Tehee
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3/assig.org
44
3/assig.org
@ -12,17 +12,18 @@ This time you can make use of a [[http://bnfc.digitalgrammars.com/][BNFC]] speci
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If you want to use Haskell then there is also a wrapper module ([[https://chalmers.instructure.com/courses/36941/file_contents/course%20files/chi/Chi.cf][~Chi.cf~]]) that exports the generated abstract syntax and some definitions that may be useful for testing your code ([[https://chalmers.instructure.com/courses/36941/file_contents/course%20files/chi/Chi.html][documentation]]). The wrapper module comes with a Cabal file ([[https://chalmers.instructure.com/courses/36941/file_contents/course%20files/chi/chi.cabal][~chi.cabal~]]) and a [[https://chalmers.instructure.com/courses/36941/file_contents/course%20files/chi/cabal.project][~cabal.project~]] file that might make installation a little easier. Here is one way to (hopefully) get started:
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- Install all dependencies properly, including suitable versions of GHC and cabal-install ([[https://www.haskell.org/downloads/][installation instructions]]), as well as [[http://bnfc.digitalgrammars.com/][BNFC]].
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- Put [[https://chalmers.instructure.com/courses/36941/file_contents/course%20files/chi/Chi.cf][~Chi.cf~]], [[https://chalmers.instructure.com/courses/36941/file_contents/course%20files/chi/Chi.hs][~Chi.hs~]], [[https://chalmers.instructure.com/courses/36941/file_contents/course%20files/chi/chi.cabal][~chi.cabal~]] and [[https://chalmers.instructure.com/courses/36941/file_contents/course%20files/chi/cabal.project][~cabal.project~]] in an otherwise empty directory.
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- Run ~bnfc --haskell Chi.cf~ in that directory.
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- Now it is hopefully possible to use standard ~cabal~ commands. You could for instance try the following (still in the same directory):
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- First use cabal repl to start GHCi.
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- Then issue the following commands at the GHCi command prompt:
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+ Install all dependencies properly, including suitable versions of GHC and cabal-install ([[https://www.haskell.org/downloads/][installation instructions]]), as well as [[http://bnfc.digitalgrammars.com/][BNFC]].
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+ Put [[https://chalmers.instructure.com/courses/36941/file_contents/course%20files/chi/Chi.cf][~Chi.cf~]], [[https://chalmers.instructure.com/courses/36941/file_contents/course%20files/chi/Chi.hs][~Chi.hs~]], [[https://chalmers.instructure.com/courses/36941/file_contents/course%20files/chi/chi.cabal][~chi.cabal~]] and [[https://chalmers.instructure.com/courses/36941/file_contents/course%20files/chi/cabal.project][~cabal.project~]] in an otherwise empty directory.
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+ Run ~bnfc --haskell Chi.cf~ in that directory.
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+ Now it is hopefully possible to use standard ~cabal~ commands. You could for instance try the following (still in the same directory):
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+ First use cabal repl to start GHCi.
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+ Then issue the following commands at the GHCi command prompt:
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#+begin_src haskell
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import Chi
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import Prelude
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pretty <$> (runDecode (decode =<<
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asDecoder (code =<< code (parse "\\x. x"))))
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pretty <$>
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(runDecode (decode =<< asDecoder
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(code =<< code (parse "\\x. x"))))
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#+end_src
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* Exercises
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@ -49,7 +50,7 @@ rec foo = \m. \n. case m of
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Give a high-level explanation of the mathematical function in $\mathbb{N} \rightarrow \mathbb{N} \rightarrow \text{Bool}$ that is implemented by this code.
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*** Answer
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The function will check for equality of the two natural numbers. If they are both $Zero()$, then it returns true, and if both are the successor of a some values, it checks if they are equal. In the other cases, it returns false.
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The function will check for equality of the two natural numbers. If they are both $\text{Zero}()$, then it returns true, and if both are the successor of a some values, it checks if they are equal. In the other cases, it returns false.
