n in Ident
i in Int
c in Char
e ::=
Type_i -- Type at level i
n -- Variable
data(n:e) -- Constructor ???
i -- Integer literal
c -- Character literal
Π(n:e).e Π{n:e}.e -- Dependant function type
λ(n).e λ{n}.e -- Function
e e e {e} -- Application
Σ(n:e).e -- Dependant pair type
e , e -- Pair
fst e -- Left projection
snd e -- Right Projection
e + e -- Disjunction
inl e -- Left injection
inr e -- Right injection
case e e e -- Catamorphism
μ(n).e -- Recursion
fold (μ(n).e) e -- Fold recursive type
unfold (μ(n).e) e -- Unfold recursive type
e ∈ e -- Term inhabits Type
?n -- Hole for inference
Typing rules
Hierarchy and hypothesis
--------------------- ----------------
Γ ⊢ Type_i : Type_i+1 Γ, x : T ⊢ x : T
Literals and constructors
l ∈ int l ∈ char
----------- ------------ -----------------
Γ ⊢ l : int Γ ⊢ l : char Γ ⊢ data(n:T) : T
Dependant function type
Γ, x : M ⊢ N : T
----------------
Γ ⊢ Π(x:M).N : T
Γ, x : A ⊢ B : T Γ, x : A ⊢ B : T
--------------------- ---------------------
Γ ⊢ λ(x).B : Π(x:A).T Γ ⊢ λ{x}.B : Π{x:A}.T
Γ ⊢ f : Π(x:M).N Γ ⊢ e : M Γ ⊢ f : Π{x:M}.N Γ ⊢ e : M
---------------------------- ----------------------------
Γ ⊢ f e : N[x=e] Γ ⊢ f {e} : N[x=e]
Γ ⊢ f : Π{x:M}.N Γ, v:M ⊢ f {v} e : N
---------------------------------------
Γ ⊢ f e : N
Dependant pair type
Γ,x : A ⊢ B : T
----------------
Γ ⊢ Σ(x:A).B : T
Γ ⊢ A : M Γ ⊢ B : N[x=A]
--------------------------
Γ ⊢ A,B : Σ(x:M).N
Γ ⊢ p : Σ(x:M).N
----------------
Γ ⊢ fst p : M
Γ ⊢ p : Σ(x:M).N
----------------------
Γ ⊢ snd p : N[x=fst p]
Disjunction
Γ ⊢ A : T Γ ⊢ B : T
---------------------
Γ ⊢ A + B : T
Γ ⊢ A : M
-----------------
Γ ⊢ inl A : M + N
Γ ⊢ A : N
-----------------
Γ ⊢ inr A : M + N
Γ ⊢ a : A + B Γ ⊢ l : A -> C Γ ⊢ r : B -> C
-----------------------------------------------
Γ ⊢ case a l r : C
Recursion
Γ, x : T ⊢ A : T
----------------
Γ ⊢ μ(x).A : T
Γ ⊢ A : N[x=μ(x).N]
---------------------------
Γ ⊢ fold(μ(x).N) A : μ(x).N
Γ ⊢ A : μ(x).N
----------------------------------
Γ ⊢ unfold(μ(x).N) A : N[x=μ(x).N]
The WeeBe application is a social media-type app built on Ktor framework that allows users to exchange various content connected with mental health, motivation, psychology, and improving oneself. Users can share posts with texts, images, videos, and links, as well as discuss the content in the comment section
Automatically generates UI demos which allow users to call any function (including composable ones) with any parameters. Useful for building demo screens in playground apps of various design systems.