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Pascal has two forms of the while loop, while and repeat. While repeats one statement (unless enclosed in a begin-end block) as long as the condition is true. The repeat statement repetitively executes a block of one or more statements through an until statement and continues repeating unless the condition is false. The main difference between ...
However a while loop will test the condition before the code within the block is executed. This means that the code is always executed first and then the expression or test condition is evaluated. This process is repeated as long as the expression evaluates to true. If the expression is false the loop terminates. A while loop sets the truth of ...
The factorial operation is encountered in many areas of mathematics, notably in combinatorics, where its most basic use counts the possible distinct sequences – the permutations – of distinct objects: there are !.
The resulting function behaves like a while or a for loop in an imperative language. Used in this way, the Y combinator implements simple recursion . The lambda calculus does not allow a function to appear as a term in its own definition as is possible in many programming languages, but a function can be passed as an argument to a higher-order ...
A classic example of recursion is the definition of the factorial function, given here in Python code: def factorial ( n ): if n > 0 : return n * factorial ( n - 1 ) else : return 1 The function calls itself recursively on a smaller version of the input (n - 1) and multiplies the result of the recursive call by n , until reaching the base case ...
function factorial (n is a non-negative integer) if n is 0 then return 1 [by the convention that 0! = 1] else if n is in lookup-table then return lookup-table-value-for-n else let x = factorial(n – 1) times n [recursively invoke factorial with the parameter 1 less than n] store x in lookup-table in the n th slot [remember the result of n! for ...
This defines the factorial function using its recursive definition. In contrast, it is more typical to define a procedure for an imperative language. In lisps and lambda calculus, functions are generally first-class citizens. Loosely, this means that functions can be inputs and outputs for other functions.
Some CFG examples: (a) an if-then-else (b) a while loop (c) a natural loop with two exits, e.g. while with an if...break in the middle; non-structured but reducible (d) an irreducible CFG: a loop with two entry points, e.g. goto into a while or for loop A control-flow graph used by the Rust compiler to perform codegen.