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lean4-htt/tests/lean/run/simprocSInt.lean
Markus Himmel 17c18752ff
feat: IntX operations and conversion theory (#7592) 
This PR adds theory about signed finite integers relating operations and
conversion functions.
2025-03-27 15:17:56 +00:00

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section
variable (x : Int)
#check_simp x = (-8 : Int8).toInt ~> x = -8
#check_simp x = (8 : Int8).toInt ~> x = 8
#check_simp x = (128 : Int8).toInt ~> x = -128
#check_simp x = (257 : Int8).toInt ~> x = 1
#check_simp x = (-8 : Int16).toInt ~> x = -8
#check_simp x = (8 : Int16).toInt ~> x = 8
#check_simp x = (32768 : Int16).toInt ~> x = -32768
#check_simp x = (65537 : Int16).toInt ~> x = 1
#check_simp x = (-8 : Int32).toInt ~> x = -8
#check_simp x = (8 : Int32).toInt ~> x = 8
#check_simp x = (2147483648 : Int32).toInt ~> x = -2147483648
#check_simp x = (4294967297 : Int32).toInt ~> x = 1
#check_simp x = (-8 : Int64).toInt ~> x = -8
#check_simp x = (8 : Int64).toInt ~> x = 8
#check_simp x = (9223372036854775808 : Int64).toInt ~> x = -9223372036854775808
#check_simp x = (18446744073709551617 : Int64).toInt ~> x = 1
end
section
end
section
variable (x : Int8)
example : Int8.toInt (-(-(-8))) + 8 = 0 := by simp +ground only
example : Int8.toInt (-8) + 8 = 0 := by simp +ground only
#check_simp (-5 : Int8).toNatClampNeg ~> 0
#check_simp (5 : Int8).toNatClampNeg ~> 5
#check_simp (-5 : Int8).toInt ~> -5
#check_simp (5 : Int8).toInt ~> 5
#check_simp x = - (-2) ~> x = 2
#check_simp x = -0 ~> x = 0
#check_simp x = - (-0) ~> x = 0
#check_simp x = - (-128) ~> x = 128
#check_simp x = - (-127) ~> x = 127
#check_simp x = 2 + 3 ~> x = 5
#check_simp x = -3 + 2 ~> x = -1
#check_simp x = 2 * -3 ~> x = -6
#check_simp x = 2 - 3 ~> x = -1
#check_simp x = 2 - -3 ~> x = 5
#check_simp x = 4 / -3 ~> x = -1
#check_simp x = -5 % 3 ~> x = -2
#check_simp True = ((3 : Int8) < -3) ~> False
#check_simp True = ((3 : Int8) ≤ -2) ~> False
#check_simp True = ((-3 : Int8) > 3) ~> False
#check_simp True = ((-3 : Int8) ≥ 4) ~> False
#check_simp True = ((3 : Int8) = -3) ~> False
#check_simp True = ((-3 : Int8) ≠ -3) ~> False
#check_simp True = ((3 : Int8) == -3) ~> False
#check_simp True = ((-3 : Int8) != -3) ~> False
#check_simp x = Int8.ofIntLE 5 (by decide) (by decide) ~> x = 5
#check_simp x = Int8.ofIntLE (-5) (by decide) (by decide) ~> x = -5
#check_simp x = Int8.ofNat 5 ~> x = 5
#check_simp x = Int8.ofNat 257 ~> x = 1
#check_simp x = Int8.ofNat 128 ~> x = -128
#check_simp x = Int8.ofInt (-129) ~> x = 127
#check_simp x = Int8.ofInt (-5) ~> x = -5
#check_simp x = Int8.ofInt 5 ~> x = 5
#check_simp x = Int8.ofInt 257 ~> x = 1
#check_simp x = Int8.ofInt 128 ~> x = -128
end
section
variable (x : Int16)
example : Int16.toInt (-(-(-16))) + 16 = 0 := by simp +ground only
example : Int16.toInt (-16) + 16 = 0 := by simp +ground only
#check_simp (-5 : Int16).toNatClampNeg ~> 0
#check_simp (5 : Int16).toNatClampNeg ~> 5
#check_simp (-5 : Int16).toInt ~> -5
#check_simp (5 : Int16).toInt ~> 5
#check_simp x = - (-2) ~> x = 2
#check_simp x = -0 ~> x = 0
#check_simp x = - (-0) ~> x = 0
#check_simp x = - (-32768) ~> x = 32768
#check_simp x = - (-32767) ~> x = 32767
#check_simp x = 2 + 3 ~> x = 5
#check_simp x = -3 + 2 ~> x = -1
#check_simp x = 2 * -3 ~> x = -6
#check_simp x = 2 - 3 ~> x = -1
#check_simp x = 2 - -3 ~> x = 5
#check_simp x = 4 / -3 ~> x = -1
#check_simp x = -5 % 3 ~> x = -2
#check_simp True = ((3 : Int16) < -3) ~> False
#check_simp True = ((3 : Int16) ≤ -2) ~> False
#check_simp True = ((-3 : Int16) > 3) ~> False
#check_simp True = ((-3 : Int16) ≥ 4) ~> False
#check_simp True = ((3 : Int16) = -3) ~> False
#check_simp True = ((-3 : Int16) ≠ -3) ~> False
#check_simp True = ((3 : Int16) == -3) ~> False
#check_simp True = ((-3 : Int16) != -3) ~> False
