Improved parser

1 files changed, 46 insertions, 2 deletions

diff --git a/README.md b/README.md
index dc01fb5..0d2c3f6 100644
--- a/README.md
+++ b/README.md
@@ -15,9 +15,17 @@ 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 +103,48 @@ 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 (`&not;`), UTF-8 (&not;), 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