Lambda Calculus Example - Lists

 home1 home2  Bib  Algorithms  Bioinfo  FP  Logic  MML  Prog.Lang and the  Book

FP
Lambda
Introduction
Examples
Bool
Ints
Lists
others

Lists and list operators are usually "built in" with programming languages based on Lambda Calculus but they can be defined in Lambda Calculus. The following example shows a way to define CONS, NIL, HD (head), TL (tail), NULL. (PRINT is a cheat because it is defined using the system's built-in lists (::), but it too could be defined in Lambda Calculus.)

 ``` let rec CONS = lambda h. lambda t. lambda f. f h t, NIL = lambda f. true, NULL = lambda L. L (lambda h. lambda t. false), HD = lambda L. L (lambda h. lambda t. h), TL = lambda L. L (lambda h. lambda t. t), PRINT = lambda L. if NULL L then '/' else (HD L)::(PRINT (TL L)) in let L = CONS 1 (CONS 2 (CONS 3 NIL)) {an e.g.} in PRINT( CONS (NULL NIL) {T} ( CONS (NULL L) {F} ( CONS (HD L) {1} ( CONS (HD (TL L)) {2} ( CONS (HD (TL (TL L))) {3} NIL))))) {/} {\fB Define (Flat) Lists From Scratch. \fP} ```
 let rec CONS = lambda h. lambda t. lambda f. f h t, NIL = lambda f. true, NULL = lambda L. L (lambda h. lambda t. false), HD = lambda L. L (lambda h. lambda t. h), TL = lambda L. L (lambda h. lambda t. t), PRINT = lambda L. if NULL L then '/' else (HD L)::(PRINT (TL L)) in let L = CONS 1 (CONS 2 (CONS 3 NIL)) {an e.g.} in PRINT( CONS (NULL NIL) {T} ( CONS (NULL L) {F} ( CONS (HD L) {1} ( CONS (HD (TL L)) {2} ( CONS (HD (TL (TL L))) {3} NIL))))) {/} {\fB Define (Flat) Lists From Scratch. \fP}

Also see [Boolean] and [Ints].

 Coding Ockham's Razor, L. Allison, Springer A Practical Introduction to Denotational Semantics, L. Allison, CUP

 Linux  Ubuntu free op. sys. OpenOffice free office suite The GIMP ~ free photoshop Firefox web browser

λ ...
 :: list cons nil the [ ] list null predicate hd head (1st) tl tail (rest)

 © L. Allison   http://www.allisons.org/ll/   (or as otherwise indicated), Faculty of Information Technology (Clayton), Monash University, Australia 3800 (6/'05 was School of Computer Science and Software Engineering, Fac. Info. Tech., Monash University, was Department of Computer Science, Fac. Comp. & Info. Tech., '89 was Department of Computer Science, Fac. Sci., '68-'71 was Department of Information Science, Fac. Sci.) Created with "vi (Linux + Solaris)",  charset=iso-8859-1,  fetched Saturday, 25-May-2024 03:18:33 AEST.