grass-tips.md

Grass Programming Tips

Examples

Printing w

wWWwwwwv ; push (lambda (x) (Out u)) := print_u
w        ; defines main
WWw      ; apply print_u main
WWWw     ; apply print_u main
WWWWw    ; apply print_u main
WWWWWw   ; apply print_u main

This prints wwww.

• The first line defines (lambda (x) (Out w)) := printw. Since the VM is at the initial state, the De Bruijn indices for Out and w are 2 = 1 + 1 and 4 = 1 + 3. The extra 1 is created by the surrounding abstraction. w is written as u to prevent it from being parsed.
• The second line defines main. In Grass, the final function at the top of the stack (here, main) is called with itself as the argument when the program starts. To handle this specification, main takes an extra unused parameter.
• printw is then called with main. The argument can be anything since it is unused.
• The De Bruijn index for printw increases (WW, WWW, WWWW, WWWWW) since the result of apply printw main are being pushed to the top of the stack as apply printw main is executed.
  • The argument w first points to main, but later points to the result of the previous apply printw main.

Destructing a Cons Cell

wWwwwwWwwwwwv ; push (cons u u)
wwv           ; push nil
w             ; def-main
WWWww         ; apply (cons u u) nil
WWWWWw        ; apply Out 1

This prints w.

1. Creates (cons w w) (w is written as u to avoid from it being parsed) Here, w is the Grass primitive function which has the De Bruijn index 4 = 1 + 3. The extra 1 is for the surrounding abstraction.
2. Creates nil
3. The definition of main starts here
4. nil is applied to (cons u u)
5. Out is applied to the top of the stack. Out is a Grass primitive, and has the De Bruijn index of 5 at this point in the program.

Resources

The following blog post (in Japanese) helped very much in understanding Grass:

• https://youz.hatenablog.com/entry/20080601/1212303662