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@@ -8,6 +8,7 @@ Logic toolbox in [Clean](http://wiki.clean.cs.ru.nl/Clean). Features include: * Evaluating expressions without atomic expressions * Generating truth tables for expressions, possibly with intermediate steps * Displaying truth tables + * Parsing strings to expressions Read further for examples. @@ -15,9 +16,17 @@ Read further for examples. ### Operators -There is one unary operator (`Op1`): `Not`. +There is one unary operator (`Op1`): `Not`. It binds stronger than all other operators. -There are four binary operators (`Op2`): `And`, `Or`, `Impl` and `Equiv`. `And` is considered left-associative; all others are considered right-associative. Associativity is only important in `toString` functions. `Expr` itself is an unambiguous recursive type. +There are four binary operators (`Op2`). In order of descending precedence: `And`, `Or`, `Impl` and `Equiv`. `And` is considered left-associative; all others are considered right-associative. Associativity is only important in `toString` functions. `Expr` itself is an unambiguous recursive type. + +The operators are represented as: + + * Not: `~` + * And: `&` + * Or: `|` + * Impl: `->` + * Equiv: `<->` ### Expressions @@ -95,12 +104,48 @@ The `truthtable` of `e15`: True | True | False | False | False True | True | True | True | True +## Parsing + +The `parse` function may be used to read an expression from a String. The following rules are used: + + * Whitespace is ignored. + * All latin letters (`[a-zA-Z]`) are considered atomic expressions + * Operators are expected in their representation described above + * True and False are expected as `1` and `0`, respectively + +A usage example is found in `LogicParser.icl`. This file, once compiled, reads the command line arguments and shows their truth tables: + + $./LogicParser -b -nt -e "~~(((A | (A -> B)) -> B) -> B)" + A | B | A -> B | A | (A -> B) | A | (A -> B) -> B | (A | (A -> B) -> B) -> B | ~((A | (A -> B) -> B) -> B) | ~~((A | (A -> B) -> B) -> B) + -------+-------+--------+--------------+-------------------+--------------------------+-----------------------------+------------------------------ + False | False | True | True | False | True | False | True + False | True | True | True | True | True | False | True + True | False | False | True | False | True | False | True + True | True | True | True | True | True | False | True + +Here, `-b` and `-nt` are common Clean options to disable outputting basic values for constructors, and disable outputting execution times, respectively. + +The option `-e` tells the parser to show the extended truth table. With this option, only the first formula is considered. Without `-e`, multiple formulas may be given (possibly with different atomic expressions), and all will be evaluated in one table: + + $./LogicParser -b -nt "~~(((A | (A -> B)) -> B) -> B)" "A & B" + A | B | ~~((A | (A -> B) -> B) -> B) | A & B + -------+-------+------------------------------+------- + False | False | True | False + False | True | True | False + True | False | True | False + True | True | True | True + False | False | True | False + False | True | True | False + True | False | True | False + True | True | True | True + ## Future ideas * Different `toString` formats for operators: HTML (`¬`), UTF-8 (¬), LaTeX (`\neg`) * Different `toString` formats for booleans: `0` and `1` or `T` and `F` instead of `True` and `False` * Simplifying expressions with atomic expressions as far as possible * Testing equivalence or impliance of expressions with atomic expressions + * Add support for multi-letter atomic expressions ## License |