March 18, 2004 abstract the lambda calculus can appear arcane on. Lecture 23 logic programming first, we describe how we will encode a lambda calculus program as a prolog term. Im doing past exam questions for my symbolic ai course. I think the reference on the subject of lambdacalculus itself still is barendregts book. Prolog with logically supported notions of modular programming, abstract datatypes, higherorder programming, and the lambdatree syntax approach to the treatment of bound. You should read at least the sections down to and including programming techniques first. Its not quite a stepbystep buildup from lambda calculus to scheme as i had hoped theres some vagueness about parsing, just to get started.
For example, a function in lambdacalculus notation such as. Beyond that it pretty much depends on what part of lambdacalculus you are interested in. These names will be either written in bold such as name or underlines such as name. Implementing lambda calculus in prolog well illustrates the power and inconvenience of pure prolog, and similarity and differences between logic variables and variables of lambda calculus. Lambda calculus, defined by alonzo church, is a kind of arithmetic of abstract function manipulation devoid of semantics. Following lecture 14, slides 2930, first write a recursive definition for the equality operation and then abstract the name of the recursive function to. It has some strong theoretical footing as, in modern language, reflexive objects in a. Implementing lambdacalculus in prolog well illustrates the power and inconvenience of pure prolog, and similarity and differences between logic variables and variables of lambdacalculus. A short introduction to the lambda calculus achim jung. The lambda calculus is a good medium to represent mathematics on a computer with the aim to exchange and store reliable mathematical knowledge. Prolog supports, consider the following declarations and clauses which describe the syntax and captureavoiding substitution operation of the lambdacalculus.
To represent the function evaluation f2 4, we use the following. Chapter 2 of luger 2009 describes predicate calculus in detail. Unlike lambda calculus, oo is not a specific mathematical formalism but rather a methodology and ontology for organizing a program. Animal x is bigger than animal y either if this has been stated as a fact or if there is an animal z for which it has been stated as a fact that animal x is bigger than animal z and it can be shown that animal z is bigger than animal y. What are some resources for learning lambda calculus. Functional programming lambda calculus tutorialspoint. Each of these is a field in itself, and i dont know of any book that covers it all. These functions can be of without names and single arguments. The toy lambda calculus interpreter can be run through the eb. Prolog is a logic programming language based on an intuitionistic fragment of churchs simple theory of types. Values are lambda expressions that have properly finished being evaluated there is nothing more to do.
Functions overview in programming terms, a function is a block of statements that performs a specific task. Lambda calculus as a formal system free and bound variables. Modern processors are just overblown turing machines. On logic programming representations of lambda terms. Lambda calculus is a framework developed by alonzo church in 1930s to study computations with functions. Prolog with logically supported notions of modular programming, abstract datatypes, higherorder programming, and the lambdatree syntax approach to the treatment of bound variables in syntax. Originally developed in order to study some mathematical properties of e ectively computable functions, this formalism has provided a strong theoretical foundation. Lecture 19 logic programming first, we describe how we will encode a lambda calculus program as a prolog term.
This can be seen as building a prolog interpreter in java. Lambda calculus examples in this handout, we look at several examples of lambda terms in order to provide a. Sample questions and answers questions are mostly from midterm and nal exams in 2006. The course is entitled lambda calculus and types and it appears in various forms. I think the reference on the subject of lambda calculus itself still is barendregts book. Which of the following language is a declarative language. At first sight, the two kinds of variables appear the same. Prolog, also written lambda prolog, is a logic programming language featuring polymorphic typing, modular programming, and higherorder programming. Lambda calculus as a programming language lambda calculus it can be used to encode programs and data, such as booleans and natural numbers it is the simplest possible programming language that is turing complete pure lisp is equivalent to lambda calculus lisp is lambda calculus, plus some additional features. Firstorder predicate logic is to logic programming as lambda calculus is to functional programming. It is intended for a course where students have already completed a basic computer science course and have learned a. There are very tight limits set on the size and running time of programs that can be run in this way. Planning using situation calculus, prolog and a mobile robot.
Prolog integrates in the calculation of its clauses according to robinsons 1965, 1970 principles of first order calculus predicate. In the pure lambda calculus, the only values are functions \x. Pdf natural language processing for prolog programmers. Here is the syntax of the lambda calculus and how we translate lambda calculus expressions to a prolog. These extensions to prolog are derived from the higherorder hereditary harrop formulas used to justify the foundations of. Constructive logic frank pfenning lecture 14 october 15, 2009 in this lecture we introduce some simple data structures such as lists, and simple algorithms on them such as as quicksort or mergesort. A function is a mapping from the elements of a domain set to the elements of a codomain set given by a rulefor example, cube. Functions accept data, process it, and return a result. I found that it very neatly builds on each chapter at an excellent pace though keep in mind i had some practice with. E to denote a function in which x is a formal argument and e is the functional body. A linear spine calculus iliano cervesato advanced engineering and sciences division itt industries, inc.
Functional languages are just the lambda calculus with a more palatable syntax. Beyond that it pretty much depends on what part of lambda calculus you are interested in. Prolog, for example, the natural representation of. Which one of the following is not a type of polymorphism acoercion boverloading coverriding dgenerics eall of them are types of polymorphism answer. What formal system provides the semantic foundation for prolog. Define in lambdacalculus an equality testing function, eq, for two numbers represented as church numerals.
Formal syntax and semantics of programming languages. A tutorial introduction to the lambda calculus raul rojas fu berlin, ws9798 abstract this paper is a short and painless introduction to the calculus. The lambdacalculus as an example of the style of nameful programming which. Shieber microtome publishing brookline, massachusetts. Lambda calculus church and kleene 1930s a unified language to manipulate and reason about functions. Lecture notes on the lambda calculus peter selinger department of mathematics and statistics dalhousie university,halifax, canada abstract this is a set of lecture notes that developed out of courses on the lambda calculus that i taught at the university of. Lisp is not based on the lambda calculus hacker news. Originally developed in order to study some mathematical properties of e ectively computable functions, this formalism has provided a. Lecture notes on the lambda calculus peter selinger department of mathematics and statistics dalhousie university,halifax, canada abstract this is a set of lecture notes that developed out of courses on the lambda calculus that i taught at the university of ottawa in 2001 and at dalhousie university in 2007 and 20.
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