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Matita
Matita is an experimental proof assistant under development at the Computer Science Department of the University of Bologna. It is a tool aiding the development of formal proofs by man–machine collaboration, providing a programming environment where formal specifications, executable algorithms and automatically verifiable correctness certificates naturally coexist. Matita is based on a dependent type system known as the calculus of (co)inductive constructions (a derivative of the calculus of constructions), and is compatible, to some extent, with Coq. The word "matita" means "pencil" in Italian (a simple and widespread editing tool). It is a reasonably small and simple application, whose architectural and software complexity is meant to be mastered by students, providing a tool particularly suited for testing innovative ideas and solutions. Matita adopts a tactic-based editing mode; (XML-encoded) proof objects are produced for storage and exchange. Main features Existential va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dependent Type
In computer science and logic, a dependent type is a type whose definition depends on a value. It is an overlapping feature of type theory and type systems. In intuitionistic type theory, dependent types are used to encode logic's quantifiers like "for all" and "there exists". In functional programming languages like Agda, ATS, Rocq (previously known as ''Coq''), F*, Epigram, Idris (programming language), Idris, and Lean (proof assistant), Lean, dependent types help reduce bugs by enabling the programmer to assign types that further restrain the set of possible implementations. Two common examples of dependent types are ''dependent functions'' and ''dependent pairs''. The return type of a dependent function may depend on the ''value'' (not just type) of one of its arguments. For instance, a function that takes a positive integer n may return an array of length n, where the array length is part of the type of the array. (Note that this is different from polymorphism and generi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Constructions
In mathematical logic and computer science, the calculus of constructions (CoC) is a type theory created by Thierry Coquand. It can serve as both a typed programming language and as constructive foundation for mathematics. For this second reason, the CoC and its variants have been the basis for Coq and other proof assistants. Some of its variants include the calculus of inductive constructions (which adds inductive types), the calculus of (co)inductive constructions (which adds coinduction), and the predicative calculus of inductive constructions (which removes some impredicativity). General traits The CoC is a higher-order typed lambda calculus, initially developed by Thierry Coquand. It is well known for being at the top of Barendregt's lambda cube. It is possible within CoC to define functions from terms to terms, as well as terms to types, types to types, and types to terms. The CoC is strongly normalizing, and hence consistent. Usage The CoC has been developed a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Assistants
In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration. This involves some sort of interactive proof editor, or other User interface, interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics. System comparison * ACL2 – a programming language, a first-order logical theory, and a theorem prover (with both interactive and automatic modes) in the Boyer–Moore tradition. * Rocq (software), Rocq (formerly known as ''Coq'') – Allows the expression of mathematical assertions, mechanically checks proofs of these assertions, helps to find formal proofs, and extracts a certified program from the constructive proof ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C (programming Language)
C (''pronounced'' '' – like the letter c'') is a general-purpose programming language. It was created in the 1970s by Dennis Ritchie and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted Central processing unit, CPUs. It has found lasting use in operating systems code (especially in Kernel (operating system), kernels), device drivers, and protocol stacks, but its use in application software has been decreasing. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the most widely used programming langu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assembly Language
In computing, assembly language (alternatively assembler language or symbolic machine code), often referred to simply as assembly and commonly abbreviated as ASM or asm, is any low-level programming language with a very strong correspondence between the instructions in the language and the architecture's machine code instructions. Assembly language usually has one statement per machine instruction (1:1), but constants, comments, assembler directives, symbolic labels of, e.g., memory locations, registers, and macros are generally also supported. The first assembly code in which a language is used to represent machine code instructions is found in Kathleen and Andrew Donald Booth's 1947 work, ''Coding for A.R.C.''. Assembly code is converted into executable machine code by a utility program referred to as an '' assembler''. The term "assembler" is generally attributed to Wilkes, Wheeler and Gill in their 1951 book '' The Preparation of Programs for an Electronic Dig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MCS-51
The Intel MCS-51 (commonly termed 8051) is a single-chip microcontroller (MCU) series developed by Intel in 1980 for use in embedded systems. The architect of the Intel MCS-51 instruction set was John H. Wharton.. Intel's original versions were popular in the 1980s and early 1990s, and enhanced binary compatible derivatives remain popular today. It is a complex instruction set computer with separate memory spaces for program instructions and data. Intel's original MCS-51 family was developed using N-type metal–oxide–semiconductor ( NMOS) technology, like its predecessor Intel MCS-48, but later versions, identified by a letter C in their name (e.g., 80C51) use complementary metal–oxide–semiconductor (CMOS) technology and consume less power than their NMOS predecessors. This made them more suitable for battery-powered devices. The family was continued in 1996 with the enhanced 8-bit MCS-151 and the 8/ 16/32-bit MCS-251 family of binary compatible microcontrollers. Whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software Specification
In computer science, formal specifications are mathematically based techniques whose purpose is to help with the implementation of systems and software. They are used to describe a system, to analyze its behavior, and to aid in its design by verifying key properties of interest through rigorous and effective reasoning tools. These specifications are ''formal'' in the sense that they have a syntax, their semantics fall within one domain, and they are able to be used to infer useful information. Motivation In each passing decade, computer systems have become increasingly more powerful and, as a result, they have become more impactful to society. Because of this, better techniques are needed to assist in the design and implementation of reliable software. Established engineering disciplines use mathematical analysis as the foundation of creating and validating product design. Formal specifications are one such way to achieve this in software engineering reliability as once predicted. O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curry–Howard Correspondence
In programming language theory and proof theory, the Curry–Howard correspondence is the direct relationship between computer programs and mathematical proofs. It is also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and the logician William Alvin Howard. It is the link between logic and computation that is usually attributed to Curry and Howard, although the idea is related to the operational interpretation of intuitionistic logic given in various formulations by L. E. J. Brouwer, Arend Heyting and Andrey Kolmogorov (see Brouwer–Heyting–Kolmogorov interpretation) and Stephen Kleene (see Realizability). The relationship has been extended to include category theory as the three-way Curry–Howard–Lambe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
