MANOOL
MANOOL is Not an Object-Oriented Language!”

Lesson 2 — Tutorial

Updated:

Factorial

The usual “Hello World” analog for functional languages consists of a recursive function definition for calculating factorial of a number. The following variation for MANOOL incorporates in addition some test code:

-- Factorial -- recursive version in MANOOL-ish ("cascading") notation
{ {extern "manool.org.18/std/0.5/all"} in
: let rec
  { Fact = -- compile-time constant binding
    { proc { N } as -- precondition: 0 <= N
    : if N == 0 then 1 else
      N * Fact[N - 1]
    }
  }
  in
  Out.WriteLine["Factorial of 10 = " Fact[10]]
}

And the following equivalent program (up to AST) is intended to make the syntactic structure of the above program a bit more apparent:

-- Factorial -- recursive version in conventional notation (equivalent to the above code, up to AST)
{ {extern "manool.org.18/std/0.5/all"} in
  { let rec
    { Fact = -- compile-time constant binding
      { proc { N } as -- precondition: 0 <= N
        { if N == 0 then 1 else
          N * Fact[N - 1]
        }
      }
    }
    in
    Out.WriteLine["Factorial of 10 = " Fact[10]]
  }
}

(here another piece of syntactic sugar is demonstrated — any two constructs {a0 a1am-1 {b0 b1bn-1}} and {a0 a1am-1: b0 b1bn-1} are always equivalent one to another).

Output:

Factorial of 10 = 3628800

How it works

  1. The expression {proc {N} as ...} resembles a lambda-expression in many languages, where N would specify a parameter and the expression that follows as would be the body. The whole expression evaluates to a procedure, which returns the result of evaluation of the body.1

  2. During compilation of the expression {let rec {Fact = ...} in ...}, a binding between Fact and the entity specified on the right-hand side of the infix operator = is injected into the scope that follows in.2 Since we use let rec and not just let here, the right-hand side expression is also included in the scope of Fact, so we can refer to it recursively.

  3. The construct {if ... then ... else ...} is a conditional expression here. During its evaluation either of the two branches is evaluated depending on whether the condition specified between if and then holds and producing the result for the whole expression.

Iterative version

Although MANOOL has a functional core, it is a multiparadigm language, for which an iterative version of the factorial function, which uses a while-loop (or for-loop), may be more appropriate:3

-- Factorial -- iterative version (in MANOOL, this is probably more appropriate for factorial)
{ {extern "manool.org.18/std/0.5/all"} in
: let
  { Fact = -- compile-time constant binding
    { proc { N } as -- precondition: 0 <= N
    : var { Res = 1 } in -- variable binding
    : do Res after -- return result
    : while N <> 0 do -- loop while N not equals zero
      Res = N * Res; N = N - 1
    }
  }
  in
  Out.WriteLine["Factorial of 10 is "; Fact[10]]
}

(the output is the same as above).

How it works

  1. During compilation of the expression {var {Res = 1} in ...}, the body expression(s), which follow in, are considered in a binding environment with a temporary variable named Res injected.4 The variable is initialized to 1 just before evaluating the body expression(s).

  2. The expression {do Res after ...} is equivalent to {do ...; Res}, which is evaluated by evaluating its constituents one by one, and thus this expression evaluates to Res.

  3. The expression {while ... do ...} is a traditional while-loop. During its evaluation, the body expression(s), which follow do, are evaluated repetitively, one by one, while the pre-condition specified between while and do holds.

  4. Res = N * Res and N = N - 1 are assignment expressions. As a side effect of an evaluation of such expression, the current value of the location specified on the left-hand side of the = operator is replaced with the value specified on the right-hand side of the = operator.

Value Comparisons, Data Typing Issues

Let's see how comparison operations work in MANOOL and how the principle of strong data typing affects certain aspects of the MANOOL semantics.

Comparing for equality

First, any pair of values in MANOOL (even of different types) can be always compared for equality/inequality, two values of different types simply being deemed unequal (even if they “look” similar):

{ {extern "manool.org.18/std/0.5/all"} in
  Out.WriteLine[2 == 2 ", " 2 <> 2 ", " "2" == "2" ", " "2" <> "2"]
  Out.WriteLine[2 == "2" ", " 2 <> "2" ", " "2" == 2 ", " "2" <> 2]
}

Output:

True, False, True, False
False, True, False, True

(In MANOOL True and False are members of a special data type Boolean.)

