diff options
author | leino <unknown> | 2014-12-12 20:46:48 -0800 |
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committer | leino <unknown> | 2014-12-12 20:46:48 -0800 |
commit | 91c4d57eb84d5d15e011902a1da1b70131e5a222 (patch) | |
tree | 6794bafdc71f6bc31c8d09496c3435658bbfc144 /Test/hofs | |
parent | 62a3e97eb61cbee0d523297ccad1f2d3bcf871c3 (diff) |
Language change: All functions and methods declared lexically outside any class are now
automatically static, and fields are no longer allowed to be declared there. Stated
differently, all heap state must now be declared inside an explicitly declared class,
and functions and methods declared outside any class can be viewed as belonging to
the module. The motivating benefit of this change is to no longer need the 'static'
keyword when declaring a module of functions and methods.
Diffstat (limited to 'Test/hofs')
-rw-r--r-- | Test/hofs/Monads.dfy | 50 |
1 files changed, 25 insertions, 25 deletions
diff --git a/Test/hofs/Monads.dfy b/Test/hofs/Monads.dfy index 9e7c5460..a221f818 100644 --- a/Test/hofs/Monads.dfy +++ b/Test/hofs/Monads.dfy @@ -4,22 +4,22 @@ abstract module Monad { type M<A>; - static function method Return(x: A): M<A> - static function method Bind(m: M<A>, f:A -> M<B>):M<B> + function method Return(x: A): M<A> + function method Bind(m: M<A>, f:A -> M<B>):M<B> reads f.reads; requires forall a :: f.requires(a); // return x >>= f = f x - static lemma LeftIdentity(x : A, f : A -> M<B>) + lemma LeftIdentity(x : A, f : A -> M<B>) requires forall a :: f.requires(a); ensures Bind(Return(x),f) == f(x); // m >>= return = m - static lemma RightIdentity(m : M<A>) + lemma RightIdentity(m : M<A>) ensures Bind(m,Return) == m; // (m >>= f) >>= g = m >>= (x => f(x) >>= g) - static lemma Associativity(m : M<A>, f:A -> M<B>, g: B -> M<C>) + lemma Associativity(m : M<A>, f:A -> M<B>, g: B -> M<C>) requires forall a :: f.requires(a); requires forall b :: g.requires(b); ensures Bind(Bind(m,f),g) == @@ -32,24 +32,24 @@ abstract module Monad { module Identity refines Monad { datatype M<A> = I(A); - static function method Return<A>(x: A): M<A> + function method Return<A>(x: A): M<A> { I(x) } - static function method Bind<A,B>(m: M<A>, f:A -> M<B>):M<B> + function method Bind<A,B>(m: M<A>, f:A -> M<B>):M<B> { var I(x) := m; f(x) } - static lemma LeftIdentity<A,B>(x : A, f : A -> M<B>) + lemma LeftIdentity<A,B>(x : A, f : A -> M<B>) { } - static lemma RightIdentity<A>(m : M<A>) + lemma RightIdentity<A>(m : M<A>) { assert Bind(m,Return) == m; } - static lemma Associativity<A,B,C>(m : M<A>, f:A -> M<B>, g: B -> M<C>) + lemma Associativity<A,B,C>(m : M<A>, f:A -> M<B>, g: B -> M<C>) { assert Bind(Bind(m,f),g) == @@ -64,26 +64,26 @@ module Identity refines Monad { module Maybe refines Monad { datatype M<A> = Just(A) | Nothing; - static function method Return<A>(x: A): M<A> + function method Return<A>(x: A): M<A> { Just(x) } - static function method Bind<A,B>(m: M<A>, f:A -> M<B>):M<B> + function method Bind<A,B>(m: M<A>, f:A -> M<B>):M<B> { match m case Nothing => Nothing case Just(x) => f(x) } - static lemma LeftIdentity<A,B>(x : A, f : A -> M<B>) + lemma LeftIdentity<A,B>(x : A, f : A -> M<B>) { } - static lemma RightIdentity<A>(m : M<A>) + lemma RightIdentity<A>(m : M<A>) { assert Bind(m,Return) == m; } - static lemma Associativity<A,B,C>(m : M<A>, f:A -> M<B>, g: B -> M<C>) + lemma Associativity<A,B,C>(m : M<A>, f:A -> M<B>, g: B -> M<C>) { assert Bind(Bind(m,f),g) == @@ -98,24 +98,24 @@ module Maybe refines Monad { module List refines Monad { datatype M<A> = Cons(hd: A,tl: M<A>) | Nil; - static function method Return<A>(x: A): M<A> + function method Return<A>(x: A): M<A> { Cons(x,Nil) } - static function method Concat(xs: M<A>, ys: M<A>): M<A> + function method Concat(xs: M<A>, ys: M<A>): M<A> { match xs case Nil => ys case Cons(x,xs) => Cons(x,Concat(xs,ys)) } - static function method Join(xss: M<M<A>>) : M<A> + function method Join(xss: M<M<A>>) : M<A> { match xss case Nil => Nil case Cons(xs,xss) => Concat(xs,Join(xss)) } - static function method Map(xs: M<A>, f: A -> B):M<B> + function method Map(xs: M<A>, f: A -> B):M<B> reads f.reads; requires forall a :: f.requires(a); { @@ -124,12 +124,12 @@ module List refines Monad { case Cons(x,xs) => Cons(f(x),Map(xs,f)) } - static function method Bind<A,B>(m: M<A>, f:A -> M<B>):M<B> + function method Bind<A,B>(m: M<A>, f:A -> M<B>):M<B> { Join(Map(m,f)) } - static lemma LeftIdentity<A,B>(x : A, f : A -> M<B>) + lemma LeftIdentity<A,B>(x : A, f : A -> M<B>) { calc { Bind(Return(x),f); @@ -141,7 +141,7 @@ module List refines Monad { } } - static lemma RightIdentity<A>(m : M<A>) + lemma RightIdentity<A>(m : M<A>) { match m case Nil => calc { @@ -166,11 +166,11 @@ module List refines Monad { } } - static lemma ConcatAssociativity<A>(xs : M<A>, ys : M<A>, zs: M<A>) + lemma ConcatAssociativity<A>(xs : M<A>, ys : M<A>, zs: M<A>) ensures Concat(Concat(xs,ys),zs) == Concat(xs,Concat(ys,zs)); {} - static lemma BindMorphism(xs : M<A>, ys: M<A>, f : A -> M<B>) + lemma BindMorphism(xs : M<A>, ys: M<A>, f : A -> M<B>) requires forall a :: f.requires(a); ensures Bind(Concat(xs,ys),f) == Concat(Bind(xs,f),Bind(ys,f)); { @@ -194,7 +194,7 @@ module List refines Monad { } } - static lemma Associativity<A,B,C>(m : M<A>, f:A -> M<B>, g: B -> M<C>) + lemma Associativity<A,B,C>(m : M<A>, f:A -> M<B>, g: B -> M<C>) { match m case Nil => calc { |