# Documentation

The abstract domain of the interpreter. Representing sets of values of a certain type.

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Fuse v into vs. That is do not only append but if we see that v is a constructor that is already contained within vs try to detect the difference between these values and merge them accordingly into a choice node further down the tree.

Merge two values into one. bot is the neutral element, top the annihilator.

Make sure constructors of recursive inductive datatypes can only occur once in each path. Values at depth > maxValueDepth are also approximated at top. We use this function to implement a simple widening operation for our abstract interpreter. Recall the widening functions is used to ensure termination in abstract interpreters.

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Widening operator that guarantees termination in our abstract interpreter.

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Check whether a certain constructor is part of a Value by name. Note that both top and bot will always true here. For bot this is because we have no information about the Value so just to be sure we don't claim the absence of a certain constructor.

Obtain the arguments of a certain constructor within the Value.

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We say that a Value is a literal iff it is only a tree of Value.ctor nodes.

Attempt to turn a Value that is representing a literal into a set of auxiliary declarations + the final FVarId of the declaration that contains the actual literal. If it is not a literal return none.

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A map from function names to the Value that the abstract interpreter produced for them.

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Storing FunctionSummaries for all functions in a .olean.

Add a Value for a function name.

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Obtain the Value for a function name if possible.

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A map from variable identifiers to the Value produced by the abstract interpreter for them.

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• The list of Decls we are operating on in InterpM. This can be a single declaration or a mutual block of declarations where their analysis might influence each other as we approach the fixpoint.

decls :
• The index of the function we are currently operating on in decls.

currFnIdx : Nat

The context of InterpM.

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• Assignments of functions in the InterpContext.

assignments :
• Values of functions in the InterpContext use during computation of the fixpoint. Afterwards they are stored into the Environment.

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@[inline]

The monad which powers the abstract interpreter.

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Get the variable Assignment of the current function.

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Get the Value of a certain function in the current block by index.

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• = do let __do_lift ← get pure __do_lift.funVals[funIdx]!
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Run f on the variable Assignment of the current function.

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Obtain the Value associated with var from the context of InterpM. If none is available return Value.bot.

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Find the value of arg using the logic of findVarValue.

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Update the assignment of var by merging the current value with newVal.

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Set the value of var to bot.

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Widen the value of the current function by v.

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Return true if the assignment of at least one parameter has been updated. Furthermore if we see that params.size != args.size we know that this is a partial application and set the values of the remaining parameters to top since it is impossible to track what will happen with them from here on.

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The actual abstract interpreter on a block of Code.

The abstract interpreter on a LetValue.

If we see a function being passed as an argument to a higher order function we cannot know what arguments it will be passed further down the line. Hence we set all of its arguments to top since anything is possible.

Rerun the abstract interpreter on all declarations except of the unsafe ones. Return whether any Value got updated in the process.

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Run inferStep until it reaches a fix point.

Use the information produced by the abstract interpeter to:

• Eliminate branches that we know cannot be hit
• Eliminate values that we know have to be constants.
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