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Modeling C preprocessor metaprograms using purely functional
Modeling C preprocessor metaprograms using purely functional

... Each constructor creates a sequence, where the first item is the name of the constructor function itself that can be used as a tag later. This makes pattern matching possible, which is explained in the next subsection. The rest of the sequence is simply holding the actual arguments provided to the c ...
ppt - Rensselaer Polytechnic Institute: Computer Science
ppt - Rensselaer Polytechnic Institute: Computer Science

... properties, independent of the existence of other (possibly malicious) entities (either computations or humans) in the system • What properties must a language have to be secure? • One way to make a language secure is to base it on capabilities – A capability is an unforgeable language entity (« tic ...
Type-indexed data types - School of Computer Science
Type-indexed data types - School of Computer Science

... but rather complex languages not intended for programmers but for compiler writers; typed intermediate languages are not built on top of an existing programming language, so there is no integration problem; and, most importantly, typed intermediate languages interpret (a representation of a) type ar ...
Post Systems in Programming Languages Pr ecis 1 Introduction
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... A term is provable in a Post system if we can nd a proof of it. The set of words provable from a Post system forms the language derived by the system. Sometimes it is necessary to consider the language derived by a Post system to be the set of strings from a subset of the signs which are provable. ...
Constructive Mathematics in Theory and Programming Practice
Constructive Mathematics in Theory and Programming Practice

... later in this paper). When working in any axiomatic system, we must take care to use only intuitionistic logic, and therefore to ensure that we do not adopt a classical axiom that implies LEM or some other nonconstructive principle. For example, in IZF we cannot adopt the common classical form of th ...
Type Classes in Haskell - Programming Research Laboratory
Type Classes in Haskell - Programming Research Laboratory

Audio Processing using Haskell
Audio Processing using Haskell

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The Clean programming language

... Clean is a general purpose functional programming language, it is widely used in  scientific research all over the world. Featuring lazy evaluation, unique type  inferencing system, and graph rewriting semantics, Clean is useful for writing  relatively bug­free programs in fewer lines of code. Clean ...
Concepts of Programming Languages A Brief Intro to Programming
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Formal Foundations of Computer Security
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Rewriting in the partial algebra of typed terms modulo AC
Rewriting in the partial algebra of typed terms modulo AC

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Programming Language Semantics with Isabelle/HOL

... especially conditional, let and case expressions. Formulas are terms of type bool. There are the basic constants True and False and the usual logical connectives (in decreasing order of precedence): ¬, ∧, ∨, −→. Equality is available in the form of the infix function = of type 0a ⇒ 0a ⇒ bool. It als ...
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Tuples and Lists(3)

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A constructive approach to nonstandard analysis*
A constructive approach to nonstandard analysis*

... metamathematical results on nonarchimedean extensions, e.g. Martin-Lof’s interpretation of infinity symbols. We also indicate how such theories might be used. Unfortunately, they have no useful external notions, such as being infinitesimal. In Section 3 we introduce a new theory, internal HA”‘, whic ...
Dedukti
Dedukti

... 1. Predicate logic does not allow the use of bound variables, except those bound by the quantifiers ∀ and ∃. For instance, it is not possible to define, in predicate logic, a unary function symbol 7→ that would bind a variable in its argument. 2. Predicate logic ignores the propositions-as-types pri ...
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... – The last thing to do in the function call is to recurse. – It is called a tail call. – The compiler implements such tail recursion as loops. In particular: If the call is tail, then it will not consume stack. • Recursive thinking extends to data types: – E.g. a binary tree is either the empty tree ...
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Algol and Haskell

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Structural Types for the Factorisation Calculus
Structural Types for the Factorisation Calculus

Algebraic Data Types - University of Edinburgh
Algebraic Data Types - University of Edinburgh

... Algebraic types are the most important component of functional programming that I haven't covered yet. We've seen lots of types: integers, floating point numbers, characters, booleans. Also ways of building types: lists, functions, tuples. All very useful, built in to Haskell. We get lists of intege ...
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Chiron: A Set Theory with Types

Classical Logic and the Curry–Howard Correspondence
Classical Logic and the Curry–Howard Correspondence

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Chapter 2

... type from Int to tuple and the length of list is not fixed. This is in contrast to the arrays in traditional imperative languages that have fixed lengths. What is exciting about lists in Haskell is that there are a lot of functions defined for accessing and manipulation of lists as well as defining ...
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classden

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Intuitionistic type theory

Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics based on the principles of mathematical constructivism. Intuitionistic type theory was introduced by Per Martin-Löf, a Swedish mathematician and philosopher, in 1972. Martin-Löf has modified his proposal a few times; his 1971 impredicative formulation was inconsistent as demonstrated by Girard's paradox. Later formulations were predicative. He proposed both intensional and extensional variants of the theory. For more detail see the section on Martin-Löf type theories below.Intuitionistic type theory is based on a certain analogy or isomorphism between propositions and types: a proposition is identified with the type of its proofs. This identification is usually called the Curry–Howard isomorphism, which was originally formulated for intuitionistic logic and simply typed lambda calculus. Type theory extends this identification to predicate logic by introducing dependent types, that is types which contain values.Type theory internalizes the interpretation of intuitionistic logic proposed by Brouwer, Heyting and Kolmogorov, the so-called BHK interpretation. The types in type theory play a similar role to sets in set theory but functions definable in type theory are always computable.
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