sbv-8.6: SMT Based Verification: Symbolic Haskell theorem prover using SMT solving.

Documentation.SBV.Examples.Uninterpreted.Deduce

Description

Demonstrates uninterpreted sorts and how they can be used for deduction. This example is inspired by the discussion at http://stackoverflow.com/questions/10635783/using-axioms-for-deductions-in-z3, essentially showing how to show the required deduction using SBV.

Synopsis

# Representing uninterpreted booleans

newtype B Source #

The uninterpreted sort B, corresponding to the carrier. To prevent SBV from translating it to an enumerated type, we simply attach an unused field

Constructors

 B ()
Instances

type SB = SBV B Source #

Handy shortcut for the type of symbolic values over B

# Uninterpreted connectives over B

and :: SB -> SB -> SB Source #

Uninterpreted logical connective and

or :: SB -> SB -> SB Source #

Uninterpreted logical connective or

not :: SB -> SB Source #

Uninterpreted logical connective not

# Axioms of the logical system

ax1 :: [String] Source #

Distributivity of OR over AND, as an axiom in terms of the uninterpreted functions we have introduced. Note how variables range over the uninterpreted sort B.

ax2 :: [String] Source #

One of De Morgan's laws, again as an axiom in terms of our uninterpeted logical connectives.

ax3 :: [String] Source #

Double negation axiom, similar to the above.

# Demonstrated deduction

Proves the equivalence NOT (p OR (q AND r)) == (NOT p AND NOT q) OR (NOT p AND NOT r), following from the axioms we have specified above. We have:

>>> test
Q.E.D.