Pdf lecture notes on the lambda calculus semantic scholar. By peter selinger, dalhousie university, benoit valiron, ecole polytechnique. Quantum lambda calculus peter selinger dalhousie university, canada benot valiron inria and ecole polytechnique, lix, palaiseau, france. Introduction to the lambda calculus iowa state university. In particular, we consider a practical version of the calculus called protoquipper, which contains the core of quipper.
The lambda calculus download ebook pdf, epub, tuebl, mobi. Pdf the lambda calculus download full pdf book download. Submitted on 22 apr 2008 v1, last revised 26 dec 20 this version, v2. The quantum lambda calculus is a typed quantum programming. Topics covered in these notes include the untyped lambda calculus, the churchrosser theorem, combinatory algebras, the simplytyped lambda calculus, the curryhoward isomorphism, weak and strong normalization. Get ebooks semantics of the probabilistic typed lambda calculus on pdf, epub, tuebl, mobi and audiobook for free. Topics covered in these notes include the untyped lambda calculus, the churchrosser theorem, combinatory algebras, the simplytyped lambda calculus. Topics covered in these notes include the untyped lambda calculus, the churchrosser theorem, the simplytyped lambda calculus, the curryhoward isomorphism, weak and strong normalization, type inference, denotational semantics, complete partial orders, and the language pcf.
Phil scott, some aspects of categories in computer science. March 18, 2004 abstract the lambda calculus can appear arcane on. Lambda calculus and types oxford department of computer. Lecture notes on the lambda calculus by peter selinger. Mathematical structures in computer science 16, 3 2006, 527552. 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. A linearnonlinear model for a computational callbyvalue. Quantum lambda calculus peter selinger dalhousie university, canada beno t valiron inria and ec ole polytechnique, lix, palaiseau, france. Quantum lambda calculus peter selinger dalhousie university, canada benot valiron inria and ecole polytechnique, lix, palaiseau, france 1. Buy lecture notes on the lambda calculus by peter selinger hardcover online at lulu.
I studied the callbyname and callbyvalue semantics of this calculus in my paper on control categories. Orderincompleteness and finite lambda reduction models. The lambda calculus is algebraic peter selinger department of mathematics and statistics university of ottawa, ottawa, ontario k1n 6n5, canada email. A linearnonlinear model for a computational callby. 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.
Semantics of the lambda mu calculus peter selinger department of mathematics, university of michigan, ann arbor, mi 481091109, u. A particular implementation of fix is currys paradoxical combinator y, represented by. Peter selinger dalhousie university halifax, canada. Semantic scholar profile for peter selinger, with 321 highly influential citations and 86 scientific research papers. My current office hours are monday 12 and wednesday 12. The book contains an introduction to the lambda calculus as the theoretical foundation of all functional programming languages. We give a categorical semantics for a callbyvalue linear. The lambda munu calculus is an extension of the simplytyped lambda calculus with firstclass control operators and disjunction types. Valiron department of mathematics and statistics, university of ottawa, ottawa, ontario k1n 6n5, canada abstract the objective of thispaper istodevelop a functional programming languagefor quantum computers. A programming language for string diagrams linearnonlinear lnl models, as described by benton, soundly model a lnl term calculus. Game semantics for quantum programming proceedings of. One feature of this lambda calculus is its linear type system, which includes a duplicability operator. Inria and cole polytechnique, lix, palaiseau, france. In the classical untyped lambda calculus, every function has a fixed point.
Our midterm will be on monday, october 21 in class. Sequent calculus is an alternative proof system for firstorder logic. Quantum lambda calculus department of mathematics and statistics. Always update books hourly, if not looking, search in the book search column. Such a lambda calculus was used by selinger and valiron as the backbone of a functional programming language for quantum computation. The lambda calculus has been created by the american logician alonzo church in the 1930s and is documented in his works published in 1941 under the title the calculi of lambda conversion. Peter selinger dalhousie university halifax, canada 1. Lecture notes on the lambda calculus nanjing university. In the lambda calculus there are a number of combinator implementations that satisfy the mathematical definition of a fixedpoint combinator.
The combinatory interpretation of the lambda calculus is known to be imperfect, because it d. Download the book contains an introduction to the lambda calculus as the theoretical foundation of all functional programming languages. The lambda calculus, treated in this book mainly in its untyped version, consists of a collection of expressions, called lambda terms, together with ways how to rewrite and identify these. A lambda calculus for quantum computation with classical control peter selinger.
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. The research on functional quantum programming started with an attempt to define a quantum extension of lambda calculus made by maymin 165 and van tonder 212. Creating highquality pdf a documents using latex 2014. According to peter selinger, the lambda calculus is algebraic pdf. Lecture notes on the lambda calculus dalhousie university.
Lo 26 dec 20 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. Mark chucarroll, lambda calculus and category theory. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Lecture notes on the lambda calculus peter selinger department of mathematics and statistics university of ottawa abstract this is a set of lecture notes for the course mathematical foundations of computation, which i taught at the university of ottawa in fall 2001.
