47 lines
1.4 KiB
Text
47 lines
1.4 KiB
Text
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import cast
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variable vec : Nat → Type
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variable concat {n m : Nat} (v : vec n) (w : vec m) : vec (n + m)
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infixl 65 ; : concat
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axiom concat_assoc {n1 n2 n3 : Nat} (v1 : vec n1) (v2 : vec n2) (v3 : vec n3) :
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(v1 ; v2) ; v3 = cast (congr2 vec (symm (Nat::add_assoc n1 n2 n3)))
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(v1 ; (v2 ; v3))
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variable empty : vec 0
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axiom concat_empty {n : Nat} (v : vec n) :
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v ; empty = cast (congr2 vec (symm (Nat::add_zeror n)))
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v
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rewrite_set simple
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-- The simplification rules used for Nat and Vectors should "mirror" each other.
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-- Concatenation is not commutative. So, by adding Nat::add_comm to the
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-- rewrite set, we prevent the simplifier from reducing the following example
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add_rewrite concat_assoc concat_empty Nat::add_assoc Nat::add_zeror Nat::add_comm : simple
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variable n : Nat
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variable v : vec n
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variable w : vec n
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variable f {A : TypeM} : A → A
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(*
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local t = parse_lean([[ f ((v ; w) ; empty ; (v ; empty)) ]])
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print(t)
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print("===>")
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local t2, pr = simplify(t, "simple")
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print(t2)
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print(pr)
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get_environment():type_check(pr)
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*)
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-- Now, if we disable Nat::add_comm, the simplifier works
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disable_rewrite Nat::add_comm : simple
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print "After disabling Nat::add_comm"
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(*
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local t = parse_lean([[ f ((v ; w) ; empty ; (v ; empty)) ]])
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print(t)
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print("===>")
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local t2, pr = simplify(t, "simple")
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print(t2)
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print(pr)
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get_environment():type_check(pr)
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*)
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