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// RUN: %dafny /print:"%t.print" "%s" > "%t"
// RUN: %diff "%s.expect" "%t"
function Apply<A,B>(f: A -> B, x: A): B
reads f.reads(x);
requires f.requires(x);
{
f(x)
}
function Apply'<A,B>(f: A -> B) : A -> B
{
x reads f.reads(x)
requires f.requires(x)
=> f(x)
}
function Compose<A,B,C>(f: B -> C, g:A -> B): A -> C
{
x reads g.reads(x)
reads if g.requires(x) then f.reads(g(x)) else {}
requires g.requires(x)
requires f.requires(g(x))
=> f(g(x))
}
function W<A>(f : (A,A) -> A): A -> A
{
x requires f.requires(x,x)
reads f.reads(x,x)
=> f(x,x)
}
function Curry<A,B,C>(f : (A,B) -> C) : A -> B -> C
{
x => y requires f.requires(x,y)
reads f.reads(x,y)
=> f(x,y)
}
function Uncurry<A,B,C>(f : A -> B -> C) : (A,B) -> C
{
(x,y) requires f.requires(x)
requires f(x).requires(y)
reads f.reads(x)
reads if f.requires(x) then f(x).reads(y) else {}
=> f(x)(y)
}
function S<A,B,C>(f : (A,B) -> C, g : A -> B): A -> C
{
x requires g.requires(x)
requires f.requires(x,g(x))
reads g.reads(x)
reads if g.requires(x) then f.reads(x,g(x)) else {}
=> f(x,g(x))
}
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