solver,isabelle,associativity,commutativity

Reasoning upto associativity and commutativity is usually done in Isabelle with the simplifier and ordered rewriting. In your example, you provide the simplifier with the associativity rule (oriented from left to right), the commutativity rule, and the left-commutativity rule. The details are explained in the Tutorial on Isabelle/HOL (Section 9.1,...

javascript,reduce,fold,associativity,commutativity

Doesn't it indeed make more sense for reduceRight to be implemented the way I did? Maybe. However, the JavaScript array iterators do not come from a pure functional programming background. Why is the native reduceRight not implemented the way I did? Because it's simpler (easier to remember) to have...

compiler-construction,programming-languages,associativity,compiler-design

Let's go over the first method first. When the small numbers are added one by one to the large number, the following will happen ten times: 10,000,000 + 1 = 10,000,001 However since the floating-point values store only seven digits of accuracy this last digit, the eight digit, will be...

javascript,assignment-operator,ecmascript-5,order-of-evaluation,associativity

Yes, your understanding about the operator order appears to be correct. ECMAScript 5 section 8.7 says: A Reference consists of three components, the base value, the referenced name and the Boolean valued strict reference flag. The base value is either undefined, an Object, a Boolean, a String, a Number, or...

Firstly, this has nothing to do with System.out.println. You'll see exactly the same effect if you use: String x = 7 + 5 + ""; String y = " " + 5 + 7; It's got everything to do with associativity. The + operator is left-associative, so the above two...

There are two different things mixed up here: expression parsing and expression evaluation. Let's start with the expression: ++a + ++a * ++a. What do we first have to do with it? Since operators + and * need two operands and ++ needs one, we have to figure out which...

The way you've written it is correct. Incidentally, you might want to reconsider your hierarchy; in regular math, −34 is −(34), not (−3)4. So you might want - 3 ^ 4 to mean - (3 ^ 4), in which case NegExp would include PowExp rather than the other way around....

haskell,lazy-evaluation,associativity

Argument against I found a proposal from 2008 in haskell-prime to make the $ and $! operators left-associative: https://ghc.haskell.org/trac/haskell-prime/wiki/ChangeDollarAssociativity There is only one argument against the proposal: "This would break a lot of code". Arguments in favour Instead, there are given four arguments in favour of left-associative ($), the last...

c++,operator-overloading,operator-keyword,associativity

When we say the associativity of * is left-to-right, we mean that the expression a*b*c*d will always evaluate as (((a*b)*c)*d). That's it. In your example, you only have one operator*, so there isn't anything to associate. What you're running into is the order of evaluation of operands. You are calling:...