12-09-2018, 09:19 PM
Hello, you agree with the following definitions.
INFIX, operator in the middle.
PREFIX, operator at the beginning.
POSTFIX, operator at the end.
EXOFIX, operator on the outside.
INFIX, operator in the middle.
PREFIX, operator at the beginning.
POSTFIX, operator at the end.
EXOFIX, operator on the outside.
PHP Code:
a union b (union as infix operator), a ∪ b (∪ as symbolic infix operator), ∪ a,b (∪ as prefix operator), ∪(a,b) (∪ as prefix functional operator), (a, b)∪ (∪ as postfix functional operator), a, b ∪ (∪ as postfix operator)
a intersection b (intersection as infix operator), a ∩ b (∩ as symbolic infix operator), ∩(a,b) (∩ as prefix functional operator), (a, b)∩ (∩ as postfix functional operator)
not a (not as prefix operator), ¬a (¬ as symbolic prefix operator), ¬(a) (¬ as prefix functional operator), a¬ (¬ as postfix operator)
ceil(a) (ceil as functional operator, ⌈a⌉ (ceil as exofix operator)
floor(a) (floor as functional operator), ⌊a⌋ as (floor as exofix operator)
abs(a) (floor as functional operator), |a| (abs as exofix operator)
root(a) (root as functional operator) √(a) (√ as symbolic functional operator)
integral() (integral as functional operator), ∫() (∫ as symbolic functional operator)
sum() (sum as functional operator), Σ() (Σ as symbolic functional operator)
product() (product as functional operator), Π() (Π as symbolic functional operator)
a <= b (<= as digraph infix operator), a ≤ b (≤ as real infix operator)
a >= b (>= as digraph infix operator), a ≥ b (≥ as real infix operator)
a != b (!= as digraph infix operator), a ≠ b (≠ as real infix operator)
factorial(a) (functional operator), a! (postfix operator)
a^3 (^ explicit infix operator) to a³ (implicit infix operator)
a^2 (^ explicit infix operator) to a² (implicit infix operator)
Example
(3+4) * (5-6) returns -7 // infix operation (standard notation)
*(+(3,4),-(5,6)) // symbolic functional prefix operation
Product(Sum(3,4),Subtraction(5,6)) // functional prefix operation
Product Sum 3,4, Subtraction 5,6 // prefix operation
3, 4 Sum, 5, 6 Subtraction, Product // postfix operation
( (3,4)Sum, (5,6)Subtraction )Product // functional postfix operation
( (3, 4)+ (5, 6)- )* // symbolic functional postfix operation
3,4 +, 5, 6 - * // symbolic postfix operation
3 4 + 5 6 - * // RPN