''' An exploration of Phil Bagwell's VList. A VList is modeled as a 5-tuple: base: VList offset: int, indexing (from 0) the base VList data list. size: int, length of the data list. last_used: to make a mutable int it's an int in a list It's a count here rather than an offset! That is, it starts from 1, rather than 0. data: a list of length size. A pointer to a VList is a two-tuple of (VList, offset) where the offset is an index into the VList's data list. ''' def cons(thing, vlist_ptr): if not vlist_ptr: return ((), 0, 1, [1], [thing]), 0 vlist, pointer_offset = vlist_ptr base, _offset, size, last_used_list, data = vlist [last_used] = last_used_list # Note that we could do this pattern # matching directly in the assignment statement on the previous line, # however, we want to keep that length-one list "last_used_list" # around so we can mutate the last_used value of "vlist". ''' During the consing of (9) the pointer offset is compared with the last used offset, LastUsed. If it is the same and less than the block size then it is simply incremented, the new entry made and LastUsed updated. ''' if pointer_offset == last_used - 1 and last_used < size: pointer_offset += 1 data[pointer_offset] = thing last_used_list[0] += 1 return vlist, pointer_offset ''' If on the other-hand the pointer offset is less than the LastUsed a cons is being applied to the tail of a longer list, as is the case with the (9). In this case a new list block must be allocated and its Base-Offset pointer set to the tail contained in the original list. The offset part being set to the point in tail that must be extended. The new entry can now be made and additional elements added. ''' # Is this where we increase the size x 2? size <<= 1 offset = 0 data = [None] * size data[offset] = thing return (vlist, pointer_offset, size, [1], data), offset def head(vlist_ptr): if not vlist_ptr: raise ValueError("Empty list has no head!") vlist, offset = vlist_ptr return vlist[-1][offset] def tail(vlist_ptr): if not vlist_ptr: raise ValueError("Empty list has no tail!") vlist, offset = vlist_ptr offset -= 1 return (vlist[:2] if vlist[0] else ()) if offset < 0 else (vlist, offset) def iter_vlist(vlist_ptr): while vlist_ptr: yield head(vlist_ptr) vlist_ptr = tail(vlist_ptr) def repr_vlist(vlist_ptr): return ' '.join(map(str, iter_vlist(vlist_ptr))) def pick(n, vlist_ptr): ''' Consider starting with a list pointer in Fig 1 then to find the nth element subtract n from the pointer offset. If the result is positive then the element is in the first block of the list at the calculated offset from the base. If the result is negative then move to the next block using the Base-Offset pointer. Add the Previous pointer offset to the negative offset. While this remains negative keep moving onto the next block. When it finally becomes positive the position of the required element has been found ''' assert n >= 0 if not vlist_ptr: raise ValueError("Empty list!") vlist, pointer_offset = vlist_ptr q = pointer_offset - n while q < 0: if not vlist: raise ValueError(f'Pick index {n} greater than length of list.') vlist, offset = vlist[:2] q += offset + 1 # Offsets in the paper count from one, not zero? return vlist[-1][q] def length(vlist_ptr): if not vlist_ptr: return 0 vlist, n = vlist_ptr while vlist: vlist, offset = vlist[:2] n += offset + 1 return n p = () p = cons(3, p)# ; print(p) p = cons(4, p)# ; print(p) p = cons(5, p)# ; print(p) p = cons(6, p)# ; print(p) p = cons(7, p)# ; print(p) p = cons(8, p)# ; print(p) print(repr_vlist(p)) for n in range(length(p)): print(pick(n, p), end=' ') print() # There is no such thing as a vlist_ptr with a null () vlist. That's an invariant. ## # In Fig 2 a list has been created with the integers (8,7,6,5,4,3) ## ## o1 = ((), 0, 1, [1], [3]) ## o2 = (o1, 0, 2, [2], [4, 5]) ## o3 = (o2, 1, 4, [3], [6, 7, 8, None]) ## ## p0 = (o3, 2) # points to 8 ## p1 = (o3, 0) # points to 6 ## ## # cons(9, p1) = o4 ## ## o4 = (o3, 0, 1, [1], [9]) ## p2 = (o4, 0) # points to 9 ## ## ## p3 = cons(10, p0) ##for i, p in enumerate((p0, p1, p2, p3)): ## print(f'p{i}') ## print(' '.join(map(str, iter_vlist(p)))) ## print() # https://pythontutor.com/visualize.html#code='''%0AAn%20exploration%20of%20Phil%20Bagwell's%20VList.