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What are lambda calculus terms?
Lambda calculus terms can be viewed as a kind of binary tree. A lambda calculus term consists of: Variables, which we can think of as leaf nodes holding strings. Applications, which we can think of as internal nodes.How do you find the free variables of a lambda term?
M ⌉ = K M ( x ∉ M) which leads to the following code, where the fv function returns the free variables of a given lambda term. Oleg Kiselyov found better bracket abstraction algorithms, but these will have to wait until our next compiler.
How do you rewrite Closed lambda terms with s and K?
Define S = λ x y z. x z ( y z) and K = λ x y. x, which in Haskell are known as (<*>) (specialized to Reader) and const . It turns out we can rewrite any closed lambda term with S and K alone. We need only implement two functions to attain Turing completeness! First, we notice S K K x = x for all x; a handy convention is to write I for S K K.How does the K combinator work in Java?
For the k combinator, we pop off the last two stack elements and push the evaluation of its first argument. For s we create two internal nodes representing xz and yz on the the heap hp, where x,y,z are the arguments of s.
Lambda calculus is a model of computation, invented by Church in the early 1930’s. Lambda calculus and Turing machines are equivalent, in the sense that any function that can be defined using one can be defined using the other.
What is the difference between pure lambda calculus and abstraction?
Note that the pure lambda calculus excludes constants, types, and primitive operators (e.g. +, *.). Note also that (by convention) application is left associative: ABC means (AB)C not A (BC), and application has higher precedence than abstraction: λx.AB means λx.