1 files changed, 28 insertions, 7 deletions
diff --git a/README.md b/README.md
index 7a79b05..5b8eca8 100644
--- a/README.md
+++ b/README.md
@@ -2,7 +2,9 @@
 
 Tiny beginnings of a parser for a toy language, written in C99.
 
-Currently only a lexer.
+Currently only capable of parsing simple arithmetic expressions, limited to
+positive numbers, addition, subtraction, multiplication, and division.
+
 
 ## Compiling
 
@@ -12,14 +14,33 @@ To build `frontend`:
 make
 ```
 
+
 ## Running
 
-Simply run `./frontend INPUT_FILE` and it should parse and print the abbreviated
-tokens (ie. `+ => +`, instead of `+ => ADD`) with spacing around it.
+Simply run `./frontend INPUT_FILE` and it should parse and print the resulting
+AST in polish notation with surrounding parenthesis,
+ie. `1 + 2 * 3` turns into `( + 1 ( * 2 3 ) )`,
+and `1 + 2 + 3` becomes `( + ( + 1 2 ) 3 )`.
+
+Example input can be found in the `program.input` file.
+
+
+## Next steps
 
-Next baby steps is to make the token type store a line, column, and length of
-the token, and the parser should ideally return an array of offsets into the
-input string of each newline (or, ideally the character AFTER `\n`). Next is
-constructing an AST of the arithmetic expression(s).
+* Allocating all memory up front, an inefficient but very simple use of memory
+  would exploit the fact that the number of lines and tokens is bounded by the total
+  number of bytes in `INPUT_FILE`, and the number of sub-expressions are bounded
+  by the number of tokens, so a naive approach is to allocate
+  `length(INPUT_FILE) * sizeof(char + line_t + expression_t)`.
+* Streaming parsing; the implementation currently supports reading a limited
+  amount of input at each step, extending it to "pause-at-X" and resume once
+  more input is available should be a trivial feat.
+* Fix precedence implementation, currently we just compare operators, which is
+  unmaintainable and inefficient once the grammar is extended.
+* Extend the arithmetic grammar to support more operators.
+* Boolean grammar parsing.
+* Argument parsing to better control the output and debug different parts of the
+  implementation.
+* Tests.
 
 Currently only simple arithmetic is implemented.