Copyright | Copyright (C) 2023 Yoo Chung |
---|---|

License | GPL-3.0-or-later |

Maintainer | dev@chungyc.org |

Safe Haskell | Safe-Inferred |

Language | GHC2021 |

Supporting definitions for logic and code problems.

# Truth tables

type BoolFunc = Bool -> Bool -> Bool Source #

Define boolean functions `and'`

, `or'`

, `nand'`

,
`nor'`

, `xor'`

, `impl'`

, and `equ'`

,
which succeed or fail according to the result of their respective operations;
e.g., `(and' a b)`

is true if and only if both `a`

and `b`

are true.
Do not use the builtin boolean operators.

A logical expression in two variables can then be written as in the following example:

\a b -> and' (or' a b) (nand' a b)

Write a function `table`

which returns
the truth table of a given logical expression in two variables.

### Notes

There is no technical reason to define the type synonym `BoolFunc`

.
However, it is a good place to explain the entire problem
without talking about writing truth table functions first,
especially for inclusion in the documentation for Problems.

The original problem for Haskell
required that the truth table be printed:
*"Now, write a predicate table/3 which prints the truth table of a given logical expression in two variables."*
It was changed here to return a list of boolean tuples, because the requirement
for I/O seemed uninteresting in the context of the rest of the problem.

Documentation for the expected semantics for each boolean function was added,
and the example for `table`

was modified to avoid sensitivity to order.

## Utility functions

printTable :: [(Bool, Bool, Bool)] -> IO () Source #

Print truth table as returned by `table`

.

Given the same pair of truth tables except for order, the output will be the same.

printTablen :: [[Bool]] -> IO () Source #

Print truth table as returned by `tablen`

.

Given the same pair of truth tables except for order, the output will be the same.

Set of functions grouped together.

Useful for passing in a particular set of functions. E.g., testing and benchmarking particular implementations.

# Propositional logic

Represents a boolean formula.

Value Bool | A constant value. |

Variable String | A variable with given name. |

Complement Formula | Logical complement. I.e., it is true only if its clause is false. |

Disjoin [Formula] | Disjunction. I.e., it is true if any of its clauses are true. |

Conjoin [Formula] | Conjunction. I.e., it is true only if all of its clauses are true. |