Dependently typed functional programming with idris. Sequential decision problems, dependently typed solutions. Dependently typed programming with idris confengine. Design and implementation edwin brady school of computer science, university of st andrews, st andrews, ky16 9sx, uk abstract many components of a dependently typed programming language are by now well understood, for. Dependently typed languages have proven useful for developing largescale verified software, but we do not have any guarantees after compiling that verified software. Recent versions of the haskell compiler ghc have a number of advanced features that allow many idioms from dependently typed programming to be encoded. Dependent types are powerful enough to encode most properties of programs, and an idris program can prove invariants at compiletime. Our goal in this work, is to present a compiler for the beluga system, that uses a very versatile internal representation that helps with the development of the system, and allows a sharing of code between several backends. If the user can supply a constructive proof that a type is inhabited i. Epic the name derives from epigram compiler is a compiler for a small. Typed closure conversion for the calculus of constructions.
Programming languages khoury college of computer sciences. Dependent types help apply type driven development and a lot of code auto generation, making the compiler and type checker an ally in developing working software instead of just getting in the way. A verified program written in a dependently typed language, such as coq, can. In this paper, we generalize our previous type theory to account for dependently typed inference rules, which are necessary to adequately represent domainspecific logics, and we present examples of using our type theory for certified software and mechanized metatheory. A b for the type of functions taking an argument xof type aand returning a result of type b, where xmay appear in b. Pages in category dependently typed programming the following 12 pages are in this category, out of 12 total. How does idris compare to other dependentlytyped programming. This is a collection of software ive written that is available for download, mostly. The expression language or calculus, which is a dependently typed lambda calculus supplemented with parametric. Dependent types are a feature of certain programming language type systems that are unusually powerful, expressive, and precise, compared with other kinds of types. Dependently typed metaprogramming edwin brady and kevin hammond school of computer science, university of st andrews, st andrews, scotland. Supplied with the distribution is a c code generator to compile executables, and a javascript code generator with support for node. However, as recursion, effects, and rich libraries are added, using types to reason about programs, specifications and proofs becomes. Then we write tests because the compiler cant help us.
We treat the type as the plan for a program, and use the compiler and type checker as our assistant, guiding us to a complete program that satisfies. Similarly, when choosing a type for a mutable variable xs in your dependently typed language, users could have to choose between a precise type such as ist and an imprecise type such as. However, there remains a significant difference between programming in haskell and in fullspectrum dependently typed languages. Functional programming 1 idris, a general purpose dependently typed programming language. Im developing mostly javascript and ethereum projects.
Dependently typed programming with singletons proceedings. Our language permits programmers to define logics using the lf logical framework, whose notion of. Fullspectrum dependently typed programming languages such as coq have had tremendous impact on the formal verification of largescale software. A compiler for the dependently typed language beluga. Full on dependently typed languages impose no such restriction, and in my career as a dependently typed showoff, ive learned to include examples of twolayer indexing in my talks, just to teach folks whove made onelayer indexing difficultbutpossible not to expect me to fold up like a house of cards. How does a dependently typed programming language cope. In type driven development, types are tools for constructing programs. Dependently typed functional programming with idris lecture 1. Despite these successes, dependently typed languages are rarely used for daytoday programming tasks. In this chapter, we show that security typed programming. New, dependently typed programming languages use principles of functional programming and advanced type systems to achieve a smoother and cleaner proof theory, so that verifying the correctness and safety of software written in these new languages is much easier.
Our previous project on integrating types and verification shows that the use of logics specific to an application domain is a promising way to verify software within a dependently typed. Which dependently typed programming languages could be used for real world application development. Agda is based on intuitionistic type theory 38, a foundational system for. Idris is a programming language designed to encourage type driven development. A discussion and analysis of the current state of dependently typed programming in haskell, demonstrating how well recent and not so recent extensions to ghc can be used for this purpose. To compare with fullspectrum languages, we present an extended example based on an agda interface for safe database access. In a dependentlytyped language, ifthenelse is a special case of elimbool, the eliminator for booleanvalued expressions whose type is.
Dependentlytyped programming languages such as coq, agda, and idris appear occasionally in academia but not at all in mainstream languages used by software practitioners. They dont exactly fit our bill, as a result of which, we write runtime code to enforce those conditions. In intuitionistic type theory, dependent types are used to encode logics quantifiers like for all and there exists. Types express a programs meaning, and checking types ensures that a program has the. This paper presents the singletons library, which generates the boilerplate code necessary for dependently typed programming using ghc.
