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A non-deterministic semantics with define-judgment-form
#lang racket
(require redex)
(define-language STLC
(e (e e)
x
v)
(v (λ (x) e)
integer
add1)
(E hole
(E e)
(v E))
(x variable-not-otherwise-mentioned))
(define reduction
(reduction-relation
STLC
(--> (in-hole E ((λ (x) e) v))
(in-hole E (subst e x v)))
(--> (in-hole E (add1 integer))
(in-hole E v)
(judgment-holds (δ add1 integer v)))))
(define-judgment-form STLC
mode : I I O
[(δ add1 integer 0)]
[(δ add1 integer v)
(where v (Σ 1 integer))])
(define-metafunction STLC
Σ : integer ... -> integer
[(Σ integer ...)
,(apply + (term (integer ...)))])
(define-metafunction STLC
subst : e x v -> e
[(subst (e_1 e_2) x v)
((subst e_1 x v) (subst e_2 x v))]
[(subst x x v) v]
[(subst x_1 x_2 v) x_1]
[(subst (λ (x) e) x v)
(λ (x) e)]
[(subst (λ (x_1) e) x_2 v)
; capture shmapture...
(λ (x_1) (subst e x_2 v))]
[(subst integer x v) integer]
[(subst add1 x v) add1])
(traces reduction (term (((λ (x) (λ (x) (x (add1 7)))) (add1 0)) add1)))
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