81b134cbb9
This PR adds about half of the needed primitives and logic for reasoning about linear integer arithmetic in programs with interesting dependent types. Things have been added in a way s.t. programs will still continue to typecheck as they did, but if you want integer literals and certain operations (e.g. *,+,<,<=,=,>=,>) to include linear inequality information by default, you need to include the '#:with-linear-integer-arithmetic' keyword at the top of your module. The other features needed to get TR to be able to check things like verified vector operations will be to ajust function types so dependencies can exist between arguments and a minor tweak to get type inference to consider the symbolic objects of functions arguments. These features should be coming shortly in a future pull request.
220 lines
7.4 KiB
Racket
220 lines
7.4 KiB
Racket
#lang racket/base
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(require "test-utils.rkt"
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rackunit racket/format
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(rep prop-rep)
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(types abbrev prop-ops)
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(for-syntax racket/base syntax/parse))
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(provide tests)
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(gen-test-main)
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(define (not-atomic-implies? y x) (not (atomic-implies? y x)))
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(define (not-implies? y x) (not (implies? y x)))
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;; binding these means props that mention #'x, #'y, and #'z
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;; will be referring to identifiers w/ variable bindings
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;; (and props about things w/o variable bindings are erased
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;; since top level ids are mutable)
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(define x 42)
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(define y 42)
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(define z 42)
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(define-syntax (implies-atomic-tests stx)
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(define-syntax-class imp-test
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(pattern (~and tst [#:not a:expr c:expr])
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#:with check #`(test-case
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(~a '(not (implies-atomic? a c)))
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#,(syntax/loc #'tst (check-false (atomic-implies? a c)))
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#,(syntax/loc #'tst (check-false (implies? a c)))))
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(pattern (~and tst [a:expr c:expr])
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#:with check #`(test-case
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(~a '(implies-atomic? a c))
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#,(syntax/loc #'tst (check-true (atomic-implies? a c)))
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#,(syntax/loc #'tst (check-true (implies? a c))))))
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(syntax-parse stx
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[(_ tst:imp-test ...)
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#'(test-suite
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"Implies Atomic"
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tst.check ...)]))
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(define-syntax (test-opposite stx)
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(define-syntax-class complementary
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(pattern #:complementary #:with check #'check-true)
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(pattern #:not-complementary #:with check #'check-false))
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(define-syntax-class contradictory
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(pattern #:contradictory #:with check #'check-true)
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(pattern #:not-contradictory #:with check #'check-false))
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(syntax-parse stx
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[(_ comp:complementary contr:contradictory p1* p2*)
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#`(test-case
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(~a '(opposite p1* p2*))
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(define p1 p1*)
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(define p2 p2*)
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#,(syntax/loc stx (comp.check (atomic-complement? p1 p2) "Complementary"))
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#,(syntax/loc stx (contr.check (atomic-contradiction? p1 p2) "Contradictory"))
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;; 'contradiction' should be strictly stronger than 'atomic-contradiction'
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;; and so we'll test both here
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#,(syntax/loc stx (contr.check (contradiction? p1 p2) "Contradictory")))]))
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(define tests
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(test-suite "Props"
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(test-suite "Opposite"
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(test-opposite #:not-complementary #:contradictory
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(-is-type 0 -Symbol)
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(-not-type 0 (Un -Symbol -String)))
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(test-opposite #:complementary #:not-contradictory
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(-is-type 0 (Un -Symbol -String))
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(-not-type 0 -Symbol))
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(test-opposite #:complementary #:contradictory
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(-not-type 0 -Symbol)
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(-is-type 0 -Symbol))
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(test-opposite #:not-complementary #:not-contradictory
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(-is-type 1 -Symbol)
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(-not-type 0 -Symbol))
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(test-opposite #:not-complementary #:not-contradictory
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(-not-type 0 -Symbol)
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(-is-type 0 -String))
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(test-opposite #:not-complementary #:not-contradictory
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(-not-type 0 -Symbol)
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(-is-type 0 -String))
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(test-opposite #:not-complementary #:contradictory
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-ff
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-ff)
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(test-opposite #:complementary #:contradictory
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-ff
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-tt)
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(test-opposite #:complementary #:not-contradictory
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-tt
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-tt)
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(test-opposite #:not-complementary #:not-contradictory
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(-leq (-lexp (list 2 (-id-path #'x))) (-id-path #'x))
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(-leq (-lexp (list 2 (-id-path #'x))) (-id-path #'x)))
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(test-opposite #:complementary #:not-contradictory
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(-leq (-lexp (list 2 (-id-path #'x))) (-id-path #'x))
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(-leq (-id-path #'x) (-lexp (list 2 (-id-path #'x)))))
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(test-opposite #:not-complementary #:contradictory
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(-leq (-id-path #'x) (-lexp 42))
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(-leq (-lexp 100) (-id-path #'x)))
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(test-opposite #:complementary #:contradictory
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(-leq (-lexp (list 2 (-id-path #'x))) (-id-path #'x))
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(negate-prop (-leq (-lexp (list 2 (-id-path #'x))) (-id-path #'x))))
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)
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(test-suite
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"Contradiction"
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(check contradiction?
