The Jack Programming Language
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Lecture Notes on Types for Part II of the Computer Science Tripos
Q Lecture Notes on Types for Part II of the Computer Science Tripos Prof. Andrew M. Pitts University of Cambridge Computer Laboratory c 2016 A. M. Pitts Contents Learning Guide i 1 Introduction 1 2 ML Polymorphism 6 2.1 Mini-ML type system . 6 2.2 Examples of type inference, by hand . 14 2.3 Principal type schemes . 16 2.4 A type inference algorithm . 18 3 Polymorphic Reference Types 25 3.1 The problem . 25 3.2 Restoring type soundness . 30 4 Polymorphic Lambda Calculus 33 4.1 From type schemes to polymorphic types . 33 4.2 The Polymorphic Lambda Calculus (PLC) type system . 37 4.3 PLC type inference . 42 4.4 Datatypes in PLC . 43 4.5 Existential types . 50 5 Dependent Types 53 5.1 Dependent functions . 53 5.2 Pure Type Systems . 57 5.3 System Fw .............................................. 63 6 Propositions as Types 67 6.1 Intuitionistic logics . 67 6.2 Curry-Howard correspondence . 69 6.3 Calculus of Constructions, lC ................................... 73 6.4 Inductive types . 76 7 Further Topics 81 References 84 Learning Guide These notes and slides are designed to accompany 12 lectures on type systems for Part II of the Cambridge University Computer Science Tripos. The course builds on the techniques intro- duced in the Part IB course on Semantics of Programming Languages for specifying type systems for programming languages and reasoning about their properties. The emphasis here is on type systems for functional languages and their connection to constructive logic. We pay par- ticular attention to the notion of parametric polymorphism (also known as generics), both because it has proven useful in practice and because its theory is quite subtle. -
Open C++ Tutorial∗
Open C++ Tutorial∗ Shigeru Chiba Institute of Information Science and Electronics University of Tsukuba [email protected] Copyright c 1998 by Shigeru Chiba. All Rights Reserved. 1 Introduction OpenC++ is an extensible language based on C++. The extended features of OpenC++ are specified by a meta-level program given at compile time. For dis- tinction, regular programs written in OpenC++ are called base-level programs. If no meta-level program is given, OpenC++ is identical to regular C++. The meta-level program extends OpenC++ through the interface called the OpenC++ MOP. The OpenC++ compiler consists of three stages: preprocessor, source-to-source translator from OpenC++ to C++, and the back-end C++ com- piler. The OpenC++ MOP is an interface to control the translator at the second stage. It allows to specify how an extended feature of OpenC++ is translated into regular C++ code. An extended feature of OpenC++ is supplied as an add-on software for the compiler. The add-on software consists of not only the meta-level program but also runtime support code. The runtime support code provides classes and functions used by the base-level program translated into C++. The base-level program in OpenC++ is first translated into C++ according to the meta-level program. Then it is linked with the runtime support code to be executable code. This flow is illustrated by Figure 1. The meta-level program is also written in OpenC++ since OpenC++ is a self- reflective language. It defines new metaobjects to control source-to-source transla- tion. The metaobjects are the meta-level representation of the base-level program and they perform the translation. -
Assignment 6: Subtyping and Bidirectional Typing
Assignment 6: Subtyping and Bidirectional Typing 15-312: Foundations of Programming Languages Joshua Dunfield ([email protected]) Out: Thursday, October 24, 2002 Due: Thursday, November 7 (11:59:59 pm) 100 points total + (up to) 20 points extra credit 1 Introduction In this assignment, you will implement a bidirectional typechecker for MinML with , , +, 1, 0, , , and subtyping with base types int and float. ! ∗ 8 9 Note: In the .sml files, most changes from Assignment 4 are indicated like this: (* new asst6 code: *) ... (* end asst6 code *) 2 New in this assignment Some things have become obsolete (and have either been removed or left • in a semi-supported state). Exceptions and continuations are no longer “officially” supported. One can now (and sometimes must!) write type annotations e : τ. The • abstract syntax constructor is called Anno. The lexer supports shell-style comments in .mml source files: any line • beginning with # is ignored. There are now two valid syntaxes for functions, the old syntax fun f (x:t1):t2 is e end • and a new syntax fun f(x) is e end. Note the lack of type anno- tations. The definition of the abstract syntax constructor Fun has been changed; its arguments are now just bindings for f and x and the body. It no longer takes two types. 1 The old syntax fun f(x:t1):t2 is e end is now just syntactic sugar, transformed by the parser into fun f(x) is e end : t1 -> t2. There are floating point numbers, written as in SML. There is a new set of • arithmetic operators +., -., *., ˜. -
Let's Get Functional
