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.
224 lines
4.0 KiB
Racket
224 lines
4.0 KiB
Racket
#lang typed/racket #:with-linear-integer-arithmetic
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(provide add-to-one)
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(: add-to-one (-> (Refine [o : Integer] (= o 1))
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Integer
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Integer))
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(define (add-to-one one n)
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(+ one n))
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(ann 42 (Refine [n : Integer] (= n 42)))
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;; constant comparisons
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(if (< 5 4)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (<= 5 4)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (= 5 4)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (>= 4 5)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (> 4 5)
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(+ "Luke," "I am your father")
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"that's impossible!")
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;; arithmetic op comparisons
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(if (< (+ 2 3) 4)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (<= (+ 2 3) (* 2 2))
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (= (+ 2 3) 4)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (>= 4 (+ 2 3))
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (> (* 2 2) (+ 2 3))
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(+ "Luke," "I am your father")
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"that's impossible!")
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;; module level bound to integers
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(define four 4)
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(if (< (+ 2 3) four)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (<= (+ 2 3) four)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (= (+ 2 3) four)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (>= four (+ 2 3))
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (> four (+ 2 3))
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(+ "Luke," "I am your father")
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"that's impossible!")
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;; module level bound to expr
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(define two+two (+ 2 2))
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(if (< (+ 2 3) two+two)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (<= (+ 2 3) two+two)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (= (+ 2 3) two+two)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (>= two+two (+ 2 3))
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (> two+two (+ 2 3))
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(+ "Luke," "I am your father")
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"that's impossible!")
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;; let binding bound to integers
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(let ([four four]
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[other-four 4]
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[two+two (+ 2 2)])
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(if (< (+ 2 3) four)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (<= (+ 2 3) four)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (= (+ 2 3) four)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (>= four (+ 2 3))
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (> four (+ 2 3))
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (< (+ 2 3) other-four)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (<= (+ 2 3) other-four)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (= (+ 2 3) other-four)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (>= other-four (+ 2 3))
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (> other-four (+ 2 3))
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (< (+ 2 3) two+two)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (<= (+ 2 3) two+two)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (= (+ 2 3) two+two)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (>= two+two (+ 2 3))
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (> two+two (+ 2 3))
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(+ "Luke," "I am your father")
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"that's impossible!"))
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(define (foo [four : (Refine [val : Integer] (= val 4))])
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(if (< (+ 2 3) four)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (<= (+ 2 3) four)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (= (+ 2 3) four)
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (>= four (+ 2 3))
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(+ "Luke," "I am your father")
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"that's impossible!")
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(if (> four (+ 2 3))
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(+ "Luke," "I am your father")
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"that's impossible!")) |