89 lines
2.5 KiB
Lua
89 lines
2.5 KiB
Lua
import("util.lua")
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-- This examples demonstrates that Lean objects are not very useful as Lua table keys.
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local f = Const("f")
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local m = {}
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local env = environment()
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env:add_var("T", Type())
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env:add_var("f", mk_arrow(Const("T"), Const("T")))
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for i = 1, 100 do
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env:add_var("a" .. i, Const("T"))
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local t = f(Const("a" .. i))
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-- Any object can be a key of a Lua table.
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-- But, Lua does not use the method __eq for comparing keys.
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-- The problem is that Lua uses its own hashcode that may not
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-- be compatible with the __eq implemantion.
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-- By non-compatible, we mean two objects my be equal by __eq, but
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-- the hashcodes may be different.
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m[t] = i
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end
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for t1, i in pairs(m) do
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local t2 = f(Const("a" .. i))
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-- print(t1, i, t2)
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assert(m[t1] == i)
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-- t1 and t2 are structurally equal
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assert(t1 == t2)
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-- t1 and t2 are different objects
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assert(not t1:is_eqp(t2))
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-- t2 is not a key of map
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assert(m[t2] == nil)
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assert(env:normalize(t1) == t1)
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assert(t1:instantiate(Const("a")) == t1)
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local t1_prime = t1:instantiate(Const("a"))
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-- t1 and t1_prime are structurally equal
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assert(t1 == t1_prime)
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-- Moreover, they are references to the same Lean object
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assert(t1:is_eqp(t1_prime))
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-- But, they are wrapped by different Lua userdata
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assert(m[t1_prime] == nil)
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end
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-- We can store elements that implement __lt and __eq metamethods in splay_maps.
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-- The implementation assumes that the elements stored in the splay map can be totally ordered by __lt
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m = splay_map()
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m:insert(Const("a"), 10)
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assert(m:contains(Const("a")))
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assert(not m:contains(Const("b")))
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assert(m:find(Const("a")) == 10)
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local a, b = Consts("a, b")
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m:insert(f(a, b), 20)
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assert(m:find(f(a, b)) == 20)
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assert(m:find(f(a, a)) == nil)
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assert(m:size() == 2)
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assert(#m == 2)
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m:erase(f(a, a))
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assert(m:size() == 2)
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m:erase(f(a, b))
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assert(m:size() == 1)
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for i = 1, 100 do
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local t = f(Const("a" .. i))
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m:insert(t, i)
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assert(m:contains(t))
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assert(m:find(t) == i)
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end
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assert(m:size() == 101)
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for i = 1, 100 do
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local t = f(Const("a" .. i))
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assert(m:find(t) == i)
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end
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-- The following call fails because integers cannot be compared with Lean expressions
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assert(not pcall(function() m:insert(10, 20) end))
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-- Splay maps copy operation is O(1)
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local m2 = m:copy()
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m2:insert(b, 20)
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assert(m:size() == 101)
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assert(m2:size() == 102)
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-- We can also traverse all elements in the map
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local num = 0
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m:for_each(
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function(k, v)
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print(tostring(k) .. " -> " .. v)
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num = num + 1
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end
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)
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assert(num == 101)
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