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Object keys in array "not a function" according to web console

I have a program that wants to take an input string, look for the name of a mathematical function in the input string and output the numbers also included in the input string with the found operation done to them.
If my input looks like this:
1 a 2 b subtract
I want it to output the number 2.
Here's my code:
function doArithment() {
"use strict";
var i = 0;
clearResults();
sepNsLs();
var found = false;
var q = 0;
var keys = Object.keys(operations);
while (q < keys.length) {
if (arrayses.letteros.indexOf(keys[q]) !== -1) {
found = true;
break;
} else if (arrayses.letteros.indexOf(keys[q]) === -1) {
q += 1;
}
}
if (found) {
var result = arrayses.numeros[0];
while (i < arrayses.numeros.length) {
if (i === 0) {
result = arrayses.numeros[0];
} else {
result = keys[q](result, arrayses.numeros[i]);
}
i += 1;
}
and the global variable is declared above the function like this
var operations = {
add: function(a, b) {
"use strict";
return Number(a) + Number(b);
},
subtract: function(a, b) {
"use strict";
return a - b;
},
multiply: function(a, b) {
"use strict";
return a * b;
},
divide: function(a, b) {
"use strict";
return a / b;
}
};
Now, my only problem it seems is that the web console says that keys[q] is not a function when I try to use it on this line to call the correct operation:
result = keys[q](result, arrayses.numeros[i]);
arrayses.letteros is the array of non-numbers I split in my input string and arrayses.numeros is the array of numbers. I'm new to Javascript, so I don't know if this is an issue of syntax or if Object.keys are unusable in this instance or if I need to find a way to convert the keys back from an array into their original variable form somehow.

add a memoization to recursive algorithm

I have written a function for partitioning a number:
var combinations = function (i) {
var mem = [];
function inner(n, r, m) {
for (var k = m; k <= n; k++) {
if (k == n) {
r.push(k);
mem[r] = 1;
return mem;
}
else {
var copy = r.slice(0);
copy.push(k);
inner(n - k, copy, k);
}
}
}
return inner(i, [], 1);
}
In second step I would like to add a memoization to this algorithm, but can't think of implementing it the right way, beause there is no return statement until the very end (when return is specified e.g. in faactorial or fibbinacci I can add the memoization).
Can anybody drive me to the right direction?
[edit]
I need this algorithm to be as fast as possible. This is a competition for a kata at codewars: link
There is a requirement it must be executed under 6000ms for input up to 330.
That's the best algorithm I can think of, except how to store the partial results.

Here's a much simpler code that works:
function nr_partitions(n) { return p(n, n); }
function p(sum,largest) {
if (largest == 0) { return 0; }
if (sum == 0) { return 1; }
if (sum < 0) { return 0; }
return p(sum, largest-1) + p(sum-largest, largest);
}
It uses a well-known recurrence, p(n,k) = p(n,k-1) + p(n-k, k), where p(n.k) denotes the number of partitions of n where the largest part is at most k (e.g. p(3, 2)=2 because we only count 1+1+1,1+2, but not 3). For k=n we get the number of all partitions of n.
Adding memozation involves storing dictionary mapping pairs (sum, largest) to p(sum, largest).

I would go along the lines of:
var cache = {};
var combinations = function (i) {
if ( cache[i] ){
return cache[i];
};
var mem = [];
function inner(n, r, m) {
for (var k = m; k <= n; k++) {
if (k == n) {
r.push(k);
mem[r] = 1;
return mem;
}
else {
var copy = r.slice(0);
copy.push(k);
inner(n - k, copy, k);
}
}
}
cache[i] = inner(i, [], 1);
return cache[i];
}
But you'll have to modify your algorithm to make use of that cache (compute the biggest terms first ?)

