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Merging 'WIP: Do Not Merge This Branch' Into Master (#3)
* add RecursionError: maximum recursion depth 1500 for while loop * One does not simply merge into master * fix some fucking errors * Update README.org * You know the rules and so do I
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‎README.org‎

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#+title: WHILE-Programme
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#+author: Felix Drees
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#+STARTUP: latexpreview
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#+OPTIONS: toc:nil tex:t # tex:verbatim num:nil
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#+keywords: while programs, turing complete, turing machines
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* while
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Parser and interpreter for the While programming language
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Parser and interpreter for the *while* programming language
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The *while* programming language is a verry simplified language, which is turing complete!
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[[https://github.com/felixbd/while/actions/workflows/ci-test.yml/badge.svg?branch=main]]
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** syntax specification via context-free type-2 grammar
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The set of *WHILE* programs is the language generated by the following grammar
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$$ G = (N, \sum, P, S) $$
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where
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$N = \{ Prog, Var, Const, Expr \}$
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(the set of non terminal Symbols)
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$\sum = \{ loop, while, do, end, +, -, ;, :=, != \} \cup \mathbb{N}_0 \cup VariableNames$
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(the set of terminal symbols)
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$S = Prog$
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(the start non terminal)
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$P = \{$
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$Prog \to Prog; Prog$
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$Prog \to Var := Expr$
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$Expr \to Var \mid Const \mid Expr + Expr \mid Expr - Expr$
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$Prog \to \textrm{loop Expr do Prog end}$
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$Prog \to \textrm{while Expr != Expr do Prog end}$
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$Var \to VariableName$ (that has to start with ascii letter and can contain digits or underscore)
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$Const \to \mathbb{N}_0$
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$\}$
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(the set of production rules)
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** semantic
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as expected, i guess ... lol
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NOTE: the subtraction is only defined in $\mathbb{N}_0$
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therefore $5 - 8$ will result in $0$
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also i added a max recursion depth like python3 to prevent users to write non terminating code ...
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(the max rec depth for a *while* loop is *1500* iterations)
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** usage
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*** example
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lets say you have a function $\psi$ for calculating a simple multiplication $a \cdot b$
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$$\psi \colon \mathbb{N}^2_0 \longrightarrow \mathbb{N}_0$$
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$$(x_1, x_2) \mapsto x_1 \cdot x_2$$
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lets calculate $420 \cdot 69$ via $\psi(v)$ where $v := (420, 69)$, the result should be $28980$.
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#+begin_src shell :exports both :results output
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cat ./examples/multiplication-func.while
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#+end_src
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#+RESULTS:
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#+begin_example
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rv := 0;
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a := 420;
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b := 69;
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while b != 0 do
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temp := rv;
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loop a do temp := temp + 1 end;
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rv := temp;
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b := b - 1
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end
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#+end_example
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since this is a bit tidies i allowed users to use expressions in the context
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- conditions
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- additions
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- and subtractions
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(refer to the grammar defined above)
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shortened (not completely while-language correct ...) version
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#+begin_src
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x0 := 0;
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x1 := 420;
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x2 := 69;
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loop x2 do x0 := x0 + x1 end
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#+end_src
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#+begin_src shell
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felix in ~/git-repos/hub/while on main ● λ stack build
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felix in ~/git-repos/hub/while on main ● λ stack run
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felix in ~/git-repos/hub/while on dev ● λ stack build
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felix in ~/git-repos/hub/while on dev ● λ stack run
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= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
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Enter the file name:
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./examples/simple.while
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[READING .WHILE FILE] "./examples/simple.while"
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./examples/multiplication-func.while
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[READING .WHILE FILE] "./examples/multiplication-func.while"
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[DONE TOKENIZE]:
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[MetaToken {getLineNumber = 1, getToken = VarToken {getVarName = "x_1"}},
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[MetaToken {getLineNumber = 1, getToken = VarToken {getVarName = "rv"}},
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MetaToken {getLineNumber = 1, getToken = AssignToken},
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MetaToken {getLineNumber = 1, getToken = ConstToken {getConstInt = 10}},
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MetaToken {getLineNumber = 1, getToken = ConstToken {getConstInt = 0}},
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MetaToken {getLineNumber = 1, getToken = SemicolonToken},
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MetaToken {getLineNumber = 2, getToken = VarToken {getVarName = "x_2"}},
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MetaToken {getLineNumber = 2, getToken = VarToken {getVarName = "a"}},
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MetaToken {getLineNumber = 2, getToken = AssignToken},
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MetaToken {getLineNumber = 2, getToken = ConstToken {getConstInt = 0}},
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MetaToken {getLineNumber = 2, getToken = ConstToken {getConstInt = 420}},
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MetaToken {getLineNumber = 2, getToken = SemicolonToken},
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MetaToken {getLineNumber = 4, getToken = WhileToken},
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MetaToken {getLineNumber = 4, getToken = VarToken {getVarName = "x_1"}},
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MetaToken {getLineNumber = 4, getToken = NotEqualToken},
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MetaToken {getLineNumber = 4, getToken = ConstToken {getConstInt = 0}},
