Pages tagged lambda_calculus:
A function accepts input and produces an output. Suppose we have a "chocolate-covering" function that produces the following outputs for the corresponding inputs: peanuts -> chocolate-covered peanuts rasins -> chocolate-covered rasins ants -> chocolate-covered ants We can use Lambda-calculus to describe such a function: Lx.chocolate-covered x This is called a lambda-expression. (Here the "L" is supposed to be a lowercase Greek "lambda" character). If we want to apply the function to an argument, we use the following syntax: Functions can also be the result of applying a lambda-expression, as with this "covering function maker": Ly.Lx.y-covered x We can use this to create a caramel-covering function: (Ly.Lx.y-covered x)caramel -> Lx.caramel-covered x (Lx.caramel-covered x)peanuts -> caramel-covered peanuts Functions can also be the inputs to other functions, as with this "apply-to-ants" function: Lf.(f)ants
An Introduction to Lambda Calculus and Scheme
http://www.jetcafe.org/jim/lambda.html
A function accepts input and produces an output. Suppose we have a "chocolate-covering" function that produces the following outputs for the corresponding inputs: peanuts -> chocolate-covered peanuts rasins -> chocolate-covered rasins ants -> chocolate-covered ants We can use Lambda-calculus to describe such a function: Lx.chocolate-covered x This is called a lambda-expression. (Here the "L" is supposed to be a lowercase Greek "lambda" character). If we want to apply the function to an argument, we use the following syntax: Functions can also be the result of applying a lambda-expression, as with this "covering function maker": Ly.Lx.y-covered x We can use this to create a caramel-covering function: (Ly.Lx.y-covered x)caramel -> Lx.caramel-covered x (Lx.caramel-covered x)peanuts -> caramel-covered peanuts Functions can also be the inputs to other functions, as with this "apply-to-ants" function: Lf.(f)ants
Lambda Calculus (at Safalra's Website)
http://safalra.com/science/lambda-calculus/
al introduction to lambda calculus