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theory Examples
imports Frontend
begin
lemma overflow: "operate Add (-1) 1 = 0"
by eval
lemma multiply_overflow: "operate Mul (2 ^ 63) 2 = 0"
by eval
lemma shift_mask: "operate Shl 7 64 = 7"
by eval
lemma shift_wrap: "operate Shl 7 65 = 14"
by eval
lemma logical_shift: "operate Shr (-1) 63 = 1"
by eval
lemma unsigned_comparison: "operate Less (-1) 1 = 0"
by eval
lemma unsigned_high_bit: "operate Less 1 (2 ^ 63) = 1"
by eval
lemma constant_fold:
"optimise (Binary Add (Literal (-1)) (Literal 1)) = Literal 0"
by eval
lemma neutral_arithmetic:
"optimise (Binary Mul (Binary Add (Input X) (Literal 0)) (Literal 1)) = Input X"
by eval
lemma neutral_bits:
"optimise (Binary And (Binary Xor (Input Y) (Literal 0)) (Literal (-1))) = Input Y"
by eval
lemma absorbing_arithmetic:
"optimise (Binary Mul (Input X) (Literal 0)) = Literal 0"
by eval
lemma absorbing_bits:
"optimise (Binary Or (Binary And (Input Y) (Literal 0)) (Literal (-1))) = Literal (-1)"
by eval
lemma dead_branch:
"optimise (Cond (Literal 0) (Input X) (Input Y)) = Input Y"
by eval
lemma equal_branches:
"optimise (Cond (Input T) (Input X) (Input X)) = Input X"
by eval
lemma stack_bound_tight:
"bounded 2 (compile (Binary Add (Input X) (Input Y)) []) 0 \<and>
\<not> bounded 1 (compile (Binary Add (Input X) (Input Y)) []) 0"
by eval
lemma literal_code:
"executable (Literal 42) = [72,184,42,0,0,0,0,0,0,0,80,88,195]"
by eval
lemma opcode_roundtrip:
"decode [72,145,72,211,232,195] = Some (Arithmetic Shr,[195])"
by eval
lemma truncated_literal: "decode [72,184,0,0] = None"
by eval
lemma unaligned_slot: "decode [72,139,132,36,1,0,0,0] = None"
by eval
lemma negative_slot: "decode [72,139,132,36,0,0,0,128] = None"
by eval
lemma lexical_shadow:
"reference ''(let x 7 (let x (+ x 2) (* x x)))'' ''1'' ''2'' ''3'' = (True,''81'' @ newline)"
by eval
lemma nested_temporaries:
"reference ''(+ 10 (let a 3 (+ a (let b 4 (* a b)))))'' ''0'' ''0'' ''0'' = (True,''25'' @ newline)"
by eval
lemma unbound_rejected: "prepare ''(let a 3 b)'' = None"
by eval
lemma trailing_rejected: "prepare ''(+ x y) 1'' = None"
by eval
lemma literal_overflow_rejected: "prepare ''18446744073709551616'' = None"
by eval
lemma hexadecimal_boundaries:
"number ''0xffffffffffffffff'' = Some (2 ^ 64 - 1) \<and>
number ''0x10000000000000000'' = None"
by eval
lemma hexadecimal_execution:
"reference ''(+ x 0XfF)'' ''0x1'' ''0'' ''0'' = (True,''256'' @ newline)"
by eval
lemma incomplete_rejected: "prepare ''(if x y)'' = None"
by eval
end
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