5 LET’S GET FUNCTIONAL I’ve mentioned several times that F# is a functional language, but as you’ve learned from previous chapters you can build rich applications in F# without using any functional techniques. Does that mean that F# isn’t really a functional language? No. F# is a general-purpose, multi paradigm language that allows you to program in the style most suited to your task. It is considered a functional-first lan- guage, meaning that its constructs encourage a functional style. In other words, when developing in F# you should favor functional approaches whenever possible and switch to other styles as appropriate. In this chapter, we’ll see what functional programming really is and how functions in F# differ from those in other languages. Once we’ve estab- lished that foundation, we’ll explore several data types commonly used with functional programming and take a brief side trip into lazy evaluation. The Book of F# © 2014 by Dave Fancher What Is Functional Programming? Functional programming takes a fundamentally different approach toward developing software than object-oriented programming. While object-oriented programming is primarily concerned with managing an ever-changing system state, functional programming emphasizes immutability and the application of deterministic functions. This difference drastically changes the way you build software, because in object-oriented programming you’re mostly concerned with defining classes (or structs), whereas in functional programming your focus is on defining functions with particular emphasis on their input and output. F# is an impure functional language where data is immutable by default, though you can still define mutable data or cause other side effects in your functions. -
(901133) Instructor: Eng
home Al-Albayt University Computer Science Department C++ Programming 1 (901133) Instructor: Eng. Rami Jaradat [email protected] 1 home Subjects 1. Introduction to C++ Programming 2. Control Structures 3. Functions 4. Arrays 5. Pointers 6. Strings 2 home 1 - Introduction to C++ Programming 3 home What is computer? • Computers are programmable devices capable of performing computations and making logical decisions. • Computers can store, retrieve, and process data according to a list of instructions • Hardware is the physical part of the compute: keyboard, screen, mouse, disks, memory, and processing units • Software is a collection of computer programs, procedures and documentation that perform some tasks on a computer system 4 home Computer Logical Units • Input unit – obtains information (data) from input devices • Output unit – outputs information to output device or to control other devices. • Memory unit – Rapid access, low capacity, stores information • Secondary storage unit – cheap, long-term, high-capacity storage, stores inactive programs • Arithmetic and logic unit (ALU) – performs arithmetic calculations and logic decisions • Central processing unit (CPU): – supervises and coordinates the other sections of the computer 5 home Computer language • Machine languages: machine dependent, it consists of strings of numbers giving machine specific instructions: +1300042774 +1400593419 +1200274027 • Assembly languages: English-like abbreviations representing elementary operations, assemblers convert assembly language to machine -
Explicitly Implicifying Explicit Constructors
Explicitly Implicifying explicit Constructors Document number: P1163R0 Date: 2018-08-31 Project: Programming Language C++, Library Working Group Reply-to: Nevin “☺” Liber, [email protected] or [email protected] Table of Contents Revision History ................................................................................................................ 3 P11630R0 .................................................................................................................................... 3 Introduction ....................................................................................................................... 4 Motivation and Scope ....................................................................................................... 5 Impact On the Standard ................................................................................................... 6 Policy .................................................................................................................................. 7 Design Decisions ................................................................................................................ 8 Technical Specifications ................................................................................................... 9 [template.bitset]........................................................................................................................ 10 [bitset.cons] .............................................................................................................................. -
Run-Time Type Information and Incremental Loading in C++
