140 lines
3.2 KiB
Plaintext
140 lines
3.2 KiB
Plaintext
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; -------------------------------------------------------------------------
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; Boogie universal background predicate
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; Copyright (c), Microsoft Corp.
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:category { industrial }
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; select/store axioms, 1 index argument
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:assumption
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(forall (?a Any) (?i Any) (?v Any)
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(= (select1 (store1 ?a ?i ?v) ?i) ?v))
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:assumption
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(forall (?a Any) (?i Any) (?j Any) (?v Any)
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(implies (!= ?i ?j)
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(=
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(select1 (store1 ?a ?i ?v) ?j)
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(select1 ?a ?j))))
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; select/store axioms, 2 index arguments
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:assumption
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(forall (?a Any) (?o Any) (?f Any) (?v Any)
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(= (select2 (store2 ?a ?o ?f ?v) ?o ?f) ?v))
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:assumption
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(forall (?a Any) (?o Any) (?f Any) (?p Any) (?g Any) (?v Any)
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(implies (!= ?o ?p)
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(=
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(select2 (store2 ?a ?o ?f ?v) ?p ?g)
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(select2 ?a ?p ?g))))
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:assumption
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(forall (?a Any) (?o Any) (?f Any) (?p Any) (?g Any) (?v Any)
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(implies (!= ?f ?g)
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(=
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(select2 (store2 ?a ?o ?f ?v) ?p ?g)
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(select2 ?a ?p ?g))))
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; formula/term axioms
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:assumption
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(forall (?x Any) (?y Any)
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(iff
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(= (boolIff ?x ?y) boolTrue)
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(iff (= ?x boolTrue) (= ?y boolTrue))))
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:assumption
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(forall (?x Any) (?y Any)
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(iff
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(= (boolImplies ?x ?y) boolTrue)
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(implies (= ?x boolTrue) (= ?y boolTrue))))
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:assumption
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(forall (?x Any) (?y Any)
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(iff
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(= (boolAnd ?x ?y) boolTrue)
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(and (= ?x boolTrue) (= ?y boolTrue))))
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:assumption
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(forall (?x Any) (?y Any)
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(iff
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(= (boolOr ?x ?y) boolTrue)
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(or (= ?x boolTrue) (= ?y boolTrue))))
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:assumption
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(forall (?x Any)
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(iff
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(= (boolNot ?x) boolTrue)
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(!= ?x boolTrue))
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:pat { (boolNot ?x) }
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)
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:assumption
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(forall (?x Any) (?y Any)
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(iff
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(= (anyEqual ?x ?y) boolTrue)
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(= ?x ?y)))
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:assumption
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(forall (?x Any) (?y Any)
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(iff
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(= (anyNeq ?x ?y) boolTrue)
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(!= ?x ?y))
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:pat { (anyNeq ?x ?y) }
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)
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:assumption
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(forall (?x Any) (?y Any)
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(iff
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(= (intLess ?x ?y) boolTrue)
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(< ?x ?y)))
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:assumption
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(forall (?x Any) (?y Any)
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(iff
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(= (intAtMost ?x ?y) boolTrue)
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(<= ?x ?y)))
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:assumption
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(forall (?x Any) (?y Any)
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(iff
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(= (intAtLeast ?x ?y) boolTrue)
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(>= ?x ?y)))
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:assumption
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(forall (?x Any) (?y Any)
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(iff
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(= (intGreater ?x ?y) boolTrue)
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(> ?x ?y)))
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; false is not true
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:assumption
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(distinct boolFalse boolTrue)
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; <: is a partial order: it is reflexive, transitive, and anti-symmetric
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; x'''60_'58_ is the encoding we use
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:assumption
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(forall (?t Any)
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(x'''60_'58_ ?t ?t)
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:pat { (x'''60_'58_ ?t ?t) }
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)
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:assumption
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(forall (?t Any) (?u Any) (?v Any)
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(implies
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(and (x'''60_'58_ ?t ?u) (x'''60_'58_ ?u ?v))
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(x'''60_'58_ ?t ?v))
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:pat { (x'''60_'58_ ?t ?u) (x'''60_'58_ ?u ?v) }
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)
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:assumption
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(forall (?t Any) (?u Any)
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(implies
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(and (x'''60_'58_ ?t ?u) (x'''60_'58_ ?u ?t))
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(= ?t ?u))
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:pat { (x'''60_'58_ ?t ?u) (x'''60_'58_ ?u ?t) }
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)
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; End Boogie universal background predicate
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; -------------------------------------------------------------------------
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