36 lines
1.2 KiB
Plaintext
36 lines
1.2 KiB
Plaintext
-- We represent `false` with a Leaf and `true` with a Stem Leaf
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false = t
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true = t t
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-- Tree Calculus representation of the Boolean `not` function
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not_TC? = t (t (t t) (t t t)) (t t (t t t))
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-- /demos/toSource.tri contains an explanation of `triage`
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triage = (\a b c : t (t a b) c)
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matchBool = (\ot of : triage
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of
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(\_ : ot)
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(\_ _ : ot)
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)
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-- Lambda representation of the Boolean `not` function
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not_Lambda? = matchBool false true
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-- Since tricu eliminates Lambda terms to SKI combinators, the tree form of many
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-- functions defined via Lambda terms are larger than the most efficient TC
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-- representation. Between different languages that evaluate to tree calculus
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-- terms, the exact implementation of Lambda elimination may differ and lead
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-- to different tree representations even if they share extensional behavior.
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-- Let's see if these are the same:
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lambdaEqualsTC = equal? not_TC? not_Lambda?
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-- Here are some checks to verify their extensional behavior is the same:
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true_TC? = not_TC? false
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false_TC? = not_TC? true
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true_Lambda? = not_Lambda? false
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false_Lambda? = not_Lambda? true
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bothTrueEqual? = equal? true_TC? true_Lambda?
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bothFalseEqual? = equal? false_TC? false_Lambda?
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