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first checks whether x is less than 5, which it is, so then the {loop body} is entered, where the printf function is run and x is incremented by 1. After completing all the statements in the loop body, the condition, (x < 5), is checked again, and the loop is executed again, this process repeating until the variable x has the value 5.
The following is a C-style While loop. It continues looping while x does not equal 3, or in other words it only stops looping when x equals 3. However, since x is initialized to 0 and the value of x is never changed in the loop, the loop will never end (infinite loop).
It is easy to see that i<=n, too, is an invariant of the loop, since i<n in line 6 can be obtained from the (modified) loop condition in line 5, and hence i<=n holds in line 11 after i has been incremented in line 10. However, when loop invariants have to be manually provided for formal program verification, such intuitively too obvious ...
An example of a primitive recursive programming language is one that contains basic arithmetic operators (e.g. + and −, or ADD and SUBTRACT), conditionals and comparison (IF-THEN, EQUALS, LESS-THAN), and bounded loops, such as the basic for loop, where there is a known or calculable upper bound to all loops (FOR i FROM 1 TO n, with neither i ...
As an illustration of this, the parity cycle (1 1 0 0 1 1 0 0) and its sub-cycle (1 1 0 0) are associated to the same fraction 5 / 7 when reduced to lowest terms. In this context, assuming the validity of the Collatz conjecture implies that (1 0) and (0 1) are the only parity cycles generated by positive whole numbers (1 and 2 ...
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the next token is ==, with precedence 0. the inner while loop is not entered. lhs is assigned 14+5 = 19; the next token is ==, with precedence 0. the outer while loop is not left. op is == (precedence 0) and the input is advanced; rhs is 19; the next token is end-of-line, which is not an operator. the inner while loop is not entered. lhs is ...
In many programming languages, only integers can be reliably used in a count-controlled loop. Floating-point numbers are represented imprecisely due to hardware constraints, so a loop such as. for X := 0.1 step 0.1 to 1.0 do. might be repeated 9 or 10 times, depending on rounding errors and/or the hardware and/or the compiler version.