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Harrop formula

In intuitionistic logic, the Harrop formulae, named after , are the class of formulaeinductively defined as follows: Atomic formulae are Harrop, including falsity (⊥);A∧B{\displaystyle A\wedge B} is Harrop provided A{\displaystyle A} and B{\displaystyle B} are;¬F{\displaystyle eg F} is Harrop for any well-formed formula F{\displaystyle F};F→A{\displaystyle F ightarrow A} is Harrop provided A{\displaystyle A} is, and F{\displaystyle F} is any well-formed formula;∀x.A{\displaystyle \forall x.A} is Harrop provided A{\displaystyle A} is.By excluding disjunction and existential quantification (except in the antecedent of implication), non-constructive predicates are avoided, which has benefits for computer implementation.

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