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34 lines
1.3 KiB
Plaintext
34 lines
1.3 KiB
Plaintext
BBT.set
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: ∀(K: *)
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∀(V: *)
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∀(cmp: ∀(a: K) ∀(b: K) Cmp)
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∀(key: K)
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∀(val: V)
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∀(map: (BBT K V))
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(BBT K V)
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= λK λV λcmp λkey λval λmap
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let P = λx ∀(key: K) ∀(val: V) (BBT K V)
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let bin = λsize λnext.key λnext.val λnext.lft λnext.rgt λkey λval
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let P = λx ∀(key: K) ∀(next.key: K) ∀(next.val: V) ∀(next.lft: (BBT K V)) ∀(next.rgt: (BBT K V)) ∀(key: K) ∀(val: V) (BBT K V)
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// Go left
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let ltn = λkey λnext.key λnext.val λnext.lft λnext.rgt λkey λval
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let new_lft = (BBT.set K V cmp key val next.lft)
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(BBT.balance K V cmp key next.key next.val new_lft next.rgt)
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// Same key, update value
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// Should we update the value or return the same tree?
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let eql = λkey λnext.key λnext.val λnext.lft λnext.rgt λkey λval
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(BBT.bin K V size next.key val next.lft next.rgt)
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// Go right
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let gtn = λkey λnext.key λnext.val λnext.lft λnext.rgt λkey λval
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let new_rgt = (BBT.set K V cmp key val next.rgt)
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(BBT.balance K V cmp key next.key next.val next.lft new_rgt)
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((~(cmp key next.key) P ltn eql gtn) key next.key next.val next.lft next.rgt key val)
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// Empty tree, create new node
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let tip = λkey λval
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(BBT.singleton K V key val)
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((~map P bin tip) key val)
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