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Note that fmap, join, append and bind are well-defined, since they're applied to progressively deeper arguments at each recursive call. The list type is an additive monad, with nil as the monadic zero and append as monadic sum. Lists form a monoid under the append operation. The identity element of the monoid is the empty list, nil.
Following Lisp, other high-level programming languages which feature linked lists as primitive data structures have adopted an append. To append lists, as an operator, Haskell uses ++, OCaml uses @. Other languages use the + or ++ symbols to nondestructively concatenate a string, list, or array.
The code above specifies a list of strings to be either empty, or a structure that contains a string and a list of strings. The self-reference in the definition permits the construction of lists of any (finite) number of strings. Another example of inductive definition is the natural numbers (or positive integers):
Amortized O(1) time appends (or prepends) are achieved by introducing a new inner node type called Append, and using it to encode a logarithmic-length list of conc-trees, strictly decreasing in height. Every Append node ap must satisfy the following invariants: 1. Level of ap.left.right is always strictly larger than the level of ap.right. 2.
Suppose that "L" is a variable pointing to the last node of a circular linked list (or null if the list is empty). To append "newNode" to the end of the list, one may do insertAfter(L, newNode) L := newNode To insert "newNode" at the beginning of the list, one may do insertAfter(L, newNode) if L = null L := newNode
Here is a list of the longest games, in terms of overtime periods, in college football history, courtesy of the NCAA: 1. Oct. 23, 2021: Illinois 20, Penn State 18 (9 OTs) 2.
‘Tis the season for toy shopping! If you’ve got a kid on your list who always wants the newest, coolest toys on the market, we’ve got you covered. We put together a list of the best toys of ...
Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})