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** (2p)
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Consider the $\chi$ term /t/ with concrete syntax $C (\lambda z.z)$:
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@ -77,14 +78,14 @@ If you use the BNFC specification above and Haskell, then the substitution funct
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Variable -> Exp -> Exp -> Exp
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#+end_src
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Test your implementation. Here are some test cases that must work:
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| Variable | Substituted term | Term | Result |
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|----------+------------------+---------------------------------------------+---------------------------------------------|
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| ~x~ | ~Z()~ | ~rec x = x~ | ~rec x = x~ |
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| ~y~ | $\lambda x.x$ | $\lambda x. (x y)$ | $\lambda x . (x (\lambda x . x))$ |
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| Variable | Substituted term | Term | Result |
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|----------+------------------+---------------------------------------------+------------------------------------------------------|
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| ~x~ | $Z()$ | $\text{rec}\ x = x$ | $\text{rec}\ x = x$ |
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| ~y~ | $\lambda x.x$ | $\lambda x. (x y)$ | $\lambda x . (x (\lambda x . x))$ |
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| ~z~ | $C(\lambda z . z)$ | $\text{case}\ z\ \text{of}\ \{ C(z) \rightarrow z \}$ | $\text{case}\ C(\lambda z. z) \ \text{of}\ \{ C(z) \rightarrow z \}$ |
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*** Answer
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See Assignment.hs
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See =Assignment.hs=.
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** (1p)
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Implement multiplication of natural numbers in $\chi$, using the representation of natural numbers given in the $\chi$ specification.
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@ -117,13 +118,13 @@ If you use the BNFC specification above and Haskell, then the interpreter should
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Test your implementation, for instance by testing that addition (defined in the [[https://chalmers.instructure.com/courses/36941/file_contents/course%20files/chi/Chi.hs][wrapper module]]) works for some inputs. If addition doesn’t work when your code is tested, then your solution will not be accepted. Also make sure that the following examples are implemented correctly:
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- The following programs should fail to terminate:
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+ $C() C()$
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+ $case \lambda x.x of {}$
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+ $case C() of { C(x) \rightarrow C() }$
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+ $case C(C()) of { C() \rightarrow C() }$
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+ $case C(C()) of { C() \rightarrow C(); C(x) \rightarrow x }$
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+ $case C() of { D() \rightarrow D() }$
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+ $(\lambda x.\lambda y.x) (rec x = x)$
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+ $\text{C}()\ \text{C}()$
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+ $\text{case}\ \lambda x.x\ \text{of}\ {}$
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+ $\text{case}\ \text{C}()\ \text{of}\ { \text{C}(x) \rightarrow \text{C}() }$
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+ $\text{case}\ \text{C}(\text{C}())\ \text{of}\ { \text{C}() \rightarrow \text{C}() }$
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+ $\text{case}\ \text{C}(\text{C}())\ \text{of}\ { \text{C}() \rightarrow \text{C}(); \text{C}(x) \rightarrow x }$
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+ $\text{case} \text{C}()\ \text{of}\ { \text{D}() \rightarrow \text{D}() }$
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+ $(\lambda x.\lambda y.x) (\text{rec}\ x = x)$
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- The following programs should terminate with specific results:
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+ The program $case C(D(),E()) of { C(x, x) \rightarrow x }$ should terminate with the value $E()$.
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+ The program $case C(\lambda x.x, Zero()) of { C(f, x) \rightarrow f x }$ should terminate with the value $Zero()$.
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@ -133,3 +134,4 @@ Test your implementation, for instance by testing that addition (defined in the
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Note that implementing a call-by-value semantics properly in a language like Haskell, which is by default non-strict, can be tricky. However, you will not fail if the only problem with your implementation is that some programs that should fail to terminate instead terminate with a “reasonable” result.
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*** Answer
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See =Assignment.hs=.
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