10a-lambda-calc

# 10a-lambda-calc - The Other Model Calculus So far we have...

This preview shows pages 1–5. Sign up to view the full content.

The Other Model: λ Calculus So far we have only looked at Turing machines as our model. Question: Where does the Church in the Church-Turing thesis come from? Answer: Alonzo Church invented the λ calculus to model computing with functions. Turns out the λ calculus is as powerful as the Turing machine, we are just not used to thinking in terms of universal computing using just functions. –p

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The Other Model: λ Calculus The next couple of lectures will show that the λ calculus and the Turing machine are equivalent in terms of computational power. 1. Introduce the λ calculus. 2. Introduce the primitive- and µ -recursive. 3. Show that the λ calculus implements the µ -recursive functions. 4. Show that a Turing machine implements the µ -recursive functions. 5. Show that a Turing machine implements the λ -calculus. 6. Show that µ -recursive functions can implement Turing machines. 7. Because of 3 we can conclude that λ calculus can implement Turing machines. 8. From 5 and 7 we conclude that the λ -calculus and Turing machines are computationally equivalent. One way to look at the λ calculus is as a term rewriting system. –p
λ Calculus 101 λ -calculus aims to model computation with functions. At the core of this calculus are λ -expressions of the form λx. E denoting functions with a parameter x and a function body E . Here is the variable x is assumed to be free in E (i.e. the variable is assumed not bound by a λ -operator). The syntax for the calculus can be summarized by the following context-free grammar, <function> ::= λ <var> . <expression> <expression> ::= <var> | <function> | <application> <application> ::= <expression><expression> Example: ( λx. x )( λf. ( λy. f y )) –p

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
λ Calculus 101 Rules: The calculus is very simple, it essentially consists of only three rules:
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 12

10a-lambda-calc - The Other Model Calculus So far we have...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online