4 research outputs found
Fix Your Types
When using existing ACL2 datatype frameworks, many theorems require type
hypotheses. These hypotheses slow down the theorem prover, are tedious to
write, and are easy to forget. We describe a principled approach to types that
provides strong type safety and execution efficiency while avoiding type
hypotheses, and we present a library that automates this approach. Using this
approach, types help you catch programming errors and then get out of the way
of theorem proving.Comment: In Proceedings ACL2 2015, arXiv:1509.0552
Second-Order Functions and Theorems in ACL2
SOFT ('Second-Order Functions and Theorems') is a tool to mimic second-order
functions and theorems in the first-order logic of ACL2. Second-order functions
are mimicked by first-order functions that reference explicitly designated
uninterpreted functions that mimic function variables. First-order theorems
over these second-order functions mimic second-order theorems universally
quantified over function variables. Instances of second-order functions and
theorems are systematically generated by replacing function variables with
functions. SOFT can be used to carry out program refinement inside ACL2, by
constructing a sequence of increasingly stronger second-order predicates over
one or more target functions: the sequence starts with a predicate that
specifies requirements for the target functions, and ends with a predicate that
provides executable definitions for the target functions.Comment: In Proceedings ACL2 2015, arXiv:1509.0552