Depending on your other requirements, you might want to consider using underscore.js which has its own _.memoize function.
The secret of memoization is that it exploits how closures work. When you define a function inside another scope, it has access to everything in that scope. When you return that function to somewhere outside the scope, it carries references to everything it can see inside the scope.
So to implement memorization, you need to make a function that returns another function, one that does the memorization check before calling the inner one.
Your code will look something like this:
/**
* Because we'll be returning "a function that returns a function" below,
* this needs to be executed immediately so combinations() is just
* a standalone function.
*/
var combinations = (function(i) {
/**
* mem needs to stay outside the scope of your inner function.
* If it's in a closure like this, JavaScript will keep its value
* around as long as combinations still exists.
*/
var mem = [];
/**
* A memoization wrapper should return a memoized function
*/
return function(i) {
/**
* Check if mem[i] is set and return it if it has been
*/
if(mem[i] !== undefined) {
console.log('returning memoized value');
return mem[i];
}
function inner(n, r, m) {
for (var k = m; k <= n; k++) {
if (k == n) {
r.push(k);
mem[r] = 1;
return mem;
}
else {
var copy = r.slice(0);
copy.push(k);
inner(n - k, copy, k);
}
}
}
/**
* If the value needs to be computed, we can set it at the same time
* as we return it instead of putting it in a temporary variable.
*/
console.log('computed');
return mem[i] = inner(i, [], 1);
}
}()); /** <--- That's the rest of the automatic execution */
console.log(combinations(5));
console.log(combinations(5));

Javascript - how to detect how many functions are being called? (multiple parentheses)

Let me propose an example that works, then follow up with what fails, highlighting the point to my question.
Here, we have 3 functions being called (1 named, 2 anonymous):
var add = function(a, b) {return a+b};
var multiply = function(a, b) {return a*b};
function myFunction(fxn) {
return function(x) {
return function(y) {
return fxn(x,y);
}
}
}
myFunction(add)(2)(3)
Understandably, this call fails:
myFunction(add)(2)(3)(4)
How would I detect how many functions are being called? In the 2nd call, I'm calling 4 functions (1 named, 3 anonymous).
How would I rewrite the myFunction function in a way that compensated for any given amount of calls? I know we can detect how many arguments a function was given, but is there a way to detect how many functions are being called? I hope I worded this correctly. Thanks.

To find out if a variable contains a reference to a function you can use below code:
if (typeof(v) === "function") alert("This is a function")
Based on above you can find out on how many nested functions there are
function myFunction() {
return function() {
return function() {
return 1 + 2;
}
}
}
var count = 0;
var v = myFunction();
while (typeof(v) === "function") {
count++;
v = v();
}
alert("Nr of nested functions: " + count)

Even if this has no practical use case I can think of, this is a possible solution:
var add = function(a, b) {
return a + b
};
var multiply = function(a, b) {
return a * b
};
var counter = 0;
var result = 0;
function myFunction(fxn) {
counter = 1;
result = 0;
return function first(x) {
++counter;
return function second(y) {
++counter;
x = result ? result : x;
result = fxn(x, y);
return second;
}
}
}
myFunction(add)(1)(2)(3)(4);
alert('Result is: ' + result + '; Parentheses count: ' + counter);

What is the difference between naming functions or not in javascript?

What is the difference between
settings = {
edit: function (key, value) {
return anotherFunction(key, value) {
return value * 2;
};
}
};
and
settings = {
edit: function edit(key, value) {
return anotherFunction(key, value) {
return value * 2;
};
}
};
?

There's no difference when executing.
However, in the second case (named function), you can call the function recursively easier because it has a name.
For example, with a named function you can do:
fact: function factorial(n) {
if(n == 0) return 1;
return n * factorial(n-1); //You can do this with a named function easily
}
Without a name, this would be tricky.
Cheers

The essential difference is better debugging. In your developer tools, the named function in your second example will appear as edit in a backtrace; your first example will appear as anonymous. This can be extremely confusing when you're 10 function deep, and they are all called anonymous.

