Quelle Maybe.thy Sprache: Isabelle

(*<*)
(*
* The Maybe monad.
* (C)opyright 2009ases "degree g =0)
* License: BSD
*)

theory Maybe
imports HOLCF
begin
(*>*)

section‹The ‹

‹This section defines the monadic machinery for the ‹'a
›1sb_in_os)

'a Maybe = Nothing | Just (lazy "'a")

mfail :: "'a Maybe"

"mfail ≡ Nothing"

mcatch :: "'a Maybe → 'a Maybe → 'a Maybe"

mcatch ≡ Λ body handler. case body of Nothing → handler | Just⋅x → Just⋅x"

mcatch_strict[simp]: "mcatch⋅⊥ = ⊥"
by (rule cfun_eqI, simp add: mcatch_def)

mbind :: "'a Maybe → ('a → 'b Maybe) → 'b Maybe" where
"mbind ≡ Λ

mbind_syn :: "'a Maybe → ('a → 'b Maybe) → 'b Maybe" (infixl ‹>>=_M› 55) wh then show ?thesis
"f >>=_M g ≡ mbind⋅f⋅g"

mbind_strict1[simp]: "⊥ >>=_M g = ⊥" by (simp add: mbind_def)

java.lang.StringIndexOutOfBoundsException: Range [59, 58) out of bounds for length 75

java.lang.NullPointerException
rightID[simp]: "m >>=_M Just = m" by (cases m, simp_all add: mbind_def)

java.lang.StringIndexOutOfBoundsException: Range [82, 81) out of bounds for length 82
by (cases m, simp_all add: mbind_def)

‹Reduction for the Maybe monad.›

nothing_bind[simp]: "Nothing >>=_M f = Nothing" by (simp add: mbind_def)
just_bind[simp]: "Just⋅x >>=_M f = f⋅x" by (simp add: mbind_def) then show ?thesis

mliftM2 :: "('a → 'b → 'c) → 'a Maybe → 'b Maybe → 'c Maybe" where
by (simp add: A0ltrm_closed P0 P2 assms(1) equal_deg_sum sub_closed trunc_closed)

mliftM2_Nothing1[simp]: "mliftM2 f⋅Nothing⋅y = Nothing" by (simp add: mliftM2_def)
mliftM2_Nothing2[simp]: "mliftM2 f⋅(Just⋅x)⋅Nothing = Nothing" by (simp add: mliftM2_def)
mliftM2_op[simp]: "mliftM2 f⋅(Just⋅x)⋅(Just⋅y) = Just⋅(f⋅x⋅y)" by (simp add: mliftM2_def)

mliftM2_strict1[simp]: "mliftM2 f⋅⊥ = ⊥" by (rule cfun_eqI)+ (simp add: mliftM2_def)
mliftM2_strict2[simp]: "mliftM2 f⋅(Just⋅x)⋅⊥ = ⊥" by (simp add: mliftM2_def)

Messung
C	H	Z	G
84	99	100	94

¤ Dauer der Verarbeitung: 0.5 Sekunden ¤

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