def make_map(): """ in scheme (define (map proc lis) (cond ((null? lis) '()) ((pair? lis) (cons (proc (car lis)) (map proc (cdr lis)))))) nil ≔ (nil) map ≔ λ: F, (cons X, Y) ↦ (cons μ(F, X), μ(map, F, Y)) _, nil ↦ nil """ f = Variable("F") x = Variable("X") y = Variable("Y") _ = Variable("_") _2 = Variable("_") m = lamb() m._name = "map" m._rules = rules([([p(f), p(cons("cons", x, y))], e(cons("cons", mu(f, [x]), mu(m, [f, y])))), ([p(_), p(nil())], e(nil()))]) return m
def make_pred(): x = Variable("x") l = lamb() l._rules = rules([ ([_p(_zero())], e(_zero())), ([pp(x) ], e(x))]) l._name = "pred" return l
def make_reverse(): a1 = Variable("acc") a2 = Variable("acc") h = Variable("head") t = Variable("tail") reverse_acc = lamb() reverse_acc._name = "r_acc" reverse_acc._rules = rules([([p(nil()), p(a1)], e(a1)), ([p(cons("cons", h, t)), p(a2)], e(mu(reverse_acc, [t, cons("cons", h, a2)])))]) l = Variable("list") reverse = lamb() reverse._rules = rules([([p(l)], mu(reverse_acc, [l, nil()]))]) reverse._name = "reverse" return reverse
def make_append(): x1 = Variable("x") x2 = Variable("x") h = Variable("head") t = Variable("tail") l = lamb() l._name = "append" l._rules = rules([([p(nil()), p(x1)], e(x1)), ([p(cons("cons", h, t)), p(x2)], e(cons("cons", h, mu(l, [t, x2]))))]) return l
def make_plus_acc(): x1 = Variable("x") x2 = Variable("x") x3 = Variable("x") y = Variable("y") a1 = Variable("accumulator") a2 = Variable("accumulator") o1 = Variable("op") l_acc = lamb() l_acc._rules = rules([ ([pp(a1), pp(_zero())], e(a1)), ([pp(a2), _p(o1) ], e(mu(l_acc, [p_(a2), o1])))]) l_acc._name = "plus/a" l = lamb() l._rules = rules([ ([pp(_zero()), pp(_zero()) ], e(_zero())), ([pp(x1) , pp(_zero()) ], e(x1)), ([pp(_zero()), pp(x2) ], e(x2)), ([pp(x3) , pp(y) ], e(mu(l_acc, [x3, y])))]) l._name = "plus" return l
def make_plus(): x1 = Variable("x") x2 = Variable("x") x3 = Variable("x") y = Variable("y") l = lamb() l._rules = rules([ ([pp(_zero()), pp(_zero())], e(_zero())), ([pp(x1) , pp(_zero())], e(x1)), ([pp(_zero()), pp(x2) ], e(x2)), ([pp(x3) , _p(y) ], e(p_(mu(l, [x3, y]))))]) l._name = "plus" return l
def make_mult_acc(): _f1 = Variable("_") _f2 = Variable("_") a1 = Variable("accumulator") a2 = Variable("accumulator") a3 = Variable("accumulator") a4 = Variable("accumulator") f1 = Variable("factor1") f2 = Variable("factor2") l_acc = lamb() l_acc._rules = rules([ ([pp(_zero()), pp(_zero()), pp(a1)], e(a1)), ([pp(_f1) , pp(_zero()), pp(a2)], e(a2)), ([pp(_zero()), pp(_f2) , pp(a3)], e(a3)), ([pp(f1) , _p(f2) , pp(a4)], e(mu(l_acc, [f1, f2, mu(_plus_acc(), [a4, f1])]))) ]) l_acc._name = "mult/a" _1 = Variable("_") _2 = Variable("_") x = Variable("x") y = Variable("y") l = lamb() l._rules = rules([ ([pp(_1) , pp(_zero())], e(_zero())), ([pp(_zero()), pp(_2) ], e(_zero())), ([pp(x) , pp(y) ], e(mu(l_acc, [x, y, _zero()]))), # ([pp(x) , _p(y) ], e(mu(_plus(),[]), mu(l, [x, y])), x))) # ([pp(x) , _p(y) ], e(mu(_plus(),[]), x, mu(l, [x, y]))))) ]) l._name = "mult" return l
def make_mult(): _1 = Variable("_") _2 = Variable("_") x = Variable("x") y = Variable("y") l = lamb() l._rules = rules([ ([pp(_1) , pp(_zero()) ], e(_zero())), ([pp(_zero()), pp(_2) ], e(_zero())), # ([pp(x) , _p(y) ], e(mu(_plus(),[]), mu(l, [x, y])), x))) ([pp(x) , _p(y) ], e(mu(_plus(),[x, mu(l, [x, y])]))) ]) l._name = "mult" return l
def make_succ(): x = Variable("x") l = lamb() l._rules= rules( [([pp(x)], e(p_(x)) )] ) l._name = "succ" return l
def make_gc_bench(): w_tStart_v0 = Variable("tStart") w_tStart_v1 = Variable("tStart") w_tStart_v2 = Variable("tStart") w_tFinish_v0 = Variable("tFinish") w_root_v0 = Variable("root") w_root_v1 = Variable("root") w_kStretchTreeDepth_v0 = Variable("kStretchTreeDepth") w_iDepth_v0 = Variable("iDepth") w_Make_Tree = lamb() w_Make_Tree._name = "MakeTree" w_Make_Tree._rules = rules([ ([p(integer(0))], e(cons("Node", nil(), nil()))), ([p(w_iDepth_v0)], e( cons("Node", mu(w_Make_Tree, [mu(_minus(), [w_iDepth_v0, integer(1)])]), mu(w_Make_Tree, [mu(_minus(), [w_iDepth_v0, integer(1)])])))) ]) w_gc_bench_cont1 = lamb() w_gc_bench_cont1._name = "gc_bench$cont0" w_gc_bench_cont1._rules = rules([( [p(w_tStart_v2), p(w_tFinish_v0), p(w_root_v1)], # we 'un-reference' e(mu(_print_int(), [mu(_minus(), [w_tFinish_v0, w_tStart_v2])])))]) w_gc_bench_cont0 = lamb() w_gc_bench_cont0._name = "gc_bench$cont0" w_gc_bench_cont0._rules = rules([([p(w_tStart_v1), p(w_root_v0)], e( mu(w_gc_bench_cont1, [ w_tStart_v1, mu(_currentmilliseconds(), []), w_root_v0, ])))]) w_gc_bench_let0 = lamb() w_gc_bench_let0._name = "gc_bench$let0" w_gc_bench_let0._rules = rules([ ([p(w_kStretchTreeDepth_v0), p(w_tStart_v0)], e( mu(w_gc_bench_cont0, [w_tStart_v0, mu(w_Make_Tree, [w_kStretchTreeDepth_v0])]))) ]) w_gc_bench = lamb() w_gc_bench._name = "gc_bench" w_gc_bench._rules = rules([( [], e( mu( w_gc_bench_let0, [ integer(18), # kStretchTreeDepth mu(_currentmilliseconds(), []), # tStart ])))]) return w_gc_bench