#check_simp x = Int16.ofIntLE 5 (by decide) (by decide) ~> x = 5
#check_simp x = Int16.ofIntLE (-5) (by decide) (by decide) ~> x = -5
#check_simp x = Int16.ofNat 5 ~> x = 5
#check_simp x = Int16.ofNat 65537 ~> x = 1
#check_simp x = Int16.ofNat 32768 ~> x = -32768
end
section
variable (x : Int32)
example : Int32.toInt (-(-(-32))) + 32 = 0 := by simp +ground only
example : Int32.toInt (-32) + 32 = 0 := by simp +ground only
#check_simp (-5 : Int32).toNatClampNeg ~> 0
#check_simp (5 : Int32).toNatClampNeg ~> 5
#check_simp (-5 : Int32).toInt ~> -5
#check_simp (5 : Int32).toInt ~> 5
#check_simp x = - (-2) ~> x = 2
#check_simp x = -0 ~> x = 0
#check_simp x = - (-0) ~> x = 0
#check_simp x = - (-2147483648) ~> x = 2147483648
#check_simp x = - (-2147483647) ~> x = 2147483647
#check_simp x = 2 + 3 ~> x = 5
#check_simp x = -3 + 2 ~> x = -1
#check_simp x = 2 * -3 ~> x = -6
#check_simp x = 2 - 3 ~> x = -1
#check_simp x = 2 - -3 ~> x = 5
#check_simp x = 4 / -3 ~> x = -1
#check_simp x = -5 % 3 ~> x = -2
#check_simp True = ((3 : Int32) < -3) ~> False
#check_simp True = ((3 : Int32) ≤ -2) ~> False
#check_simp True = ((-3 : Int32) > 3) ~> False
#check_simp True = ((-3 : Int32) ≥ 4) ~> False
#check_simp True = ((3 : Int32) = -3) ~> False
#check_simp True = ((-3 : Int32) ≠ -3) ~> False
#check_simp True = ((3 : Int32) == -3) ~> False
#check_simp True = ((-3 : Int32) != -3) ~> False
#check_simp x = Int32.ofIntLE 5 (by decide) (by decide) ~> x = 5
#check_simp x = Int32.ofIntLE (-5) (by decide) (by decide) ~> x = -5
#check_simp x = Int32.ofNat 5 ~> x = 5
#check_simp x = Int32.ofNat 4294967297 ~> x = 1
#check_simp x = Int32.ofNat 2147483648 ~> x = -2147483648
end
section
variable (x : Int64)
example : Int64.toInt (-(-(-64))) + 64 = 0 := by simp +ground only
example : Int64.toInt (-64) + 64 = 0 := by simp +ground only
#check_simp (-5 : Int64).toNatClampNeg ~> 0
#check_simp (5 : Int64).toNatClampNeg ~> 5
#check_simp (-5 : Int64).toInt ~> -5
#check_simp (5 : Int64).toInt ~> 5
#check_simp x = - (-2) ~> x = 2
#check_simp x = -0 ~> x = 0
#check_simp x = - (-0) ~> x = 0
#check_simp x = - (-9223372036854775808) ~> x = 9223372036854775808
#check_simp x = - (-9223372036854775807) ~> x = 9223372036854775807
#check_simp x = 2 + 3 ~> x = 5
#check_simp x = -3 + 2 ~> x = -1
#check_simp x = 2 * -3 ~> x = -6
#check_simp x = 2 - 3 ~> x = -1
#check_simp x = 2 - -3 ~> x = 5
#check_simp x = 4 / -3 ~> x = -1
#check_simp x = -5 % 3 ~> x = -2
#check_simp True = ((3 : Int32) < -3) ~> False
#check_simp True = ((3 : Int32) ≤ -2) ~> False
#check_simp True = ((-3 : Int32) > 3) ~> False
#check_simp True = ((-3 : Int32) ≥ 4) ~> False
#check_simp True = ((3 : Int32) = -3) ~> False
#check_simp True = ((-3 : Int32) ≠ -3) ~> False
#check_simp True = ((3 : Int32) == -3) ~> False
#check_simp True = ((-3 : Int32) != -3) ~> False
#check_simp x = Int64.ofIntLE 5 (by decide) (by decide) ~> x = 5
#check_simp x = Int64.ofIntLE (-5) (by decide) (by decide) ~> x = -5
#check_simp x = Int64.ofNat 5 ~> x = 5
#check_simp x = Int64.ofNat 18446744073709551617 ~> x = 1
#check_simp x = Int64.ofNat 9223372036854775808 ~> x = -9223372036854775808
end
section
#check_simp ISize.toNatClampNeg 2147483648 !~>
#check_simp ISize.toNatClampNeg 2147483647 ~> 2147483647
#check_simp ISize.toNatClampNeg (-1) ~> 0
#check_simp ISize.toNatClampNeg 0 ~> 0
#check_simp ISize.toNatClampNeg 1 ~> 1
#check_simp ISize.toNatClampNeg (-2147483649) !~>
#check_simp ISize.toNatClampNeg (-2147483648) ~> 0
#check_simp ISize.toInt 2147483648 !~>
#check_simp ISize.toInt 2147483647 ~> 2147483647
#check_simp ISize.toInt (-1) ~> -1
#check_simp ISize.toInt 0 ~> 0
#check_simp ISize.toInt 1 ~> 1
#check_simp ISize.toInt (-2147483649) !~>
#check_simp ISize.toInt (-2147483648) ~> -2147483648
end
-- see also simpSInt.lean
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