Prior to oplss, students should have the following software ready on their laptops coq 8. Its much more focused on getting stuff done than agda is. Domainspecific logics are a promising way to verify. A monad for typed tactic programming in coq in this paper, we present a new languagemtacfor typed tactic programming in coq. I will mostly be writing toy applications at first, after that maybe web development or a simple dbms. The certicoq project aims to build a provencorrect compiler for dependently typed, functional languages, such as gallinathe core language of the coq proof assistant. The most basic depen dent type is the dependent function type, where the result type depends on the value of the argument.
Researchers have also developed several other dependently typed programming languages such as agda, aura, ats, cayenne, epigram, f, f7, fine, guru, pcml5, ur, etc. A library, singletons, to better support dependently typed programming in haskell. Why dependent haskell is the future of software development. Like beluga and veriml, mtac supports generalpurpose tactic programming in a direct functional style. Im looking for a dependently typed language that i can use to learn more about the concept of proving statements about my programs, but i also want to apply those learnings to my reallife work. Another is to make it generalized enough to solve many problems if you want e. Agda is the name of both the dependently typed functional programming language, and the interactive proof assistant to work with the language, based on typed holes 41 implemented as an emacs mode. It allows to write structured, recursive dependently typed functions, automatically find their realization in the core type theory and generate proofs to ease reasoning on them. As a result, ghc implementors have responded with extensions to haskells type system, such as gadts, type families, and datatype promotion.
Advanced programming languages, based on dependent types, enable program verification alongside program development, thus making them an ideal tool for building fully verified, high assurance software. Licata introduction this dissertation describes progress on programming with domainspeci. Dependently typed languages like idris 14 can give rise to such detailed type level specifications, that the compiler can in some cases generate code from a functions type automatically if it. Why dependently typed programming will one day rock your world. A dependently typed functional programming language idrislangidris. In short, we propose to design a dependently typed imperative programming language for studying the use of dependent types in practical imperative programming at both source level and assembly level. We present a compiler for definitions made by pattern matching on inductive families in the coq system. Many of the programs that beluga is specially well suited for writing can benefit from a compiler.
Students should install agda, following the direction at my oplss page students might find it helfpul to peruse some of the tutorials listed there, but no prior knowledge of agda will be assumed. Morrisett is a fellow of the acm and has received a number of awards for his research on programming languages, type systems, and software security, including a presidential early career award for scientists and engineers, an ibm faculty fellowship, an nsf career award, and an alfred p. The proof checking feature makes dependently typed languages closely related to proof assistants. Dependently typed functional languages promise to prevent broad classes of errors and vulnerabilities, and to enable program verification to proceed sidebyside with development. Why dependently typed programming will one day rock your. The last decade has seen many success stories for verified programming with dependent types, including the compcert verified c compiler, verified libraries for concurrency and security, and machinechecked proofs of results like the four color theorem and the feitthompson theorem. Dependently typed programming with idris functional conf. In computer science and logic, a dependent type is a type whose definition depends on a value. In functional programming languages like agda, ats, coq, f, epigram, and idris, dependent types may help reduce bugs. Apr 04, 2020 a dependently typed functional programming language idrislangidrisdev. I care about dependently typed programming dtp because i find it intriguing and challenging, but there is no way i want it anywhere near any code base that i work on. Or in other words, parameterizing a type definition over a value.
Dependently typed programming with domainspecific logics. Programming languages projects khoury college of computer. The beluga programming environment is an example of such a system. Dependently typed array programs dont go wrong sciencedirect. However, as recursion, effects, and rich libraries are added, using types to reason about programs, specifications and proofs becomes challenging. Idris is a research project to create a dependently typed programming language. We expect this study can eventually lead to the production of software that is not only more robust but also less costly to maintain. New publications and drafts typepreserving compilation via dependently typed syntax andreas abel 2020. Why you should care about dependently typed programming. Rather, me and you and everyone we know will have a whole new framework in which to think, learn, and interact with the world.
It can be viewed as a function from types to types. Idris, as suggested by twey, is the closest candidate to a real world dependently typed language. Many issues remain to be resolved, including but not limited to. The current version, originally known as agda 2, is a full rewrite, which should be considered a new language that shares a name and. Dependently typed language best suited to real world. Idris has full dependent pattern matching like agda and tactic based theorem proving like coq. A major complication resulting from introducing dependent types is that pure type inference for the.