Other operations

Any pair of integral values can be also compared for less-than as well as less-than-or-equal, greater-than, and greater-then-or-equal:

{ {extern "manool.org.18/std/0.5/all"} in
  Out.WriteLine[2 <  3 ", " 3 < 2 ", " 2 <  2] -- less-than
  Out.WriteLine[2 <= 3 ", " 2 > 3 ", " 2 >= 3] -- less-than-or-equal, greater-than, greater-then-or-equal
}

Output:

True, False, False
True, False, False

On the other hand, two values of different types cannot be compared for less-than, etc.; also, the + operator cannot be applied to an integer and a string and vice versa:

{{extern "manool.org.18/std/0.5/all"} in Out.WriteLine[2 < "3"]} -- run-time error
{{extern "manool.org.18/std/0.5/all"} in Out.WriteLine[2 + "3"]} -- run-time error
{{extern "manool.org.18/std/0.5/all"} in Out.WriteLine["2" + 3]} -- run-time error

Output:

Uncaught signal TypeMismatch
====== invocation backtrace ======
00 at (<anonymous>) 1:56-1:62 evaluating
======== end of backtrace ========

(The expression does not evaluate to any value here; such outcome is called in MANOOL signaling an exception.)

And in the following example, the string "2" does not even “know” how to compare itself for less-than with another value, even with another string:

{{extern "manool.org.18/std/0.5/all"} in Out.WriteLine["2" < "3"]} -- run-time error
{{extern "manool.org.18/std/0.5/all"} in Out.WriteLine["2" < 3]} -- run-time error

Output:

Uncaught signal UnrecognizedOperation
====== invocation backtrace ======
00 at (<anonymous>) 1:56-1:62 evaluating
======== end of backtrace ========

Type predicates

For many data types in MANOOL, there exists a type predicate, a Boolean-valued procedure that determines whether its argument belongs to the underlying type:

{ {extern "manool.org.18/std/0.5/all"} in
  Out.WriteLine[2.IsI48[] ", " "2".IsI48[]] -- is "2" an integer?
  Out.WriteLine[2.IsS8[]  ", " "2".IsS8[]]  -- is "2" a string?
}

Output:

True, False
False, True

Compound Conditions

You can express complex conditions by using operators & (conjunction for Booleans), | (disjunction for Booleans), and ~ (negation for Booleans). The operators & and | are short-circuiting (the right-hand side is unevaluated unless strictly necessary):

{{extern "manool.org.18/std/0.5/all"} in Out.WriteLine["2".IsI48[] & ("2" < 3 "), " ~"2".IsI48[] | ("2" < 3)]}

Output:

False, True

More Exceptions

The MANOOL specification is precise about which exception is signaled in each particular erroneous case. We are already familiar with two of them: TypeMismatch and UnrecognizedOperation. Let's look at other basic signals:5

First, an inappropriate number of arguments is reported by signaling InvalidInvocation as in

{{extern "manool.org.18/std/0.5/all"} in Neg[2; 3]}

Arithmetic exceptions

Overflows during arithmetic operations are reported using signals:

{{extern "manool.org.18/std/0.5/all"} in MaxI48 + 1}

Signals: Overflow

The same applies to division by zero and other operations near a pole of the argument (e.g. near zero for logarithms):

{{extern "manool.org.18/std/0.5/all"} in 1 / 0}

Signals: DivisionByZero

In other cases Undefined may be signaled:

{{extern "manool.org.18/std/0.5/all"} in 0 / 0}
{{extern "manool.org.18/std/0.5/all"} in 1.Rem[0]}

Signals: Undefined

Quiz

Try to figure out what is going on here (you should have acquired all the clues after completing Lesson 3):

{{extern "manool.org.18/std/0.5/all"} in Out.WriteLine[(&)]}

Compilation error:

(<anonymous>) 1:42-1:62 Error: not an R-value expression (nested in this context)

And here:

{{extern "manool.org.18/std/0.5/all"} in Out.WriteLine[then]}

Compilation error:

(<anonymous>) 1:42-1:58 Error: unbound keyword (nested in this context)

Continue

Updated:
  1. In MANOOL, a proc-expression does not implicitly capture temporary variables from its initial binding environment (by default, the body of proc-expression is simply excluded from the scope of such variables). This is due to a deliberate language design decision.

  2. That entity is obtained in full at compile-time.

  3. The MANOOL specification does not require tail-call optimizations, though this is not the only reason.

  4. Temporary variables in MANOOL (including procedure parameters) are statically scoped.

  5. Your program in MANOOL can catch and react on any signal, and they are also used as a general control-flow mechanism.