Category:Lambdatalk: Difference between revisions

Line 25:

-> 2+3 is equal to 5

==B) {lambda talk}~~'s foundations~~==

==B) more about {lambda talk}==

{lambda talk} is freely inspired by the λ-calculus. At the lowest level a {lambda talk} expression is exclusively made of words, abstractions and applications:

=== structure & evaluation

expression is [word|abstraction|application]*

Line 50:

Line 52:

What can be done with so little?

===Examples===

Hello World

Line 91:

Line 95:

{CAR {CONS Hello World}} -> World

===about the implementation===

===Implementation===

{lambda talk} is not implemented following the standard process, code -> tokens -> tree -> eval. '''The code is a string from beginning to end'''. At each keyboard input, the code is processed by a single function, do_eval(), which returns words sent to the browser for the final evaluation and display:

Line 114:

Line 118:

- lambdas accept de facto '''partial function application''': called with a number of values lesser than its arity, a lambda memorizes the given values and returns a new lambda waiting for the rest.

===and?===

⚫

Upon these foundations, after '''Alonzo Church''', we could define the set of natural numbers [ZERO, ONE, TWO, ...] and their associate operators, [SUCC, ADD, MUL, POWER, PRED, ...] allowing to build iterations and recursions. For instance, computing factorials:

⚫

Upon these foundations, after '''Alonzo Church''', we could define the set of natural numbers [ZERO, ONE, TWO, ...] and their associate operators, [SUCC, ADD, MUL, POWER, PRED, ...] allowing to build '''iterations''' and ''recursions'''. For instance, computing factorials:

{CHURCH