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A dictionary is a tuple that corresponds to an instance declaration, and contains values that correspond to the definitions given in the instance declaration for each class member.
Constraint Eq(a) must be specified as the context for the headEq[(a)] of the instance declaration.
Each instance declaration instance(PRightarrow pi )where... introduces an axiom scheme (forall,overline{alpha }.,PRightarrow pi ), where (overline{alpha } = { tv}(PRightarrow pi )).
Each instance declaration (mathtt{instance },PRightarrow pi,mathtt{where },overline{x} = overline{e}) of a class (C) generates a dictionary (d_pi.) Each component in (d_pi ) is a function that takes one dictionary for each constraint in the (possibly empty) sequence (overline{P}) and yields the translation of (e_i,) the value bound by (x_i) in the instance declaration.
Each constraint in a context (P) of an instance declaration (PRightarrow C,overline{tau }) must have the form (C,a), where (a) is a type variable occurring in (overline{tau }).
Flag -XFlexibleInstances can be used by GHC users to avoid enforcing condition (2), i.e., to allow the head of a constraint in an instance declaration to be arbitrarily nested.
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The set of constraint axioms (Theta ) is induced by class and instance declarations of a program.
This section summarizes the restrictions imposed on class and instance declarations in Haskell, Haskell+mptcs and in GHC, and GHC compilation flags used to avoid these restrictions.
Context reduction can also occur due to the presence of superclass class declarations, but we only consider the case of instance declarations in this paper, which is the more complex process.
Restrictions imposed on class and instance declarations in Haskell, in Haskell+mptcs and in GHC, and GHC compilation flags used to avoid these restrictions [20], are summarized in Sect. 2.
For example, the following instance declarations specify definitions of the equality operator for types Int and for polymorphic lists, respectively: For a base type, like Int, a corresponding predefined operation is provided.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com