Commit da66d1f0 authored by Sven Wille's avatar Sven Wille

partial functions

parent 04dee6ee
......@@ -4,6 +4,19 @@ namespace http://mathhub.info/MitM/smglom/calculus ❚
import base http://mathhub.info/MitM/Foundation ❚
import ts http://mathhub.info/MitM/smglom/typedsets ❚
import ms http://mathhub.info/MitM/smglom/measures ❚
import calc http://mathhub.info/MitM/smglom/calculus ❚
import exr http://mathhub.info/MitM/smglom/arithmetics ❚
theory IntervalPartition : base:?Logic =
include ?Intervals ❙
partitionOfInterval : interval ⟶ type ❘ = [i] ❙
theory UpperLowerSum : base:?Logic =
theory DarbouxIntegral : base:?Logic =
......
......@@ -100,4 +100,6 @@ theory Series : base:?Logic =
axiom_partialSumStep : {G : metricMonoid} ⊦ ∀[S : G^ω] ∀[n] parSum S (succ_nat_lit n) ≐ (G.op) (parSum S n) (S (succ_nat_lit n)) ❙
prop_convergent : {G : metricMonoid} G^ω ⟶ prop ❘ = [G][S] prop_convergent G ([n] parSum S n) ❙
series : {G : metricMonoid, S: G^ω} dom G ❘ = [G,S] lim (partialSum G S) ❘ # SUM 2 ❙
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namespace http://mathhub.info/MitM/smglom/typedsets ❚
import base http://mathhub.info/MitM/Foundation ❚
import fnd http://mathhub.info/MitM/Foundation ❚
import ts http://mathhub.info/MitM/smglom/typedsets ❚
// this file is mainly for documentation purposes on different ways on how to implement partial functions ❚
theory partialFunctions1 : base:?Logic =
include fnd:?OptionType ❙
a : type ❙
bla : 𝒰 100 ❘ = Option a ❙
partialFunction : type ⟶ type ⟶ 𝒰 100 ❘= [a,b] a ⟶ Option b❙
theory partialFunctions2 : base:?Logic =
include ts:?TypedSets ❙
partialFunction : type ⟶ type ⟶ type ❘ = [d,c] {' domain : set d , f : d ⟶ c'} ❘ # 1 →p 2❙
getDomain : {a : type} {b : type} partialFunction a b ⟶ set a❙
applyPartialFunction : {d : type} {c : type} d →p c ⟶ ❙
theory partialFunctions3 : base:?Logic =
// use arbitary ❙
// u se sigme ❚
// use subset with proof ❚
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