Coq formalization of "concept parameters" for "generic" programming in STLC.
The first step is to add simple concepts and models into STLC:
look at cpSTLCa* files in cpSTLC.
Concepts contain function signatures only, models define those functions.
A program in cpSTLCa consists of concepts' and models' definitions and
a term in STLC extended with concept parametrization and model application.
Here is an example of well-typed cpSTLCa program:
concept MonoidNat
ident : Nat
op : Nat -> Nat -> Nat
endc
model MNPlus of MonoidNat
ident = 0
op = \x:Nat.\y:Nat. x + y
endm
model MNMult of MonoidNat
ident = 1
op = \x:Nat.\y:Nat. x * y
endm
(* accOrTwice takes MonoidNat concept parameter
and two nats, x and y,
and either accumulates x and y using monoid binary operation
(if x is not equal to identity element)
or accumulates y and y (if x is equal to identity element)
*)
let
accOrTwice = \m#MonoidNat. \x:Nat.\y:Nat. if x == m.ident
then m.op y y
else m.op x y
in
(* sum of 3 5*)
accOrTwice # MNSum 3 5