It is the basis for functional programming like turing machines are the foundation of imperative. In the parts conversion, reduction, theories, and models the view is respectively algebraic, computational, with more coinductive identifications, and. Functions a function may be viewed as a set of ordered pairs where. Semantics of the probabilistic typed lambda calculus e. The lambda calculus has been created by the american logician alonzo church in the 1930s. In a series of papers, selinger and coauthors try to find.
First, we study models of the untyped lambda calculus. We give a categorical semantics for a callbyvalue linear lambda calculus. Combinatory logic is a higherorder functions theory. 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. Quantum lambda calculus chapter 4 semantic techniques in. One interpretation of the untyped lambda calculus is as a programming language where evaluation proceeds by performing reductions on an expression until it is in normal form. Lecture notes on the lambda calculus paperback november 26, 2014 by peter selinger author see all formats and editions hide other formats and editions. Viewed pu rely as a naming device, however, it is a straighforward extension of ordinar y mathematical notation. Abstract we discuss the design of a typed lambda calculus for quantum computation. We develop a linear logical framework within the hybrid system and use it to reason about the type system of a quantum lambda calculus.
Lecture notes on the lambda calculus pdf 106p this notes contains the details about the untyped lambda calculus, the churchrosser theorem, combinatory algebras, the curryhoward isomorphism, polymorphism, weak and strong normalization, denotational semantics of pcf. Also it forms a compact language to denote mathematical proofs logic provides a formal language in which mathematical statements can be formulated and provides deductive power to derive these. Request pdf enriching a linearnonlinear lambda calculus. Our second contribution lifts the expressive power of the dagger lambda calculus, to that of a quantum programming language, by adding. For quantum programming, selinger and valiron have proved that a linear version. A lambda calculus for quantum computation with classical control volume 16 issue 3 peter selinger, benoit valiron skip to main content we use cookies to distinguish you from other users and to provide you with a better experience on our websites. Topics covered in these notes include the untyped lambda calculus, the churchrosser theorem, combinatory algebras, the simplytyped lambda calculus, the curryhoward isomorphism, weak and strong normalization, type inference, denotational semantics, complete partial. Topics covered in these notes include the untyped lambda calculus, the.
A lambda calculus for quantum computation with classical control p selinger, b valiron international conference on typed lambda calculi and applications, 354368, 2005. 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. Peter selinger, lecture notes on the lambda calculus. We discuss the design of a typed lambda calculus for quantum computation. The presentation will explain the basics of pi calculus, and show how lambda calculus can be simulated in pi calculus.
The course is entitled lambda calculus and types and it appears in various forms. Quipper is a quantum programming language under active development and recently has gained much popularity among the quantum. Lecture notes on the lambda calculus pdf 106p download book. Peter selinger submitted on 22 apr 2008 v1, last revised 26 dec 20 this version, v2 abstract. An implementation of the lambda munu calculus 1998. Robin milner, joachim parrow, david walker, a calculus of mobile processes, part i, 1989. A mathematical investigation of programming paradigms peter selinger andre scedrov the search for mathematical models of computational phenomena often leads to problems that are of independent mathematical interest. The midterm covers everything up to the october 11 class, i. A short introduction to the lambda calculus achim jung. This is a set of lecture notes that developed out of courses on the lambda calculus that. On coinduction and quantum lambda calculi drops schloss. Lecture notes on the lambda calculus download link. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext.
A lambda calculus for quantum computation with classical control. Semantics for a quantum programming language by operator. This is a set of lecture notes that developed out of courses on the lambda calculus that the author taught at the university of ottawa in 2001 and at dalhousie university in 2007 and 20. Lecture notes on the lambda calculus pdf 106p download. Pdf a linearnonlinear model for a computational call.
Lambda calculus is a language with clear operational and denotational semantics capable of expressing algorithms. Lecture notes on the lambda calculus peter selinger department of mathematics and statistics dalhousie. A tutorial on proof systems and typed lambda calculi. It was first formulated by alonzo church as a way to formalize mathematics through the notion of functions, in contrast to the field of set theory. A lambda calculus function or term is an implementation of a mathematical function.
Topics covered in these notes include the untyped lambda calculus, the churchrosser theorem, combinatory algebras, the simplytyped. The idea is due to sch on nkel 1924 but is often called currying, after h. 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. The objective of this paper is to develop a functional programming language for quantum computers. Selected problems of this kind are investigated in this thesis. 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 universityin2007. We develop a lambda calculus for the classical control. Introduction to categorical logic peter selinger dalhousie university. Lecture notes on the lambda calculus department of mathematics.
Formalization of metatheory of the quipper quantum. A linearnonlinear model for a computational callbyvalue lambda calculus extended abstract. A lambda calculus for quantum computation with classical control volume 16 issue 3 peter selinger, benoit valiron. Mathematical structures in computer science 14, 4 2004, 527586. Peter selinger dalhousie university, halifax, canada arxiv. Deductive lambda calculus considers what happens when lambda terms are regarded as mathematical expressions. There are more than 1 million books that have been enjoyed by people from all over the world. 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. Michele pagani, peter selinger, and benoit valiron. The lambda calculus is a formalism of highorder functions and it is a logical basis of some important classical functional programming languages, such as lisp, scheme, ml and haskell. Lambda calculus as a workflow model by peter kelly, paul coddington, and andrew wendelborn. A lambda calculus for quantum computation with classical.
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