Run-time Type Information and Incremental Loading in C++ Murali Vemulapati Sriram Duvvuru Amar Gupta WP #3772 September 1993 PROFIT #93-11 Productivity From Information Technology "PROFIT" Research Initiative Sloan School of Management Massachusetts Institute of Technology Cambridge, MA 02139 USA (617)253-8584 Fax: (617)258-7579 Copyright Massachusetts Institute of Technology 1993. The research described herein has been supported (in whole or in part) by the Productivity From Information Technology (PROFIT) Research Initiative at MIT. This copy is for the exclusive use of PROFIT sponsor firms. Productivity From Information Technology (PROFIT) The Productivity From Information Technology (PROFIT) Initiative was established on October 23, 1992 by MIT President Charles Vest and Provost Mark Wrighton "to study the use of information technology in both the private and public sectors and to enhance productivity in areas ranging from finance to transportation, and from manufacturing to telecommunications." At the time of its inception, PROFIT took over the Composite Information Systems Laboratory and Handwritten Character Recognition Laboratory. These two laboratories are now involved in research re- lated to context mediation and imaging respectively. LABORATORY FOR ELEC RONICS A CENTERCFORENTER COORDINATION LABORATORY ) INFORMATION S RESEARCH RESE CH E53-310, MITAL"Room Cambridge, MA 02M142-1247 Tel: (617) 253-8584 E-Mail: [email protected] Run-time Type Information and Incremental Loading in C++ September 13, 1993 Abstract We present the design and implementation strategy for an integrated programming environment which facilitates specification, implementation and execution of persistent C++ programs. Our system is implemented in E, a persistent programming language based on C++. The environment provides type identity and type persistence, i.e., each user-defined class has a unique identity and persistence across compilations. -
The Cool Reference Manual∗
The Cool Reference Manual∗ Contents 1 Introduction 3 2 Getting Started 3 3 Classes 4 3.1 Features . 4 3.2 Inheritance . 5 4 Types 6 4.1 SELF TYPE ........................................... 6 4.2 Type Checking . 7 5 Attributes 8 5.1 Void................................................ 8 6 Methods 8 7 Expressions 9 7.1 Constants . 9 7.2 Identifiers . 9 7.3 Assignment . 9 7.4 Dispatch . 10 7.5 Conditionals . 10 7.6 Loops . 11 7.7 Blocks . 11 7.8 Let . 11 7.9 Case . 12 7.10 New . 12 7.11 Isvoid . 12 7.12 Arithmetic and Comparison Operations . 13 ∗Copyright c 1995-2000 by Alex Aiken. All rights reserved. 1 8 Basic Classes 13 8.1 Object . 13 8.2 IO ................................................. 13 8.3 Int................................................. 14 8.4 String . 14 8.5 Bool . 14 9 Main Class 14 10 Lexical Structure 14 10.1 Integers, Identifiers, and Special Notation . 15 10.2 Strings . 15 10.3 Comments . 15 10.4 Keywords . 15 10.5 White Space . 15 11 Cool Syntax 17 11.1 Precedence . 17 12 Type Rules 17 12.1 Type Environments . 17 12.2 Type Checking Rules . 18 13 Operational Semantics 22 13.1 Environment and the Store . 22 13.2 Syntax for Cool Objects . 24 13.3 Class definitions . 24 13.4 Operational Rules . 25 14 Acknowledgements 30 2 1 Introduction This manual describes the programming language Cool: the Classroom Object-Oriented Language. Cool is a small language that can be implemented with reasonable effort in a one semester course. Still, Cool retains many of the features of modern programming languages including objects, static typing, and automatic memory management. -
Kodak Color Control Patches Kodak Gray
Kodak Color Control Patches 0 - - _,...,...,. Blue Green Yellow Red White 3/Color . Black Kodak Gray Scale A 1 2 a 4 s -- - --- - -- - -- - -- -- - A Study of Compile-time Metaobject Protocol :J/1\'-(Jt.-S~..)(:$/;:t::;i':_;·I'i f-.· 7 •[:]f-. :::JJl. (:~9 ~~Jf'?E By Shigeru Chiba chiba~is.s.u-tokyo.ac.jp November 1996 A Dissertation Submitted to Department of Information Science Graduate School of Science The Un iversity of Tokyo In Partial Fulfillment of the Requirements For the Degree of Doctor of Science. Copyright @1996 by Shigeru Chiba. All Rights Reserved. - - - ---- - ~-- -- -~ - - - ii A Metaobject Protocol for Enabling Better C++ Libraries Shigeru Chiba Department of Information Science The University of Tokyo chiba~is.s.u-tokyo.ac.jp Copyrighl @ 1996 by Shi geru Chiba. All Ri ghts Reserved. iii iv Abstract C++ cannot be used to implement control/data abstractions as a library if their implementations require specialized code for each user code. This problem limits programmers to write libraries in two ways: it makes some kinds of useful abstractions that inherently require such facilities impossi ble to implement, and it makes other abstractions difficult to implement efficiently. T he OpenC++ MOP addresses this problem by providing li braries the ability to pre-process a program in a context-sensitive and non-local way. That is, libraries can instantiate specialized code depending on how the library is used and, if needed, substitute it for the original user code. The basic protocol structure of the Open C++ MOP is based on that of the CLOS MOP, but the Open C++ MOP runs metaobjects only at compile time. -
1 Simply-Typed Lambda Calculus