Unlike those languages, however, mtac is not a separate language, but rather a simple extension to coq. Bramble is a dependently typed programming language, written using sexpressions. Robert harper, chair karl crary frank pfenning greg morrisett, harvard university. Dependently typed programming with domainspecific logics daniel r. To put the rest in context, maybe its easiest to explain why idris exists at all. Dependently typed languages have proven useful for developing largescale fully verified software, but we do not have any guarantees after compiling that verified software. It is an overlapping feature of type theory and type systems. Wellestablished dependently typed languages like coq provide a highly reliable way to build and check formal proofs. In typedriven development, types are tools for constructing programs. Dependently typed languages like idris allow us to encode a wide range of invariants into the type itself allowing us to possibly have zero runtime errors. In this work we develop and present a compiler for the system. Id recommend agda as the better vehicle for getting to grips with the ideas behind dependently typed programming, but idris is the more practical option. Haskell enforces a phase separation between runtime values and compiletime.
Dtal improves upon tal, enabling certain important compiler optimizations such as runtime array bound check elimination and tag check elimination. Securitytyped programming within dependently typed. Students without prior experience using coq are strongly encouraged to install the software and study the earlier chapters of software foundations on their own before the school begins. This dissertation describes progress on programming with domainspecific specification logics in dependently typed programming languages. When the day comes to start running software on our brains, well only need to upload one program. The expression language or calculus, which is a dependentlytyped lambda calculus supplemented with parametric, recursive algebraic datatypes, records, and fixpoint. Idris, a general purpose dependently typed programming.
We describe our experiences using this dependently typed haskell to construct a performancecritical library that is a key component in a number of verification tools. Ive found the benefits are simply not worth the immense cost they impose in terms of mental. Furthermore, we present a way of compiling the uniquely powerful pattern language supported by beluga. Are dependent types insanity or the future of software development. Bramble is a dependentlytyped programming language, written using sexpressions. More information about code generators can be found on the wiki. A verified program written in a dependently typed language, such as coq, can be type checked to ensure that the program meets its specification. The original agda system was developed at chalmers by catarina coquand in 1999. We define a dependent programming language in which programmers can define and compute with domainspecific logics, such as an accesscontrol logic that statically prevents unauthorized access to controlled resources. Agda is a dependently typed functional programming language originally developed by ulf norell at chalmers university of technology with implementation described in his phd thesis. Its current version agda 2 is a complete rewrite instigated by ulf. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Coq has been used to specify and prove the full functional correctness the compcert c compiler 27, the certikos os kernel 20, 21, and implementations of cryptographic primitives and protocols 6, 8. My experience has been that making contracts part of the type makes for very fragile type signatures that are very annoying to work with.
Apr 26, 2014 ive seen the future, and its dependently typed. Distributed applications are difficult to program reliably and securely. A provedcorrect compiler consists of a highlevel functional specification, machineverified proofs of important properties, such as safety and correctness, and a. Domainspecific logics are a promising way to verify software, using a logic tailored to a style of programming or. We present a dependently typed assembly language dtal in which the type system supports the use of a restricted form of dependent types, reaping some bene ts of dependent types at the assembly level.
As type inference is undecidable for dependently typed languages, idris cannot offer the full type inference that haskell supports, and so more type annotations will be needed. Dependently typed programming, however, is yet to be considered a practical tool and an ef. That said, rust wouldnt likely be dependently typed but it will never diminish the value of either rust or dependently typed. As in coq, there are really a few distinct languages involved. Securitytyped programming within dependently typed programming.
Conference paper cister research centre in realtime and. Dependently typed programming, however, is yet to be considered a practical tool and an efficient device to ensure program correctness and to reduce development costs. His recent work examines type preserving compilation of dependently typed programming language like coq, a technique that can enable preserving security and correctness invariants of verified software through compilation and statically enforcing those invariants in the lowlevel assemblylike code generated by compilers. I expect both will coexist for long time, as there are considerable pros and cons for each directions. Idris, a generalpurpose dependently typed programming.
Looking for a dependently typed language that i can use in. Because of full dependent types in idris, the programmer can focus more on modelling the domain with types and waste less time fixing common bugs that the type checker will catch. Dependently typed haskell in industry experience report. List, that is, a dependent pair indicating that the int part of list is fixed but the n part can be changed by mutations. Secure distributed programming with valuedependent types. Mccosh, typebased specialization in a telescoping compiler for matlab, master thesis tr03412, rice university, houston, texas, usa, 2003. We treat the type as the plan for a program, and use the compiler and type checker as our. Is compiler for dependent type much harder than an intepreter. A language is called dependently typed if it also offers the 4th possibility, namely defining functions from values to types.
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