Typage monomorphe à la Curry

M::= x|
cte |
hM, Mi |
M M |
λx.M |
x=M M
x:int = 3 x+ 1
x= 3 x+ 1
x:int = 4 ( y:int =x+ 1 x∗y))
x= 4 ( y=x+ 1 x∗y))
Γ`x: Γ(x) Γ `cte :T C(cte)
Γ`M:A→BΓ`N:A
Γ`M N :B
Γ, x :A`M:B
Γ`λx.M :A→B
Γ`M:AΓ`N:B
Γ` hM, Ni:A×B
Γ`M:AΓ, x :A`N:B
Γ`x=M N :B

`λx.x :int →int `λx.x :bool →bool
T ype(Γ, λx.M) = A→B A
T ype((Γ, x :A), M) = B
T ype(Γ, x =M N) = B A
T ype(Γ, M) = A
T ype((Γ, x :A), N) = B
MxM
αx
NMαN
ST C ST C(fst) = α×β→α

M SE(M)
M SE(M)
x{αM. =αx}
cte {αM. =ST C(cte)}
hN, Li {αM. =αN×αL} ∪ SE(N)∪SE(L)
N L {αN. =αL→αM} ∪ SE(N)∪SE(L)
λx.N {αM. =αx→αN} ∪ SE(N)
x=N L {αM. =αL;αx. =αN} ∪ SE(N)∪SE(L)
σ SE(M)
∆`M:τ(αM) ∆ = {x:τ(αx)|x∈F V (M)}τ
σ
∆A
∆`M:A SE(M)
M∆`M:A
A σ(αM)σ
SE(M)