Enhancing Show-and-Tell with a polymorphic type system and higher-order functions

2002 ◽  
Author(s):  
M.A. Najork ◽  
E. Golin
Keyword(s):  
Type System ◽  
Higher Order ◽  
Polymorphic Type ◽  
Higher Order Functions

scholarly journals A Complete Calculus of Monotone and Antitone Higher-Order Functions

10.29007/3n54 ◽  
2018 ◽  
Author(s):  
Thomas Icard ◽  
Lawrence Moss
Keyword(s):  
Type System ◽  
Lambda Calculus ◽  
Higher Order ◽  
Typed Lambda Calculus ◽  
Higher Order Functions

This paper adds monotonicity and antitonicity information to the typed lambda calculus, thereby providing a foundation for the Monotonicity Calculus first developed by van Benthem and others. We establish properties of the type system, propose a syntax, semantics, and proof calculus, and prove completeness for the calculus with respect to hierarchies of monotone and antitone functions over base preorders.

scholarly journals Helmholtz: A Verifier for Tezos Smart Contracts Based on Refinement Types

2021 ◽  
pp. 262-280
Author(s):  
Yuki Nishida ◽  
Hiromasa Saito ◽  
Ran Chen ◽  
Akira Kawata ◽  
Jun Furuse ◽  
...  
Keyword(s):  
Type System ◽  
Higher Order ◽  
Smart Contracts ◽  
Static Verification ◽  
Smt Solver ◽  
The Core ◽  
Verification Conditions ◽  
Refinement Types ◽  
Characteristic Features ◽  
Higher Order Functions

AbstractA smart contract is a program executed on a blockchain, based on which many cryptocurrencies are implemented, and is being used for automating transactions. Due to the large amount of money that smart contracts deal with, there is a surging demand for a method that can statically and formally verify them.This tool paper describes our type-based static verification tool Helmholtz for Michelson, which is a statically typed stack-based language for writing smart contracts that are executed on the blockchain platform Tezos. Helmholtz is designed on top of our extension of Michelson’s type system with refinement types. Helmholtz takes a Michelson program annotated with a user-defined specification written in the form of a refinement type as input; it then typechecks the program against the specification based on the refinement type system, discharging the generated verification conditions with the SMT solver Z3. We briefly introduce our refinement type system for the core calculus Mini-Michelson of Michelson, which incorporates the characteristic features such as compound datatypes (e.g., lists and pairs), higher-order functions, and invocation of another contract. Helmholtz successfully verifies several practical Michelson programs, including one that transfers money to an account and that checks a digital signature.

scholarly journals Reachability types: tracking aliasing and separation in higher-order functional programs

2021 ◽  
Vol 5 (OOPSLA) ◽  
pp. 1-32
Author(s):  
Yuyan Bao ◽  
Guannan Wei ◽  
Oliver Bračevac ◽  
Yuxuan Jiang ◽  
Qiyang He ◽  
...  
Keyword(s):  
Functional Programming ◽  
Type System ◽  
Type Systems ◽  
Higher Order ◽  
Ownership Type ◽  
Ownership Transfer ◽  
Reachability Sets ◽  
Programming Patterns ◽  
New Type ◽  
Higher Order Functions

Ownership type systems, based on the idea of enforcing unique access paths, have been primarily focused on objects and top-level classes. However, existing models do not as readily reflect the finer aspects of nested lexical scopes, capturing, or escaping closures in higher-order functional programming patterns, which are increasingly adopted even in mainstream object-oriented languages. We present a new type system, λ * , which enables expressive ownership-style reasoning across higher-order functions. It tracks sharing and separation through reachability sets, and layers additional mechanisms for selectively enforcing uniqueness on top of it. Based on reachability sets, we extend the type system with an expressive flow-sensitive effect system, which enables flavors of move semantics and ownership transfer. In addition, we present several case studies and extensions, including applications to capabilities for algebraic effects, one-shot continuations, and safe parallelization.

Building language towers with Ziggurat

2008 ◽  
Vol 18 (5-6) ◽  
pp. 707-780 ◽  
Author(s):  
DAVID FISHER ◽  
OLIN SHIVERS
Keyword(s):  
Assembly Language ◽  
Flow Analysis ◽  
Type System ◽  
Type Systems ◽  
Higher Order ◽  
Language System ◽  
Static Semantics ◽  
Language Level ◽  
Concrete Syntax ◽  
Polymorphic Type

AbstractZiggurat is a meta-language system that permits programmers to develop Scheme-like macros for languages with nontrivial static semantics, such as C or Java (suitably encoded in an S-expression concrete syntax). Ziggurat permits language designers to construct ‘towers’ of language levels with macros; each level in the tower may have its own static semantics, such as type systems or flow analyses. Crucially, the static semantics of the languages at two adjacent levels in the tower can be connected, allowing improved reasoning power at a higher level to be reflected down to the static semantics of the language level below. We demonstrate the utility of the Ziggurat framework by implementing higher level language facilities as macros on top of an assembly language, utilizing static semantics such as termination analysis, a polymorphic type system and higher order flow analysis.

scholarly journals Voigt Transform and Umbral Image

2020 ◽  
Vol 25 (3) ◽  
pp. 49
Author(s):  
Silvia Licciardi ◽  
Rosa Maria Pidatella ◽  
Marcello Artioli ◽  
Giuseppe Dattoli
Keyword(s):  
Spectroscopic Studies ◽  
Higher Order ◽  
Point Of View ◽  
The Other ◽  
Pivotal Role ◽  
Umbral Calculus ◽  
Laguerre Functions ◽  
Hermite And Laguerre Functions ◽  
Higher Order Functions ◽  
Voigt Function

In this paper, we show that the use of methods of an operational nature, such as umbral calculus, allows achieving a double target: on one side, the study of the Voigt function, which plays a pivotal role in spectroscopic studies and in other applications, according to a new point of view, and on the other, the introduction of a Voigt transform and its possible use. Furthermore, by the same method, we point out that the Hermite and Laguerre functions, extension of the corresponding polynomials to negative and/or real indices, can be expressed through a definition in a straightforward and unified fashion. It is illustrated how the techniques that we are going to suggest provide an easy derivation of the relevant properties along with generalizations to higher order functions.

A system of constructor classes: overloading and implicit higher-order polymorphism

1995 ◽  
Vol 5 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Mark P. Jones
Keyword(s):  
Type System ◽  
Type Systems ◽  
Natural Generalization ◽  
Higher Order ◽  
Functional Language ◽  
Effective Algorithm ◽  
Prototype Implementation ◽  
Type Classes

AbstractThis paper describes a flexible type system that combines overloading and higher-order polymorphism in an implicitly typed language using a system of constructor classes—a natural generalization of type classes in Haskell. We present a range of examples to demonstrate the usefulness of such a system. In particular, we show how constructor classes can be used to support the use of monads in a functional language. The underlying type system permits higher-order polymorphism but retains many of the attractive features that have made Hindley/Milner type systems so popular. In particular, there is an effective algorithm that can be used to calculate principal types without the need for explicit type or kind annotations. A prototype implementation has been developed providing, amongst other things, the first concrete implementation of monad comprehensions known to us at the time of writing.

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