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@ -8,15 +8,15 @@ permalink : /Connectives/
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module plta.Connectives where
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\end{code}
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This chapter introduces the basic logical connectives, by observing
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a correspondence between connectives of logic and data types,
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a principle known as *Propositions as Types*.
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This chapter introduces the basic logical connectives, by observing a
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correspondence between connectives of logic and data types, a
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principle known as _Propositions as Types_.
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+ *conjunction* is *product*
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+ *disjunction* is *sum*
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+ *true* is *unit type*
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+ *false* is *empty type*
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+ *implication* is *function space*
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* _conjunction_ is _product_
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* _disjunction_ is _sum_
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* _true_ is _unit type_
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* _false_ is _empty type_
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* _implication_ is _function space_
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## Imports
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@ -4,18 +4,18 @@ layout : page
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permalink : /Lambda/
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---
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*Add a couple of simpler examples* ``id · `zero`` and ``twoᶜ · sucᶜ · `zero``.
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*Experiment with defining variables* smart constructor `` ƛ`_⇒_ ``
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*Todo: Experiment with defining variable names* smart constructor `` ƛ`_⇒_ ``
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\begin{code}
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module plta.Lambda where
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\end{code}
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<!--
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[This chapter was originally based on Chapter _Stlc_
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of _Software Foundations_ (_Programming Language Foundations_).
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It has now been updated, but if you spot any plagiarism
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please let me know. – P]
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-->
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The _lambda-calculus_, first published by the logician Alonzo Church in
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1932, is a core calculus with only three syntactic constructs:
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@ -1369,7 +1369,7 @@ det β-zero β-zero = refl
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det (β-suc VL) (ξ-case L—→L″) = ⊥-elim (V¬—→ (V-suc VL) L—→L″)
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det (β-suc _) (β-suc _) = refl
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det β-μ β-μ = refl
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-- \end{code}
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\end{code}
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The proof is by induction over possible reductions. We consider
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three typical cases.
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