List of Import References :
See BOOL
See DENOTATION
SIGNATURE Bool
$Date: 2011-09-28 12:04:46 +0200 (Mi, 28. Sep 2011) $ ($Revision: 715 $)
Symbolic names: T, F; long names: true, false
FUN T F: bool
Symbolic name: ~; long names: not, id
FUN id not: bool -> bool
Constant Functions
FUN true false T F : bool -> bool
Long names for existing symbolic names.
FUN equiv xor : bool ** bool -> bool
Symbolic names for existing long names.
FUN /\ \/ : bool ** bool -> bool
Negate and and or
FUN nand nor /~\ \~/ : bool ** bool -> bool
Implication
FUN implies => : bool ** bool -> bool
Functions which ignore one argument.
FUN 1st 2nd n1st n2nd : bool ** bool -> bool
Functions which ignore both arguments.
FUN true false T F : bool ** bool -> bool
Orderings with false less than true
FUN < <= > >= : bool ** bool -> bool
This gives all 16 possible binary boolean functions with the following truth table.
A | B | : | F, false | /\, and | > | 1st | < | 2nd | |=, xor | \/, or |
| false | false | : | false | false | false | false | false | false | false | false |
| false | true | : | false | false | false | false | true | true | true | true |
| true | false | : | false | false | true | true | false | false | true | true |
| true | true | : | false | true | false | true | false | true | false | true |
| A | B | : | T, true | /~\, nand | <=, =>, implies | n1st | >= | n2nd | =, equiv | \~/, nor |
| false | false | : | true | true | true | true | true | true | true | true |
| false | true | : | true | true | true | true | false | false | false | false |
| true | false | : | true | true | false | false | true | true | false | false |
| true | true | : | true | false | true | false | true | false | true | false |
! is defined for denotations "true" and "false" only.
FUN ! : denotation -> bool
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