There are three reasons to give a function an inherent name. The first is that everyone does it. It's what everyone is used to.
function factorial(n) {
var accum = 1, i;
for (i = 1; i <= n; i++) {
accum *= i;
}
return accum;
}
The second is to understand stack traces better, as #meagar wrote.
The third is to let you write call functions recursively.
var factorial = function(n) {
var a = 1;
return (function factRecursive(k, a) {
if (k >= 2) {return factRecursive(k - 1, k * a)}
else {return a;}
})(n, a);
}

How to parse pure functions

Let's say you have the following function
var action = (function () {
var a = 42;
var b = 2;
function action(c) {
return a + 4 * b + c;
}
return action;
}());
// how would you parse action into it's serialized LISP / AST format?
var parsed = parse(action);
Is it possible to have a function that takes a reference to the function action and outputs say the LISP format (lambda (c) (plus (plus 42 (multiply 4 2)) c))
We're allowed to put some restrictions on what action can be.
the body should only be a single expression
it should be a pure function
any free variables are constants
The main question is given a function you can invoke with a range of inputs and it's source code can you discover the correct value to substitute the free variables with?
For the above example you know that a and b are constant and you could intellectually plot the output for a few values and see the pattern and then just know what the constants are.
Question:
How would you write a function that takes a function reference and it's source code and produces some form of AST for the function with any free variables substituted for their run-time values.
An example of an AST format would be the LISP equivalent of the code.
I basically want to serialize and deserialize the function and have it behave the same
It should be noted that the problem becomes trivial if you pass { a: a, b: b } to the analysis function. That would be cheating.
Use-case:
I want to generate a language agnostic form of a pure JavaScript function so I can effectively pass it to C++ without requiring the user of my library to use a DSL to create this function
Let's imagine you had a database driver
var cursor = db.table("my-table").map(function (row) {
return ["foo", row.foo]
})
You want to determine at run-time what the function is and convert it into an AST format so that you can use your efficient query builder to convert it into SQL or whatever query engine your database has.
This means you don't have to write:
var cursor = db.table("my-table").map(function (rowQueryObject) {
return db.createArray(db.StringConstant("foo"), rowQueryObject.getProperty("foo"))
})
Which is a function the DB library can execute with a query object and have you build the query object transformation without verbose methods.

