Import–export (logic)

<p>In <a href="/facts/Propositional_logic/MNt5v31V">propositional logic</a>, import-export is a name given to the propositional form of <a href="/facts/Exportation_(logic)/MF4ctlzl">Exportation</a>:
</p>

(
        P
        →
        (
        Q
        →
        R
        )
        )
        ↔
        (
        (
        P
        ∧
        Q
        )
        →
        R
        )
      
    
    {\displaystyle (P\rightarrow (Q\rightarrow R))\leftrightarrow ((P\land Q)\rightarrow R)}
  
.
<p>This already holds in <a href="/facts/Minimal_logic/bIzUKg1A">minimal logic</a>, and thus also in <a href="/facts/Classical_logic/ls62MAms">classical logic</a>, where the conditional operator "
  
    
      
        →
      
    
    {\displaystyle \rightarrow }
  
" is taken as <a href="/facts/Material_conditional/hYf4b7AE">material implication</a>.
In the <a href="/facts/Curry-Howard_correspondence/Q3eVu60u">Curry-Howard correspondence</a> for intuitionistic logics, it can be realized through <a href="/facts/Currying/AmD3PP5B">currying</a> and uncurrying.
</p>

Import–export (logic) open-in-new

Import–export (logic)