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(-is-type #'x (-pair -String -String))
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(-is-type (-car-of (-id-path #'x)) -Symbol))
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(check contradiction?
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(-is-type (-car-of (-id-path #'x)) (-pair -String -String))
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(-is-type (-cdr-of (-car-of (-id-path #'x))) -Symbol))
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(check contradiction?
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(-is-type (-car-of (-id-path #'x)) -Symbol)
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(-is-type #'x (-pair -String -String)))
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(check contradiction?
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(-is-type (-cdr-of (-car-of (-id-path #'x))) -Symbol)
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(-is-type (-car-of (-id-path #'x)) (-pair -String -String)))
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(check contradiction?
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(-not-type (-car-of (-id-path #'x)) -String)
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(-is-type #'x (-pair -String -String)))
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(check contradiction?
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(-is-type #'x (-pair -String -String))
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(-not-type (-car-of (-id-path #'x)) -String))
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(check contradiction?
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(-not-type (-car-of (-cdr-of (-id-path #'x))) -String)
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(-is-type (-cdr-of (-id-path #'x)) (-pair -String -String)))
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(check contradiction?
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(-is-type (-cdr-of (-id-path #'x)) (-pair -String -String))
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(-not-type (-car-of (-cdr-of (-id-path #'x))) -String))
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(check contradiction?
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(-leq (-id-path #'x) (-lexp 0))
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(-leq (-lexp 1) (-id-path #'x))))
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(implies-atomic-tests
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[-tt -tt]
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[-ff -ff]
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[#:not -tt -ff]
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[(-is-type 0 -Symbol) -tt]
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[-ff (-is-type 0 -Symbol)]
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[(-is-type 0 -Symbol)
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(-is-type 0 (Un -String -Symbol))]
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[#:not
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(-is-type 0 (Un -String -Symbol))
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(-is-type 0 -Symbol)]
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[(-not-type 0 (Un -String -Symbol))
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(-not-type 0 -Symbol)]
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[#:not
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(-not-type 0 -Symbol)
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(-not-type 0 (Un -String -Symbol))]
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[#:not
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(-is-type 0 -Symbol)
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(-is-type 1 -Symbol)]
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[(-is-type #'x -Symbol)
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(-is-type #'x -Symbol)]
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[(-is-type #'x -Symbol)
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(-or (-is-type 1 -Symbol) (-is-type #'x -Symbol))]
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[(-and (-is-type 1 -Symbol) (-is-type #'x -Symbol))
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(-is-type #'x -Symbol)]
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[(-is-type #'x -Symbol)
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(-not-type #'x (-val #f))]
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[(-leq (-id-path #'x) (-lexp 42))
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(-leq (-id-path #'x) (-lexp 50))]
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[#:not
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(-leq (-id-path #'x) (-lexp 50))
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(-leq (-id-path #'x) (-lexp 42))])
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(test-suite "Simplification"
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(check-equal?
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(-and (-is-type #'x -Symbol) (-not-type #'x (-val #f)))
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(-is-type #'x -Symbol))
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(check-equal?
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(-and (-not-type #'x (-val #f)) (-is-type #'x -Symbol))
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(-is-type #'x -Symbol))
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(check-equal?
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(-and (-is-type #'y (-val #f))
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(-or (-is-type #'y (-val #f))
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(-is-type #'x (-val #f))))
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(-is-type #'y (-val #f)))
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(check-equal?
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(-and (-not-type #'y (-val #f))
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(-or (-not-type #'y (-val #f))
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(-not-type #'x (-val #f))))
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(-not-type #'y (-val #f)))
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(check-equal?
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(-or (-not-type #'y (-val #f))
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(-leq (-id-path #'x) (-lexp 42))
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(-leq (-id-path #'x) (-lexp 50)))
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(-or (-not-type #'y (-val #f))
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(-leq (-id-path #'x) (-lexp 50))))
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(check-equal?
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(-and (-is-type (-id-path #'z) (-val #f))
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(-or (-not-type #'y (-val #f))
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(-leq (-lexp 50) (-id-path #'x))
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(-leq (-id-path #'x) (-lexp 50))))
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(-is-type (-id-path #'z) (-val #f))))
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))
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