CS 4110 – Programming Languages and Logics Lecture #18: Simply Typed λ-calculus A type is a collection of computational entities that share some common property. For example, the type int represents all expressions that evaluate to an integer, and the type int ! int represents all functions from integers to integers. The Pascal subrange type [1..100] represents all integers between 1 and 100. You can see types as a static approximation of the dynamic behaviors of terms and programs. Type systems are a lightweight formal method for reasoning about behavior of a program. Uses of type systems include: naming and organizing useful concepts; providing information (to the compiler or programmer) about data manipulated by a program; and ensuring that the run-time behavior of programs meet certain criteria. In this lecture, we’ll consider a type system for the lambda calculus that ensures that values are used correctly; for example, that a program never tries to add an integer to a function. The resulting language (lambda calculus plus the type system) is called the simply-typed lambda calculus (STLC). 1 Simply-typed lambda calculus The syntax of the simply-typed lambda calculus is similar to that of untyped lambda calculus, with the exception of abstractions. Since abstractions define functions tht take an argument, in the simply-typed lambda calculus, we explicitly state what the type of the argument is. That is, in an abstraction λx : τ: e, the τ is the expected type of the argument. The syntax of the simply-typed lambda calculus is as follows. It includes integer literals n, addition e1 + e2, and the unit value ¹º. -
Generic Immutability and Nullity Types for an Imperative Object-Oriented Programming Language with flexible Initialization
Generic Immutability and Nullity Types for an imperative object-oriented programming language with flexible initialization James Elford June 21, 2012 Abstract We present a type system for parametric object mutability and ref- erence nullity in an imperative object oriented language. We present a simple but powerful system for generic nullity constraints, and build on previous work to provide safe initialization of objects which is not bound to constructors. The system is expressive enough to handle initialization of cyclic immutable data structures, and to enforce their cyclic nature through the type system. We provide the crucial parts of soundness ar- guments (though the full proof is not yet complete). Our arguments are novel, in that they do not require auxiliary runtime constructs (ghost state) in order to express or demonstrate our desired properties. 2 Contents 1 Introduction 4 1.1 In this document . .5 2 Background 6 2.1 Parametric Types . .6 2.1.1 Static Polymorphism through Templates . .7 2.1.2 Static Polymorphism through Generic Types . 12 2.2 Immutability . 18 2.2.1 Immutability in C++ .................... 19 2.2.2 Immutability in Java and C# ............... 21 2.2.3 An extension to Java's immutability model . 21 2.2.4 Parametric Immutability Constraints . 24 2.3 IGJ: Immutability Generic Java .................. 25 2.4 Nullity . 27 2.5 Areas of commonality . 30 3 Goals 32 4 Existing systems in more detail 34 4.1 The initialization problem . 34 4.2 What do we require from initialization? . 35 4.3 Approaches to initialization . 37 4.4 Delay Types and initialization using stack-local regions . -
Query Rewriting Using Views in a Typed Mediator
Язык СИНТЕЗ как ядро канонической информационной модели Л. А. Калиниченко ([email protected]) C. А. Ступников ([email protected]) Lecture outline Objectives of the language Frame language: semi-structured capabilities Type system of SYNTHESIS Classes and metaclasses Assertions Processes, workflows Formulae facilities of the language 2 History of the language . Preliminary draft version published in 1991 . First version published in 1993 . English version prepared in 1995 and extended in 1997 . Current version in English published in 2007 3 The SYNTHESIS is a multipurpose language The language is oriented on the following basic kinds of application: . serving as a kernel of the canonical information model; . providing facilities for unifying representation of heterogeneous information models of different kinds (of data, services, processes, ontologies); . providing sufficient modeling facilities for formalized definitions of mediators for various subject domains; . supporting mediation-based design of information systems; . providing modeling facilities for mediator and resource specifications for the mediation architecture; . serving for semantic reconciliation of the mediator and resource specifications to form compositions of resources refining mediator specifications; . serving as an interface for users during problem formulation and solving in various applications 4 Mediation orientation . Two different approaches to the problem of integrated representation of multiple information resources for an IS are distinguished: 1. moving from resources to problems (resource driven approach) 2. moving from an application to resources (application driven approach) The SYNTHESIS language is oriented on support of application-driven approach for mediation-based IS development. The mediator's layer is introduced to provide the users with the metainformation uniformly characterizing subject definitions in the canonical information model – providing application domain conceptual schema .