ⓘ ATS (programming language)

ATS (programming language)

ⓘ ATS (programming language)

ATS is a programming language designed to unify programming with formal specification. ATS has support for combining theorem proving with practical programming through the use of advanced type systems. A past version of The Computer Language Benchmarks Game has demonstrated that the performance of ATS is comparable to that of the C and C++ programming languages. By using theorem proving and strict type checking, the compiler can detect and prove that its implemented functions are not susceptible to bugs such as division by zero, memory leaks, buffer overflow, and other forms of memory corruption by verifying pointer arithmetic and reference counting before the program compiles. Additionally, by using the integrated theorem-proving system of ATS, the programmer may make use of static constructs that are intertwined with the operative code to prove that a function attains its specification.


1. History

ATS is derived mostly from the ML and OCaml programming languages. An earlier language, Dependent ML, by the same author has been incorporated by the language.

The latest version of ATS1 Anairiats was released as v0.2.12 on 2015-01-20. The first version of ATS2 Postiats was released in September 2013.


2. Theorem proving

The primary focus of ATS is to support theorem proving in combination with practical programming. With theorem proving one can prove, for instance, that an implemented function does not produce memory leaks. It also prevents other bugs that might otherwise only be found during testing. It incorporates a system similar to those of proof assistants which usually only aim to verify mathematical proofs - except ATS uses this ability to prove that the implementations of its functions operate correctly, and produce the expected output.

As a simple example, in a function using division, the programmer may prove that the divisor will never equal zero, preventing a division by zero error. Lets say, the divisor X was computed as 5 times the length of list A. One can prove, that in the case of a non-empty list, X is non-zero, since X is the product of two non-zero numbers 5 and the length of A. A more practical example would be proving through reference counting that the retain count on an allocated block of memory is being counted correctly for each pointer. Then one can know, and quite literally prove, that the object will not be deallocated prematurely, and that memory leaks will not occur.

The benefit of the ATS system is that since all theorem proving occurs strictly within the compiler, it has no effect on the speed of the executable program. ATS code is often harder to compile than standard C code, but once it compiles the programmer can be certain that it is running correctly to the degree specified by their proofs assuming the compiler and runtime system are correct.

In ATS proofs are separate from implementation, so it is possible to implement a function without proving it if the programmer so desires.


3. Data representation

According to the author Hongwei Xi, ATSs efficiency is largely due to the way that data is represented in the language and tail-call optimizations which are generally important for the efficiency of functional programming languages. Data can be stored in a flat or unboxed representation rather than a boxed representation.


4.1. Theorem Proving: An introductory case Propositions

dataprop expresses predicates as algebraic types.

Predicates in pseudo‑code somewhat similar to ATS source see below for valid ATS source:

FACTn, r iff factn = r MULn, m, prod iff n * m = prod FACTn, r = FACT0, 1 | FACTn, r iff FACTn-1, r1 and MULn, r1, r // for n > 0 // expresses factn = r iff r = n * r1 and r1 = factn-1

In ATS code:

where FACT int, int is a proof type


4.2. Theorem Proving: An introductory case Example

Non tail-recursive factorial with proposition or "Theorem" proving through the construction dataprop.

The evaluation of fact1n-1 returns a pair proof_n_minus_1 | result_of_n_minus_1 which is used in the calculation of fact1n. The proofs express the predicates of the proposition.


4.3. Theorem Proving: An introductory case Part 1 algorithm and propositions

existential quantification. |. proof | value. flat tuple or variadic function parameters tuple. termination metric

5. Features

Basic types

  • int literals: 255, 0377, 0xFF, unary minus as ~ as in ML
  • double
  • char a
  • bool true, false
  • string "abc"

Tuples and records

prefix or none means direct, flat or unboxed allocation prefix means indirect or boxed allocation special

With | as separator, some functions return wrapped the result value with an evaluation of predicates

val predicate_proofs | values = myfunct params


{.} universal quantification 0 p_buf

See val and var declarations

  • ATS - V was discontinued with the ATS line in 2019. The fourth generation V series was the first to incorporate Cadillac s new Escala design language
  • 2014. St John s College is a member of the Association of Trust Schools ATS and the International Boys Schools Coalition IBSC The Headmaster is
  • in the order it was introduced. The following programming languages support linear or affine types: ATS Clean Idris Mercury Rust F LinearML Alms Linear
  • House Preparatory School is a member of the Association of Trust Schools ATS and the Head is a member of the Conference of Heads of Independent Schools
  • Government of the United States of America concerning Aerodrome Facilities. ATS 4 of 1947. Australian Treaty Series. Australasian Legal Information Institute
  • director of the center. In 2004, the ATS renewed the seminary s Master of Divinity program for ten years. In 2014, the ATS accreditation was extended for the
  • and other market participants. The ATS is distinguished from exchanges and associations in that the volumes for ATS trades are comparatively low, and the
  • official language plus a number of countries where Spanish, or any language closely related to it, is an important or significant language Spanish is

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