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Category:Lambdatalk: Difference between revisions
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-> 2+3 is equal to 5
==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]*
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What can be done with so little?
===Examples===
Hello World
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{CAR {CONS Hello World}} -> World
===about the 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:
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- 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
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