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MetaToken {getLineNumber = 4, getToken = DoToken},
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MetaToken {getLineNumber = 5, getToken = VarToken {getVarName = "x_1"}},
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MetaToken {getLineNumber = 5, getToken = AssignToken},
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MetaToken {getLineNumber = 5, getToken = VarToken {getVarName = "x_1"}},
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MetaToken {getLineNumber = 5, getToken = MinusToken},
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MetaToken {getLineNumber = 5, getToken = ConstToken {getConstInt = 1}},
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MetaToken {getLineNumber = 5, getToken = SemicolonToken},
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MetaToken {getLineNumber = 6, getToken = LoopToken},
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MetaToken {getLineNumber = 6, getToken = VarToken {getVarName = "x_1"}},
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MetaToken {getLineNumber = 6, getToken = DoToken},
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MetaToken {getLineNumber = 6, getToken = VarToken {getVarName = "x_2"}},
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MetaToken {getLineNumber = 3, getToken = VarToken {getVarName = "b"}},
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MetaToken {getLineNumber = 3, getToken = AssignToken},
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MetaToken {getLineNumber = 3, getToken = ConstToken {getConstInt = 69}},
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MetaToken {getLineNumber = 3, getToken = SemicolonToken},
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MetaToken {getLineNumber = 5, getToken = WhileToken},
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MetaToken {getLineNumber = 5, getToken = VarToken {getVarName = "b"}},
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MetaToken {getLineNumber = 5, getToken = NotEqualToken},
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MetaToken {getLineNumber = 5, getToken = ConstToken {getConstInt = 0}},
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MetaToken {getLineNumber = 5, getToken = DoToken},
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MetaToken {getLineNumber = 6, getToken = VarToken {getVarName = "temp"}},
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MetaToken {getLineNumber = 6, getToken = AssignToken},
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MetaToken {getLineNumber = 6, getToken = VarToken {getVarName = "x_2"}},
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MetaToken {getLineNumber = 6, getToken = PlusToken},
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MetaToken {getLineNumber = 6, getToken = VarToken {getVarName = "x_1"}},
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MetaToken {getLineNumber = 6, getToken = EndToken},
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MetaToken {getLineNumber = 7, getToken = EndToken}]
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MetaToken {getLineNumber = 6, getToken = VarToken {getVarName = "rv"}},
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MetaToken {getLineNumber = 6, getToken = SemicolonToken},
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MetaToken {getLineNumber = 7, getToken = LoopToken},
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MetaToken {getLineNumber = 7, getToken = VarToken {getVarName = "a"}},
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MetaToken {getLineNumber = 7, getToken = DoToken},
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MetaToken {getLineNumber = 7, getToken = VarToken {getVarName = "temp"}},
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MetaToken {getLineNumber = 7, getToken = AssignToken},
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MetaToken {getLineNumber = 7, getToken = VarToken {getVarName = "temp"}},
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MetaToken {getLineNumber = 7, getToken = PlusToken},
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MetaToken {getLineNumber = 7, getToken = ConstToken {getConstInt = 1}},
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MetaToken {getLineNumber = 7, getToken = EndToken},
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MetaToken {getLineNumber = 7, getToken = SemicolonToken},
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MetaToken {getLineNumber = 8, getToken = VarToken {getVarName = "rv"}},
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MetaToken {getLineNumber = 8, getToken = AssignToken},
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MetaToken {getLineNumber = 8, getToken = VarToken {getVarName = "temp"}},
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MetaToken {getLineNumber = 8, getToken = SemicolonToken},
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MetaToken {getLineNumber = 10, getToken = VarToken {getVarName = "b"}},
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MetaToken {getLineNumber = 10, getToken = AssignToken},
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MetaToken {getLineNumber = 10, getToken = VarToken {getVarName = "b"}},
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MetaToken {getLineNumber = 10, getToken = MinusToken},
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MetaToken {getLineNumber = 10, getToken = ConstToken {getConstInt = 1}},
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MetaToken {getLineNumber = 11, getToken = EndToken}]
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[DONE PARSING AST]:
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Sequential
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(Assignment "x_1" (Constant {getConst = 10}))
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(Sequential
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(Assignment "x_2" (Constant {getConst = 0}))
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(While
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(Neq (Variable {getVar = "x_1"}) (Constant {getConst = 0}))
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(Sequential
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(Assignment "x_1" (Subtract (Variable {getVar = "x_1"}) (Constant {getConst = 1})))
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(Loop
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(Variable {getVar = "x_1"})
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(Assignment "x_2" (Add (Variable {getVar = "x_2"}) (Variable {getVar = "x_1"})))))))
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(Assignment "rv" (Constant {getConst = 0}))
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(Sequential
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(Assignment "a" (Constant {getConst = 420}))
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(Sequential
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(Assignment "b" (Constant {getConst = 69}))
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(While
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(Neq (Variable {getVar = "b"}) (Constant {getConst = 0}))
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(Sequential
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(Assignment "temp" (Variable {getVar = "rv"}))
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(Sequential
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(Loop
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(Variable {getVar = "a"})
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(Assignment "temp" (Add (Variable {getVar = "temp"}) (Constant {getConst = 1}))))
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(Sequential
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(Assignment "rv" (Variable {getVar = "temp"}))
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(Assignment "b" (Subtract (Variable {getVar = "b"}) (Constant {getConst = 1})))))))))
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[OUTPUT OF EVALUATION]:
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[("x_2",285),("x_1",0)]
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[("temp",28980),("b",0),("a",420),("rv",28980)]
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= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
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felix in ~/git-repos/hub/while on main ● λ
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felix in ~/git-repos/hub/while on dev ● λ
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#+end_src
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*** compile

‎examples/multiplication-func.while‎

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rv := 0;
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a := 420;
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b := 69;
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while b != 0 do
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temp := rv;
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loop a do temp := temp + 1 end;
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rv := temp;
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b := b - 1
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end

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