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48 lines
1.8 KiB
Plaintext
48 lines
1.8 KiB
Plaintext
Monad
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: ∀(M: ∀(T: *) *) *
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= λM
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$(self: (Monad M))
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∀(P: ∀(x: (Monad M)) *)
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∀(new:
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∀(bind: ∀(A: *) ∀(B: *) ∀(a: (M A)) ∀(b: ∀(a: A) (M B)) (M B))
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∀(pure: ∀(A: *) ∀(a: A) (M A))
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(P (Monad.new M bind pure)))
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(P self)
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Monad.new
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: ∀(M: ∀(T: *) *)
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∀(bind: ∀(A: *) ∀(B: *) ∀(a: (M A)) ∀(b: ∀(a: A) (M B)) (M B))
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∀(pure: ∀(A: *) ∀(a: A) (M A))
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(Monad M)
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= λM λbind λpure
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~λP λnew
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(new bind pure)
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// TODO: lawful monads https://wiki.haskell.org/Monad_laws
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//Monad
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//: ∀(M: ∀(T: *) *) *
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//= λM
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//$self
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//∀(P: ∀(x: (Monad M)) *)
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//∀(new:
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//∀(bind: ∀(A: *) ∀(B: *) ∀(a: (M A)) ∀(b: ∀(a: A) (M B)) (M B))
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//∀(pure: ∀(A: *) ∀(a: A) (M A))
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//∀(id_L: ∀(A: *) ∀(a: A) ∀(f: ∀(a: A) (M A)) (Equal (M A) (bind A A (pure A a) f) (f a)))
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//∀(id_R: ∀(A: *) ∀(m: (M A)) (Equal (M A) (bind A A m pure) m))
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//∀(asoc: ∀(A: *) ∀(B: *) ∀(C: *) ∀(m: (M A)) ∀(f: ∀(a: A) (M B)) ∀(g: ∀(b: B) (M C)) (Equal (M C) (bind B C (bind A B m f) g) (bind A C m (λx (bind B C (f x) g)))))
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//(P (Monad.new M bind pure id_L id_R asoc)))
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//(P self)
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//Monad.new
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//: ∀(M: ∀(T: *) *)
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//∀(bind: ∀(A: *) ∀(B: *) ∀(a: (M A)) ∀(b: ∀(a: A) (M B)) (M B))
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//∀(pure: ∀(A: *) ∀(a: A) (M A))
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//∀(id_L: ∀(A: *) ∀(a: A) ∀(f: ∀(a: A) (M A)) (Equal (M A) (bind A A (pure A a) f) (f a)))
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//∀(id_R: ∀(A: *) ∀(m: (M A)) (Equal (M A) (bind A A m pure) m))
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//∀(asoc: ∀(A: *) ∀(B: *) ∀(C: *) ∀(m: (M A)) ∀(f: ∀(a: A) (M B)) ∀(g: ∀(b: B) (M C)) (Equal (M C) (bind B C (bind A B m f) g) (bind A C m (λx (bind B C (f x) g)))))
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//(Monad M)
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//= λM λbind λpure λid_L λid_R λasoc
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//~λP λnew
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//(new bind pure id_L id_R asoc)
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