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Yes, these can all be viewed as operators at the type level, but they're not all completely analogous. Most of these are type constructors in that they're formation operators for types, though type-level application is simply a type operator. $\to$ may be viewed as an ordinary type constructor. In Pierce's notation, this is denoted $\lambda X . \lambda Y . ...


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It depends on the programming language. It's up to each language to specify whether this is legal or not, and what it means. In many languages this would be legal. It is called variable shadowing.


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There is a paper titled Implicit Parameters: Dynamic Scoping with Static Types that discusses just such a system. The implement a slightly different system from Scala under the name "implicit parameters". By having compiler automatically generate implicit parameters in any function that calls other functions with implicit parameters the problem becomes ...


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It is in many languages legal to create a variable in an inner scope with the same name as a variable in an outer scope. The problem is that this may have been done by accident, and you never wanted to create a second variable, or that you use the inner variable when you wanted to use the outer one. For that reason, many compilers will issue a warning in ...


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I will give you two main reasons why MPI and OpenMP dominate. The first one is that they are standards. There are several available implementations, and you can be sure to find them available on every possible supercomputer machine. This is strictly related to the concept of portability: you write your parallel code and, if you do not use anything else ...


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If I recall correctly, this was chapter 5 or 6 of John Harrison's Handbook of Practical Logic and Automated Reasoning. Jon Sterling wrote some notes for a recitation a year or two back, specifically for an LCF prover using sequent calculus.


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These sorts of terms in type theory are not always used completely consistently. However, type operators are generally type-level functions: that is, they take as arguments some number of types and return a single type. Type constructors are a specific kind of type operator for which the return type is free in the sense that it is a new type on its arguments....


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