%0A%0AA%20VList%20is%20modeled%20as%20a%205-tuple%3A%0A%20%20%20%20base%3A%20VList%0A%20%20%20%20offset%3A%20int,%20indexing%20%28from%200%29%20the%20base%20VList%20data%20list.%0A%20%20%20%20size%3A%20int,%20length%20of%20the%20data%20list.%0A%20%20%20%20last_used%3A%20to%20make%20a%20mutable%20int%20it's%20an%20int%20in%20a%20list%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20It's%20a%20count%20here%20rather%20than%20an%20offset!%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20That%20is,%20it%20starts%20from%201,%20rather%20than%200.%0A%20%20%20%20data%3A%20a%20list%20of%20length%20size.%0A%0AA%20pointer%20to%20a%20VList%20is%20a%20two-tuple%20of%20%28VList,%20offset%29%20where%0Athe%20offset%20is%20an%20index%20into%20the%20VList's%20data%20list.%0A%0A'''%0A%0A%0Adef%20cons%28thing,%20vlist_ptr%29%3A%0A%20%20%20%20if%20not%20vlist_ptr%3A%0A%20%20%20%20%20%20%20%20return%20%28%28%29,%200,%201,%20%5B1%5D,%20%5Bthing%5D%29,%200%0A%0A%20%20%20%20%28base,%20_offset,%20size,%20last_used_list,%20data%29,%20pointer_offset%20%3D%20vlist_ptr%0A%20%20%20%20%5Blast_used%5D%20%3D%20last_used_list%0A%0A%20%20%20%20'''%0A%20%20%20%20During%20the%20consing%20of%20%289%29%20the%20pointer%20offset%20is%20compared%20with%20the%0A%20%20%20%20last%20used%20offset,%20LastUsed.%20If%20it%20is%20the%20same%20and%20less%20than%20the%20block%0A%20%20%20%20size%20then%20it%20is%20simply%20incremented,%20the%20new%20entry%20made%20and%20LastUsed%0A%20%20%20%20updated.%0A%20%20%20%20'''%0A%0A%20%20%20%20if%20pointer_offset%20%3D%3D%20last_used%20-%201%20and%20last_used%20%3C%20size%3A%0A%20%20%20%20%20%20%20%20pointer_offset%20%2B%3D%201%0A%20%20%20%20%20%20%20%20data%5Bpointer_offset%5D%20%3D%20thing%0A%20%20%20%20%20%20%20%20last_used_list%5B0%5D%20%3D%20last_used%20%2B%201%0A%20%20%20%20%20%20%20%20return%20vlist_ptr%5B0%5D,%20pointer_offset%0A%0A%20%20%20%20'''%0A%20%20%20%20If%20on%20the%20other-hand%20the%20pointer%20offset%20is%20less%20than%20the%20LastUsed%20a%0A%20%20%20%20cons%20is%20being%20applied%20to%20the%20tail%20of%20a%20longer%20list,%20as%20is%20the%20case%0A%20%20%20%20with%20the%20%289%29.%20In%20this%20case%20a%20new%20list%20block%20must%20be%20allocated%20and%20its%0A%20%20%20%20Base-Offset%20pointer%20set%20to%20the%20tail%20contained%20in%20the%20original%20list.%0A%20%20%20%20The%20offset%20part%20being%20set%20to%20the%20point%20in%20tail%20that%20must%20be%20extended.%0A%20%20%20%20The%20new%20entry%20can%20now%20be%20made%20and%20additional%20elements%20added.%0A%20%20%20%20'''%0A%0A%20%20%20%20%23%20Is%20this%20where%20we%20increase%20the%20size%20x%202%3F%0A%20%20%20%20size%20%3C%3C%3D%201%0A%20%20%20%20data%20%3D%20%5BNone%5D%20*%20size%0A%20%20%20%20data%5B0%5D%20%3D%20thing%0A%20%20%20%20return%20%28vlist_ptr%5B0%5D,%20pointer_offset,%20size,%20%5B1%5D,%20data%29,%200%0A%0A%0A%0Ap%20%3D%20%28%29%0Ap%20%3D%20cons%283,%20p%29%23%20%3B%20print%28p%29%0Ap%20%3D%20cons%284,%20p%29%23%20%3B%20print%28p%29%0Ap%20%3D%20cons%285,%20p%29%23%20%3B%20print%28p%29%0Ap%20%3D%20cons%286,%20p%29%23%20%3B%20print%28p%29%0Ap%20%3D%20cons%287,%20p%29%23%20%3B%20print%28p%29%0Ap%20%3D%20cons%288,%20p%29%23%20%3B%20print%28p%29%0A&cumulative=false&heapPrimitives=nevernest&mode=edit&origin=opt-frontend.js&py=3&rawInputLstJSON=%5B%5D&textReferences=false