Lambda Abstraction

Pattern matching lambda

Anonymous pattern matching functions can be defined using the syntax:

\ { p11 .. p1n -> e1 ; … ; pm1 .. pmn -> em }

(where, as usual, \ and -> can be replaced by λ and →). Internally this is translated into a function definition of the following form:

.extlam p11 .. p1n = e1
…
.extlam pm1 .. pmn = em

This means that anonymous pattern matching functions are generative. For instance, refl will not be accepted as an inhabitant of the type

(λ { true → true ; false → false }) ==
(λ { true → true ; false → false })

because this is equivalent to extlam1 ≡ extlam2 for some distinct fresh names extlam1 and extlam2. Currently the where and with constructions are not allowed in (the top-level clauses of) anonymous pattern matching functions.

Examples:

and : Bool → Bool → Bool
and = λ { true x → x ; false _ → false }

xor : Bool → Bool → Bool
xor = λ { true  true  → false
        ; false false → false
        ; _     _     → true
        }

fst : {A : Set} {B : A → Set} → Σ A B → A
fst = λ { (a , b) → a }

snd : {A : Set} {B : A → Set} (p : Σ A B) → B (fst p)
snd = λ { (a , b) → b }