Here is a full solution (using catalog of variables which is accessible by the parse function):
var CONSTANTS = {
a: 42,
b: 2,
c: 4
};
function test() {
return a + 4 * b + c;
}
function getReturnStatement(func) {
var funcStr = func.toString();
return (/return\s+(.*?);/g).exec(funcStr)[1];
}
function replaceVariables(expr) {
var current = '';
for (var i = 0; i < expr.length; i += 1) {
while (/[a-zA-Z_$]/.test(expr[i]) && i < expr.length) {
current += expr[i];
i += 1;
}
if (isNumber(CONSTANTS[current])) {
expr = expr.replace(current, CONSTANTS[current]);
}
current = '';
}
return expr;
}
function isNumber(arg) {
return !isNaN(parseInt(arg, 10));
}
function tokenize(expr) {
var tokens = [];
for (var i = 0; i < expr.length; i += 1) {
if (isWhitespace(expr[i])) {
continue;
} else if (isOperator(expr[i])) {
tokens.push({
type: 'operator',
value: expr[i]
});
} else if (isParentheses(expr[i])) {
tokens.push({
type: 'parant',
value: expr[i]
});
} else {
var num = '';
while (isNumber(expr[i]) && i < expr.length) {
num += expr[i];
i += 1;
}
i -= 1;
tokens.push({
type: 'number',
value: parseInt(num, 10)
});
}
}
return tokens;
}
function toPrefix(tokens) {
var operandStack = [],
operatorStack = [],
current,
top = function (stack) {
if (stack) {
return stack[stack.length - 1];
}
return undefined;
};
while (tokens.length) {
current = tokens.pop();
if (current.type === 'number') {
operandStack.push(current);
} else if (current.value === '(' ||
!operatorStack.length ||
(getPrecendence(current.value) >
getPrecendence(top(operatorStack).value))) {
operatorStack.push(current);
} else if (current.value === ')') {
while (top(operatorStack).value !== '(') {
var tempOperator = operatorStack.pop(),
right = operandStack.pop(),
left = operandStack.pop();
operandStack.push(tempOperator, left, right);
}
operatorStack.pop();
} else if (getPrecendence(current.value) <=
getPrecendence(top(operatorStack).value)) {
while (operatorStack.length &&
getPrecendence(current.value) <=
getPrecendence(top(operatorStack).value)) {
tempOperator = operatorStack.pop();
right = operandStack.pop();
left = operandStack.pop();
operandStack.push(tempOperator, left, right);
}
}
}
while (operatorStack.length) {
tempOperator = operatorStack.pop();
right = operandStack.pop();
left = operandStack.pop();
operandStack.push(tempOperator, left, right);
}
return operandStack;
}
function isWhitespace(arg) {
return (/^\s$/).test(arg);
}
function isOperator(arg) {
return (/^[*+\/-]$/).test(arg);
}
function isParentheses(arg) {
return (/^[)(]$/).test(arg);
}
function getPrecendence(operator) {
console.log(operator);
switch (operator) {
case '*':
return 4;
case '/':
return 4;
case '+':
return 2;
case '-':
return 2;
default:
return undefined;
}
}
function getLispString(tokens) {
var result = '';
tokens.forEach(function (e) {
if (e)
switch (e.type) {
case 'number':
result += e.value;
break;
case 'parant':
result += e.value;
break;
case 'operator':
result += getOperator(e.value);
break;
default:
break;
}
result += ' ';
});
return result;
}
function getOperator(operator) {
switch (operator) {
case '+':
return 'plus';
case '*':
return 'multiplicate';
case '-':
return 'minus';
case '\\':
return 'divide';
default:
return undefined;
}
}
var res = getReturnStatement(test);
console.log(res);
res = replaceVariables(res);
console.log(res);
var tokens = tokenize(res);
console.log(tokens);
var prefix = toPrefix(tokens);
console.log(prefix);
console.log(getLispString(prefix));
I just wrote it so there might be some problems in the style but I think that the idea is clear.
You can get the function body by using the .toString method. After that you can use regular expression to match the return statement
(/return\s+(.*?);/g).exec(funcStr)[1];
Note that here you must use semicolons for successful match! In the next step all variables are transformed to number values using the CONSTANTS object (I see that you have some parameters left so you may need little modifications here). After that the string is being tokenized, for easier parsing. In next step the infix expression is transformed into a prefix one. At the last step I build a string which will make the output looks like what you need (+ - plus, - - minus and so on).

Since I'm not sure you're able to get the method's body after having invoked it, here is an alternative solution:
var a = 42;
var b = 2;
function action(c) {
return a + 4 * b + c;
}
/**
* get the given func body
* after having replaced any available var from the given scope
* by its *real* value
*/
function getFunctionBody(func, scope) {
// get the method body
var body = func.toString().replace(/^.*?{\s*((.|[\r\n])*?)\s*}.*?$/igm, "$1");
var matches = body.match(/[a-z][a-z0-9]*/igm);
// for each potential var
for(var i=0; i<matches.length; i++) {
var potentialVar = matches[i];
var scopedValue = scope[potentialVar];
// if the given scope has the var defined
if(typeof scopedValue !== "undefined") {
// add "..." for strings
if(typeof scopedValue === "string") {
scopedValue = '"' + scopedValue + '"';
}
// replace the var by its scoped value
var regex = new RegExp("([^a-z0-9]+|^)" + potentialVar + "([^a-z0-9]+|$)", "igm");
var replacement = "$1" + scopedValue + "$2";
body = body.replace(regex, replacement);
}
}
return body;
}
// calling
var actionBody = getFunctionBody(action, this);
// log
alert(actionBody);
Prints:
return 42 + 4 * 2 + c;
DEMO
You would then have to implement your own function toLISP(body) or any function else you may need.
Note that it won't work for complex scoped variables such as var a = {foo: "bar"}.