A recognizer for positive integers. These are the integers starting from one and counting up.

> (posp 0)

nil

> (posp 1)

t

> (posp 2)

t

> (posp 2187)

t

> (posp -47)

nil

> (posp 13/31)

nil

procedure

(< a b)  boolean

  a : rational
  b : rational

procedure

(> a b)  boolean

  a : rational
  b : rational

procedure

(<= a b)  boolean

  a : rational
  b : rational

procedure

(>= a b)  boolean

  a : rational
  b : rational
Numeric comparison functions.

> (< 4 78)

t

> (< 99 2)

nil

> (< 8 8)

nil

> (<= 3 4)

t

> (<= 3 3)

t

> (<= 3 2)

nil

> (> 8 -3)

t

> (> -8 3)

nil

> (>= 6 6)

t

> (>= 7 6)

t

procedure

(+ a b)  rational

  a : rational
  b : rational

procedure

(- a b)  rational

  a : rational
  b : rational

procedure

(* a b)  rational

  a : rational
  b : rational

procedure

(/ a b)  rational

  a : rational
  b : rational/non-zero

procedure

(unary-- a)  rational

  a : rational

procedure

(unary-/ a)  rational

  a : rational/non-zero
Basic arithmetic operations.

> (+ 2 2)

4

> (+ 1 (+ 2 3))

6

> (+ 6 1)

7

> (* 6 7)

42

> (* 9 3)

27

> (* 45/77 11)

45/7

> (- 15 8)

7

> (- 8 15)

-7

> (/ 42 7)

6

> (/ 47 2)

47/2

> (/ 46 6)

23/3

> (unary-- 98)

-98

> (unary-- -32)

32

> (unary-/ 54)

1/54

> (unary-/ 1/29)

29